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Recent Advances in Robust Optimization and Robustness:An OverviewVirginie Gabrel∗and C´e cile Murat†and Aur´e lie Thiele‡July2012AbstractThis paper provides an overview of developments in robust optimization and robustness published in the aca-demic literature over the pastfive years.1IntroductionThis review focuses on papers identified by Web of Science as having been published since2007(included),be-longing to the area of Operations Research and Management Science,and having‘robust’and‘optimization’in their title.There were exactly100such papers as of June20,2012.We have completed this list by considering 726works indexed by Web of Science that had either robustness(for80of them)or robust(for646)in their title and belonged to the Operations Research and Management Science topic area.We also identified34PhD disserta-tions dated from the lastfive years with‘robust’in their title and belonging to the areas of operations research or management.Among those we have chosen to focus on the works with a primary focus on management science rather than system design or optimal control,which are broadfields that would deserve a review paper of their own, and papers that could be of interest to a large segment of the robust optimization research community.We feel it is important to include PhD dissertations to identify these recent graduates as the new generation trained in robust optimization and robustness analysis,whether they have remained in academia or joined industry.We have also added a few not-yet-published preprints to capture ongoing research efforts.While many additional works would have deserved inclusion,we feel that the works selected give an informative and comprehensive view of the state of robustness and robust optimization to date in the context of operations research and management science.∗Universit´e Paris-Dauphine,LAMSADE,Place du Mar´e chal de Lattre de Tassigny,F-75775Paris Cedex16,France gabrel@lamsade.dauphine.fr Corresponding author†Universit´e Paris-Dauphine,LAMSADE,Place du Mar´e chal de Lattre de Tassigny,F-75775Paris Cedex16,France mu-rat@lamsade.dauphine.fr‡Lehigh University,Industrial and Systems Engineering Department,200W Packer Ave Bethlehem PA18015,USA aure-lie.thiele@2Theory of Robust Optimization and Robustness2.1Definitions and BasicsThe term“robust optimization”has come to encompass several approaches to protecting the decision-maker against parameter ambiguity and stochastic uncertainty.At a high level,the manager must determine what it means for him to have a robust solution:is it a solution whose feasibility must be guaranteed for any realization of the uncertain parameters?or whose objective value must be guaranteed?or whose distance to optimality must be guaranteed? The main paradigm relies on worst-case analysis:a solution is evaluated using the realization of the uncertainty that is most unfavorable.The way to compute the worst case is also open to debate:should it use afinite number of scenarios,such as historical data,or continuous,convex uncertainty sets,such as polyhedra or ellipsoids?The answers to these questions will determine the formulation and the type of the robust counterpart.Issues of over-conservatism are paramount in robust optimization,where the uncertain parameter set over which the worst case is computed should be chosen to achieve a trade-off between system performance and protection against uncertainty,i.e.,neither too small nor too large.2.2Static Robust OptimizationIn this framework,the manager must take a decision in the presence of uncertainty and no recourse action will be possible once uncertainty has been realized.It is then necessary to distinguish between two types of uncertainty: uncertainty on the feasibility of the solution and uncertainty on its objective value.Indeed,the decision maker generally has different attitudes with respect to infeasibility and sub-optimality,which justifies analyzing these two settings separately.2.2.1Uncertainty on feasibilityWhen uncertainty affects the feasibility of a solution,robust optimization seeks to obtain a solution that will be feasible for any realization taken by the unknown coefficients;however,complete protection from adverse realiza-tions often comes at the expense of a severe deterioration in the objective.This extreme approach can be justified in some engineering applications of robustness,such as robust control theory,but is less advisable in operations research,where adverse events such as low customer demand do not produce the high-profile repercussions that engineering failures–such as a doomed satellite launch or a destroyed unmanned robot–can have.To make the robust methodology appealing to business practitioners,robust optimization thus focuses on obtaining a solution that will be feasible for any realization taken by the unknown coefficients within a smaller,“realistic”set,called the uncertainty set,which is centered around the nominal values of the uncertain parameters.The goal becomes to optimize the objective,over the set of solutions that are feasible for all coefficient values in the uncertainty set.The specific choice of the set plays an important role in ensuring computational tractability of the robust problem and limiting deterioration of the objective at optimality,and must be thought through carefully by the decision maker.A large branch of robust optimization focuses on worst-case optimization over a convex uncertainty set.The reader is referred to Bertsimas et al.(2011a)and Ben-Tal and Nemirovski(2008)for comprehensive surveys of robust optimization and to Ben-Tal et al.(2009)for a book treatment of the topic.2.2.2Uncertainty on objective valueWhen uncertainty affects the optimality of a solution,robust optimization seeks to obtain a solution that performs well for any realization taken by the unknown coefficients.While a common criterion is to optimize the worst-case objective,some studies have investigated other robustness measures.Roy(2010)proposes a new robustness criterion that holds great appeal for the manager due to its simplicity of use and practical relevance.This framework,called bw-robustness,allows the decision-maker to identify a solution which guarantees an objective value,in a maximization problem,of at least w in all scenarios,and maximizes the probability of reaching a target value of b(b>w).Gabrel et al.(2011)extend this criterion from afinite set of scenarios to the case of an uncertainty set modeled using intervals.Kalai et al.(2012)suggest another criterion called lexicographicα-robustness,also defined over afinite set of scenarios for the uncertain parameters,which mitigates the primary role of the worst-case scenario in defining the solution.Thiele(2010)discusses over-conservatism in robust linear optimization with cost uncertainty.Gancarova and Todd(2012)studies the loss in objective value when an inaccurate objective is optimized instead of the true one, and shows that on average this loss is very small,for an arbitrary compact feasible region.In combinatorial optimization,Morrison(2010)develops a framework of robustness based on persistence(of decisions)using the Dempster-Shafer theory as an evidence of robustness and applies it to portfolio tracking and sensor placement.2.2.3DualitySince duality has been shown to play a key role in the tractability of robust optimization(see for instance Bertsimas et al.(2011a)),it is natural to ask how duality and robust optimization are connected.Beck and Ben-Tal(2009) shows that primal worst is equal to dual best.The relationship between robustness and duality is also explored in Gabrel and Murat(2010)when the right-hand sides of the constraints are uncertain and the uncertainty sets are represented using intervals,with a focus on establishing the relationships between linear programs with uncertain right hand sides and linear programs with uncertain objective coefficients using duality theory.This avenue of research is further explored in Gabrel et al.(2010)and Remli(2011).2.3Multi-Stage Decision-MakingMost early work on robust optimization focused on static decision-making:the manager decided at once of the values taken by all decision variables and,if the problem allowed for multiple decision stages as uncertainty was realized,the stages were incorporated by re-solving the multi-stage problem as time went by and implementing only the decisions related to the current stage.As thefield of static robust optimization matured,incorporating–ina tractable manner–the information revealed over time directly into the modeling framework became a major area of research.2.3.1Optimal and Approximate PoliciesA work going in that direction is Bertsimas et al.(2010a),which establishes the optimality of policies affine in the uncertainty for one-dimensional robust optimization problems with convex state costs and linear control costs.Chen et al.(2007)also suggests a tractable approximation for a class of multistage chance-constrained linear program-ming problems,which converts the original formulation into a second-order cone programming problem.Chen and Zhang(2009)propose an extension of the Affinely Adjustable Robust Counterpart framework described in Ben-Tal et al.(2009)and argue that its potential is well beyond what has been in the literature so far.2.3.2Two stagesBecause of the difficulty in incorporating multiple stages in robust optimization,many theoretical works have focused on two stages.Regarding two-stage problems,Thiele et al.(2009)presents a cutting-plane method based on Kelley’s algorithm for solving convex adjustable robust optimization problems,while Terry(2009)provides in addition preliminary results on the conditioning of a robust linear program and of an equivalent second-order cone program.Assavapokee et al.(2008a)and Assavapokee et al.(2008b)develop tractable algorithms in the case of robust two-stage problems where the worst-case regret is minimized,in the case of interval-based uncertainty and scenario-based uncertainty,respectively,while Minoux(2011)provides complexity results for the two-stage robust linear problem with right-hand-side uncertainty.2.4Connection with Stochastic OptimizationAn early stream in robust optimization modeled stochastic variables as uncertain parameters belonging to a known uncertainty set,to which robust optimization techniques were then applied.An advantage of this method was to yield approaches to decision-making under uncertainty that were of a level of complexity similar to that of their deterministic counterparts,and did not suffer from the curse of dimensionality that afflicts stochastic and dynamic programming.Researchers are now making renewed efforts to connect the robust optimization and stochastic opti-mization paradigms,for instance quantifying the performance of the robust optimization solution in the stochastic world.The topic of robust optimization in the context of uncertain probability distributions,i.e.,in the stochastic framework itself,is also being revisited.2.4.1Bridging the Robust and Stochastic WorldsBertsimas and Goyal(2010)investigates the performance of static robust solutions in two-stage stochastic and adaptive optimization problems.The authors show that static robust solutions are good-quality solutions to the adaptive problem under a broad set of assumptions.They provide bounds on the ratio of the cost of the optimal static robust solution to the optimal expected cost in the stochastic problem,called the stochasticity gap,and onthe ratio of the cost of the optimal static robust solution to the optimal cost in the two-stage adaptable problem, called the adaptability gap.Chen et al.(2007),mentioned earlier,also provides a robust optimization perspective to stochastic programming.Bertsimas et al.(2011a)investigates the role of geometric properties of uncertainty sets, such as symmetry,in the power offinite adaptability in multistage stochastic and adaptive optimization.Duzgun(2012)bridges descriptions of uncertainty based on stochastic and robust optimization by considering multiple ranges for each uncertain parameter and setting the maximum number of parameters that can fall within each range.The corresponding optimization problem can be reformulated in a tractable manner using the total unimodularity of the feasible set and allows for afiner description of uncertainty while preserving tractability.It also studies the formulations that arise in robust binary optimization with uncertain objective coefficients using the Bernstein approximation to chance constraints described in Ben-Tal et al.(2009),and shows that the robust optimization problems are deterministic problems for modified values of the coefficients.While many results bridging the robust and stochastic worlds focus on giving probabilistic guarantees for the solutions generated by the robust optimization models,Manuja(2008)proposes a formulation for robust linear programming problems that allows the decision-maker to control both the probability and the expected value of constraint violation.Bandi and Bertsimas(2012)propose a new approach to analyze stochastic systems based on robust optimiza-tion.The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory,with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem.The authors show that the performance analysis questions become highly structured optimization problems for which there exist efficient algorithms that are capable of solving problems in high dimensions.They also demonstrate that the proposed approach achieves computationally tractable methods for(a)analyzing queueing networks,(b)designing multi-item,multi-bidder auctions with budget constraints,and (c)pricing multi-dimensional options.2.4.2Distributionally Robust OptimizationBen-Tal et al.(2010)considers the optimization of a worst-case expected-value criterion,where the worst case is computed over all probability distributions within a set.The contribution of the work is to define a notion of robustness that allows for different guarantees for different subsets of probability measures.The concept of distributional robustness is also explored in Goh and Sim(2010),with an emphasis on linear and piecewise-linear decision rules to reformulate the original problem in aflexible manner using expected-value terms.Xu et al.(2012) also investigates probabilistic interpretations of robust optimization.A related area of study is worst-case optimization with partial information on the moments of distributions.In particular,Popescu(2007)analyzes robust solutions to a certain class of stochastic optimization problems,using mean-covariance information about the distributions underlying the uncertain parameters.The author connects the problem for a broad class of objective functions to a univariate mean-variance robust objective and,subsequently, to a(deterministic)parametric quadratic programming problem.The reader is referred to Doan(2010)for a moment-based uncertainty model for stochastic optimization prob-lems,which addresses the ambiguity of probability distributions of random parameters with a minimax decision rule,and a comparison with data-driven approaches.Distributionally robust optimization in the context of data-driven problems is the focus of Delage(2009),which uses observed data to define a”well structured”set of dis-tributions that is guaranteed with high probability to contain the distribution from which the samples were drawn. Zymler et al.(2012a)develop tractable semidefinite programming(SDP)based approximations for distributionally robust individual and joint chance constraints,assuming that only thefirst-and second-order moments as well as the support of the uncertain parameters are given.Becker(2011)studies the distributionally robust optimization problem with known mean,covariance and support and develops a decomposition method for this family of prob-lems which recursively derives sub-policies along projected dimensions of uncertainty while providing a sequence of bounds on the value of the derived policy.Robust linear optimization using distributional information is further studied in Kang(2008).Further,Delage and Ye(2010)investigates distributional robustness with moment uncertainty.Specifically,uncertainty affects the problem both in terms of the distribution and of its moments.The authors show that the resulting problems can be solved efficiently and prove that the solutions exhibit,with high probability,best worst-case performance over a set of distributions.Bertsimas et al.(2010)proposes a semidefinite optimization model to address minimax two-stage stochastic linear problems with risk aversion,when the distribution of the second-stage random variables belongs to a set of multivariate distributions with knownfirst and second moments.The minimax solutions provide a natural distribu-tion to stress-test stochastic optimization problems under distributional ambiguity.Cromvik and Patriksson(2010a) show that,under certain assumptions,global optima and stationary solutions of stochastic mathematical programs with equilibrium constraints are robust with respect to changes in the underlying probability distribution.Works such as Zhu and Fukushima(2009)and Zymler(2010)also study distributional robustness in the context of specific applications,such as portfolio management.2.5Connection with Risk TheoryBertsimas and Brown(2009)describe how to connect uncertainty sets in robust linear optimization to coherent risk measures,an example of which is Conditional Value-at-Risk.In particular,the authors show the link between polyhedral uncertainty sets of a special structure and a subclass of coherent risk measures called distortion risk measures.Independently,Chen et al.(2007)present an approach for constructing uncertainty sets for robust opti-mization using new deviation measures that capture the asymmetry of the distributions.These deviation measures lead to improved approximations of chance constraints.Dentcheva and Ruszczynski(2010)proposes the concept of robust stochastic dominance and shows its applica-tion to risk-averse optimization.They consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint and develop necessary and sufficient conditions of optimality for such optimization problems in the convex case.In the nonconvex case,they derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem.2.6Nonlinear OptimizationRobust nonlinear optimization remains much less widely studied to date than its linear counterpart.Bertsimas et al.(2010c)presents a robust optimization approach for unconstrained non-convex problems and problems based on simulations.Such problems arise for instance in the partial differential equations literature and in engineering applications such as nanophotonic design.An appealing feature of the approach is that it does not assume any specific structure for the problem.The case of robust nonlinear optimization with constraints is investigated in Bertsimas et al.(2010b)with an application to radiation therapy for cancer treatment.Bertsimas and Nohadani (2010)further explore robust nonconvex optimization in contexts where solutions are not known explicitly,e.g., have to be found using simulation.They present a robust simulated annealing algorithm that improves performance and robustness of the solution.Further,Boni et al.(2008)analyzes problems with uncertain conic quadratic constraints,formulating an approx-imate robust counterpart,and Zhang(2007)provide formulations to nonlinear programming problems that are valid in the neighborhood of the nominal parameters and robust to thefirst order.Hsiung et al.(2008)present tractable approximations to robust geometric programming,by using piecewise-linear convex approximations of each non-linear constraint.Geometric programming is also investigated in Shen et al.(2008),where the robustness is injected at the level of the algorithm and seeks to avoid obtaining infeasible solutions because of the approximations used in the traditional approach.Interval uncertainty-based robust optimization for convex and non-convex quadratic programs are considered in Li et al.(2011).Takeda et al.(2010)studies robustness for uncertain convex quadratic programming problems with ellipsoidal uncertainties and proposes a relaxation technique based on random sampling for robust deviation optimization sserre(2011)considers minimax and robust models of polynomial optimization.A special case of nonlinear problems that are linear in the decision variables but convex in the uncertainty when the worst-case objective is to be maximized is investigated in Kawas and Thiele(2011a).In that setting,exact and tractable robust counterparts can be derived.A special class of nonconvex robust optimization is examined in Kawas and Thiele(2011b).Robust nonconvex optimization is examined in detail in Teo(2007),which presents a method that is applicable to arbitrary objective functions by iteratively moving along descent directions and terminates at a robust local minimum.3Applications of Robust OptimizationWe describe below examples to which robust optimization has been applied.While an appealing feature of robust optimization is that it leads to models that can be solved using off-the-shelf software,it is worth pointing the existence of algebraic modeling tools that facilitate the formulation and subsequent analysis of robust optimization problems on the computer(Goh and Sim,2011).3.1Production,Inventory and Logistics3.1.1Classical logistics problemsThe capacitated vehicle routing problem with demand uncertainty is studied in Sungur et al.(2008),with a more extensive treatment in Sungur(2007),and the robust traveling salesman problem with interval data in Montemanni et al.(2007).Remli and Rekik(2012)considers the problem of combinatorial auctions in transportation services when shipment volumes are uncertain and proposes a two-stage robust formulation solved using a constraint gener-ation algorithm.Zhang(2011)investigates two-stage minimax regret robust uncapacitated lot-sizing problems with demand uncertainty,in particular showing that it is polynomially solvable under the interval uncertain demand set.3.1.2SchedulingGoren and Sabuncuoglu(2008)analyzes robustness and stability measures for scheduling in a single-machine environment subject to machine breakdowns and embeds them in a tabu-search-based scheduling algorithm.Mittal (2011)investigates efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions,with a focus on robust scheduling and service operations.Examples considered include parallel machine scheduling problems with the makespan objective,appointment scheduling and assortment optimization problems with logit choice models.Hazir et al.(2010)considers robust scheduling and robustness measures for the discrete time/cost trade-off problem.3.1.3Facility locationAn important question in logistics is not only how to operate a system most efficiently but also how to design it. Baron et al.(2011)applies robust optimization to the problem of locating facilities in a network facing uncertain demand over multiple periods.They consider a multi-periodfixed-charge network location problem for which they find the number of facilities,their location and capacities,the production in each period,and allocation of demand to facilities.The authors show that different models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer,larger facilities.?investigate a robust version of the location transportation problem with an uncertain demand using a2-stage formulation.The resulting robust formulation is a convex(nonlinear)program,and the authors apply a cutting plane algorithm to solve the problem exactly.Atamt¨u rk and Zhang(2007)study the networkflow and design problem under uncertainty from a complexity standpoint,with applications to lot-sizing and location-transportation problems,while Bardossy(2011)presents a dual-based local search approach for deterministic,stochastic,and robust variants of the connected facility location problem.The robust capacity expansion problem of networkflows is investigated in Ordonez and Zhao(2007),which provides tractable reformulations under a broad set of assumptions.Mudchanatongsuk et al.(2008)analyze the network design problem under transportation cost and demand uncertainty.They present a tractable approximation when each commodity only has a single origin and destination,and an efficient column generation for networks with path constraints.Atamt¨u rk and Zhang(2007)provides complexity results for the two-stage networkflow anddesign plexity results for the robust networkflow and network design problem are also provided in Minoux(2009)and Minoux(2010).The problem of designing an uncapacitated network in the presence of link failures and a competing mode is investigated in Laporte et al.(2010)in a railway application using a game theoretic perspective.Torres Soto(2009)also takes a comprehensive view of the facility location problem by determining not only the optimal location but also the optimal time for establishing capacitated facilities when demand and cost parameters are time varying.The models are solved using Benders’decomposition or heuristics such as local search and simulated annealing.In addition,the robust networkflow problem is also analyzed in Boyko(2010),which proposes a stochastic formulation of minimum costflow problem aimed atfinding network design andflow assignments subject to uncertain factors,such as network component disruptions/failures when the risk measure is Conditional Value at Risk.Nagurney and Qiang(2009)suggests a relative total cost index for the evaluation of transportation network robustness in the presence of degradable links and alternative travel behavior.Further,the problem of locating a competitive facility in the plane is studied in Blanquero et al.(2011)with a robustness criterion.Supply chain design problems are also studied in Pan and Nagi(2010)and Poojari et al.(2008).3.1.4Inventory managementThe topic of robust multi-stage inventory management has been investigated in detail in Bienstock and Ozbay (2008)through the computation of robust basestock levels and Ben-Tal et al.(2009)through an extension of the Affinely Adjustable Robust Counterpart framework to control inventories under demand uncertainty.See and Sim (2010)studies a multi-period inventory control problem under ambiguous demand for which only mean,support and some measures of deviations are known,using a factor-based model.The parameters of the replenishment policies are obtained using a second-order conic programming problem.Song(2010)considers stochastic inventory control in robust supply chain systems.The work proposes an inte-grated approach that combines in a single step datafitting and inventory optimization–using histograms directly as the inputs for the optimization model–for the single-item multi-period periodic-review stochastic lot-sizing problem.Operation and planning issues for dynamic supply chain and transportation networks in uncertain envi-ronments are considered in Chung(2010),with examples drawn from emergency logistics planning,network design and congestion pricing problems.3.1.5Industry-specific applicationsAng et al.(2012)proposes a robust storage assignment approach in unit-load warehouses facing variable supply and uncertain demand in a multi-period setting.The authors assume a factor-based demand model and minimize the worst-case expected total travel in the warehouse with distributional ambiguity of demand.A related problem is considered in Werners and Wuelfing(2010),which optimizes internal transports at a parcel sorting center.Galli(2011)describes the models and algorithms that arise from implementing recoverable robust optimization to train platforming and rolling stock planning,where the concept of recoverable robustness has been defined in。

High Throughput CABAC EntropyCoding in HEVCVivienne Sze,Member,IEEE,and Madhukar Budagavi,Senior Member,IEEEAbstract—Context-adaptive binary arithmetic coding(CAB-AC)is a method of entropy codingfirst introduced in H.264/A VC and now used in the newest standard High Efficiency Video Coding(HEVC).While it provides high coding efficiency,the data dependencies in H.264/A VC CABAC make it challenging to parallelize and thus,limit its throughput.Accordingly,during the standardization of entropy coding for HEVC,both coding efficiency and throughput were considered.This paper highlights the key techniques that were used to enable HEVC to potentially achieve higher throughput while delivering coding gains relative to H.264/A VC.These techniques include reducing context coded bins,grouping bypass bins,grouping bins with the same context, reducing context selection dependencies,reducing total bins, and reducing parsing dependencies.It also describes reductions to memory requirements that benefit both throughput and implementation costs.Proposed and adopted techniques up to draft international standard(test model HM-8.0)are discussed. In addition,analysis and simulation results are provided to quantify the throughput improvements and memory reduction compared with H.264/A VC.In HEVC,the maximum number of context-coded bins is reduced by8×,and the context memory and line buffer are reduced by3×and20×,respectively.This paper illustrates that accounting for implementation cost when designing video coding algorithms can result in a design that enables higher processing speed and lowers hardware costs,while still delivering high coding efficiency.Index Terms—Context-adaptive binary arithmetic coding (CABAC),entropy coding,high-efficiency video coding(HEVC), video coding.I.IntroductionH IGH EFFICIENCY Video Coding(HEVC)is currentlybeing developed by the Joint Collaborative Team for Video Coding(JCT-VC).It is expected to deliver up to a 50%higher coding efficiency compared to its predecessor H.264/A VC.HEVC uses several new tools for improving coding efficiency,including larger block and transform sizes, additional loopfilters,and highly adaptive entropy coding. While high coding efficiency is important for reducing the transmission and storage cost of video,processing speed and area cost also need to be considered in the development of next-generation video coding to handle the demand for higher resolution and frame rates.Manuscript received April16,2012;revised July7,2012;accepted August 21,2012.Date of publication October2,2012;date of current version January 8,2013.This paper was recommended by Associate Editor F.Wu.The authors are with Texas Instruments,Dallas,TX75243USA(e-mail: sze@;madhukar@).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TCSVT.2012.2221526Context-adaptive binary arithmetic coding(CABAC)[1]is a form of entropy coding used in H.264/A VC[2]and also in HEVC[3].While CABAC provides high coding efficiency, its data dependencies cause it to be a throughput bottleneck for H.264/A VC video codecs[4].This makes it difficult to support the growing throughput requirements for next-generation video codecs.Furthermore,since high throughput can be traded off for power savings using voltage scaling [5],the serial nature of CABAC limits the battery life for video codecs that reside on mobile devices.This limitation is a critical concern,as a significant portion of the video codecs today are battery operated.Accordingly,both coding efficiency and throughput improvement tools,and the tradeoff between these requirements,were investigated in the standard-ization of entropy coding for HEVC.The tradeoff between coding efficiency and throughput exists,since dependencies are a result of removing redundancy,which improves coding efficiency;however,dependencies make parallel processing difficult,which degrades throughput.This paper describes how CABAC entropy coding has evolved from H.264/A VC to HEVC(Draft International Stan-dard,HM-8.0)[3],[6].While both coding efficiency and throughput improvement tools are discussed,the focus of this paper will be on tools that increase throughput while maintaining coding efficiency.Section II provides an overview of CABAC entropy coding.Section III explains the cause of the throughput bottleneck.Section IV describes several key techniques used to improve the throughput of the CABAC engine.Sections V and VI describe how these techniques are applied to prediction unit(PU)coding and transform unit(TU) coding,respectively.Section VII compares the overall CABAC throughput and memory requirements of H.264/A VC and HEVC for both common conditions and worst-case conditions.II.CABAC Entropy CodingEntropy coding is a form of lossless compression used at the last stage of video encoding(and thefirst stage of video decoding),after the video has been reduced to a series of syntax elements.Syntax elements describe how the video sequence can be reconstructed at the decoder.This includes the method of prediction(e.g.,spatial or temporal prediction,intra prediction mode,and motion vectors)and prediction error,also referred to as residual.Table I shows the syntax elements used in HEVC and H.264/A VC.These syntax elements describe properties of the coding unit(CU),1051-8215/$31.00c 2012IEEETABLE ICABAC Coded Syntex Elements in HEVC and H.264/AVCHEVC H.264/A VCsplit−cu−flag,pred−mode−flag,part−mode,pcm−flag,mb−type,sub−mb−type,Coding unit Block structure and cu−transquant−bypass−flag,skip−flag,cu−qp−delta−abs,mb−skip−flag,mb−qp−delta, (CU)quantization cu−qp−delta−sign,end−of−slice−flag end−of−slice−flag,mb−field−decoding−flagprev−intra4x4−pred−mode−flag,prev−intra−luma−pred−flag,mpm−idx,prev−intra8×8−pred−mode−flag, Intra mode coding rem−intra−luma−pred−mode,rem−intra4x4−pred−mode,intra−chroma−pred−mode rem−intra8x8−pred−mode,intra−chroma−pred−mode Prediction unit merge−flag,merge−idx,inter−pred−idc,(PU)ref−idx−l0,ref−idx−l1,Motion data abs−mvd−greater0−flag,abs−mvd−greater1−flag,ref−idx−l0,ref−idx−l1,mvd−l0,mvd−l1abs−mvd−minus2,mvd−sign−flag,mvp−l0−flag,mvp−l1−flagno−residual−syntax−flag,split−transform−flag,cbf−luma,coded−block−flag,cbf−cb,cbf−cr,transform−skip−flag,last−significant−coded−block−pattern,coeff−x−prefix,last−significant−coeff−y−prefix,last−significant−transform−size−8x8−flag,Transform Unit (TU)Transform coefficient coeff−x−suffix,last−significant−coeff−y−suffix,coded−sub−significant−coeff−flag, coding block−flag,significant−coeff−flag,coeff−abs−level−last−significant−coeff−flag, greater1−flag,coeff−abs−level−greater2−flag,coeff−abs−level−coeff−abs−level−minus1,remaining,coeff−sign−flag coeff−sign−flag Sample adaptive sao−merge−left−flag,sao−merge−up−flag,sao−type−idx−luma,Loopfilter(LF)offset(SAO)sao−type−idx−chroma,sao−offset−abs,sao−offset−sign,n/a parameters sao−band−position,sao−eo−class−luma,sao−eo−class−chromaprediction unit(PU),transform unit(TU),and loopfilter(LF) of a coded block of pixels.For a CU,the syntax elements describe the block structure and whether the CU is inter or intra predicted.For a PU,the syntax elements describe the intra prediction mode or a set of motion data.For a TU,the syntax elements describe the residual in terms of frequency position,sign,and magnitude of the quantized transform coefficients.The LF syntax elements are sent once per largest coding unit(LCU),and describe the type(edge or band)and offset for sample adaptive offset in-loopfiltering. Arithmetic coding is a type of entropy coding that can achieve compression close to the entropy of a sequence by effectively mapping the symbols(i.e.,syntax elements)to codewords with a noninteger number of bits.In H.264/A VC, CABAC provides a9%to14%improvement over the Huffman-based CA VLC[1].In an early test model for HEVC (HM-3.0),CABAC provides a5%–9%improvement over CA VLC[7].CABAC involves three main functions:binarization,con-text modeling,and arithmetic coding.Binarization maps the syntax elements to binary symbols(bins).Context modeling estimates the probability of the bins.Finally,arithmetic coding compresses the bins to bits based on the estimated probability.A.BinarizationSeveral different binarization processes are used in HEVC, including unary(U),truncated unary(TU),k th-order Exp-Golomb(EGk),andfixed length(FL).These forms of binarization were also used in H.264/A VC.These various methods of binarization can be explained in terms of how they would signal an unsigned value N.An example is also provided in Table II.1)Unary coding involves signaling a bin string of lengthN+1,where thefirst N bins are1and the last bin isTABLE IIExample of Different Binarizations Used in HEVC Unary(U)Truncated Exp-Golomb Fixed N unary(TU)(EGk)length(FL)cMax=7k=0cMax=7 000100011010010001211011001101031110111000100011411110111100010110051111101111100011010161111110111111000111110711111110111111100010001110.The decoder searches for a0to determine when thesyntax element is complete.2)Truncated unary coding has one less bin than unarycoding by setting a maximum on the largest possible value of the syntax element(cMax).When N+1<cMax, the signaling is the same as unary coding.However, when N+1=cMax,all bins are1.The decoder searches for a0up to cMax bins to determine when the syntax element is complete.3)k th order Exp-Golomb is a type of universal code.Thedistribution can be changed based on the k parameter.More details can be found in[1].4)Fixed length uses afixed number of bins,ceil(log2(cMax+1)),with most significant bits signaled before least significant bits.The binarization process is selected based on the type of syntax element.In some cases,binarization also de-pends on the value of a previously processed syntax ele-ments(e.g.,the binarization of coeff−abs−level−remaining depends on the previous coefficient levels)or slice pa-rameters that indicate if certain modes are enabled(e.g., the binarization of partition mode,part−mode,depends on whether asymmetric motion partition is enabled).The ma-jority of the syntax elements use the binarization pro-cesses listed in Table II,or some combination of them(e.g.,coeff−abs−level−remaining uses U(prefix)+FL(suffix)[8];cu−qp−delta−abs uses TU(prefix)+EG0(suffix)[9]). However,certain syntax elements(e.g.,part−mode and intra−chroma−pred−mode)use custom binarization processes.B.Context ModelingContext modeling provides an accurate probability estimate required to achieve high coding efficiency.Accordingly,it is highly adaptive and different context models can be used for different bins and the probability of that context model is updated based on the values of the previously coded bins. Bins with similar distributions often share the same context model.The context model for each bin can be selected based on the type of syntax element,bin position in syntax element(binIdx),luma/chroma,neighboring information,etc.A context switch can occur after each bin.The probability models are stored as7-b entries[6-b for the probability state and1-b for the most probable symbol(MPS)]in a context memory and addressed using the context index computed by the context selection logic.HEVC uses the same probability update method as H.264/A VC;however,the context selection logic has been modified to improve throughput.C.Arithmetic CodingArithmetic coding is based on recursive interval division.A range,with an initial value of0to1,is divided into two subintervals based on the probability of the bin.The encoded bits provide an offset that,when converted to a binary fraction, selects one of the two subintervals,which indicates the value of the decoded bin.After every decoded bin,the range is updated to equal the selected subinterval,and the interval division process repeats itself.The range and offset have limited bit precision,so renormalization is required whenever the range falls below a certain value to prevent underflow. Renormalization can occur after each bin is decoded. Arithmetic coding can be done using an estimated proba-bility(context coded),or assuming equal probability of0.5 (bypass coded).For bypass coded bins,the division of the range into subintervals can be done by a shift,whereas a look up table is required for the context coded bins.HEVC uses the same arithmetic coding as H.264/A VC.III.Throughput BottleneckCABAC is a well-known throughput bottleneck in the video codec implementations(particularly,at the decoder). The throughput of CABAC is determined based on the number of binary symbols(bins)that it can process per second.The throughput can be improved by increasing the number of bins that can be processed in a cycle.However,the data dependencies in CABAC make processing multiple bins in parallel difficult and costly toachieve.Fig.1.Three key operations in CABAC:binarization,context selection,and arithmetic coding.Feedback loops in the decoder are highlighted with dashed lines.Fig.1highlights the feedback loops in the CABAC decoder. Below is a list and description of these feedback loops.1)The updated range is fed back for recursive intervaldivision.2)The updated context is fed back for an accurate proba-bility estimate.3)The context selection depends on the type of syntaxelement.At the decoder,the decoded bin is fed back to determine whether to continue processing the same syntax element,or to switch to another syntax element.If a switch occurs,the bin may be used to determine which syntax element to decode next.4)The context selection also depends on the bin position inthe syntax element(binIdx).At the decoder,the decoded bin is fed back to determine whether to increment binIdx and continue to decode the current syntax element,or set binIdx equal to0and switch to another syntax element. Note that the context update and range update feedback loops are simpler than the context selection loops and thus do not affect throughput as severely.If the context of a bin depends on the value of another bin being decoded in parallel, then speculative computations are required,which increases area cost and critical path delay[10].The amount of specula-tion can grow exponentially with the number of parallel bins which limits the throughput that can be achieved[11].Fig.2 shows an example of the speculation tree for significance map in H.264/A VC.Thus,the throughput bottleneck is primarily due to the context selection dependencies.IV.Techniques to Improve Throughput Several techniques were used to improve the throughput of CABAC in HEVC.There was a lot of effort spent in determining how to use these techniques with minimal coding loss.They were applied to various parts of entropy coding in HEVC and will be referred to throughout the rest of this paper.1)Reduce Context Coded Bins:Throughput is limited for context coded bins due to the data dependencies described in Section III.However,it is easier to process bypass coded bins in parallel since they do not have the data dependencies related to context selection(i.e.,feedback loops2,3,and4in Fig.1). In addition,arithmetic coding for bypass bins is simpler as it only requires a right shift versus a table look up for context coded bins.Thus,the throughput can be improved by reducing the number of context coded bins and using bypass coded bins instead[12]–[14].Fig.2.Context speculation required to achieve 5×parallelism when processing the significance map in H.264/A VC.i =coefficient position,i 1=MaxNumCoeff(BlockType)−1,EOB =end of block,SIG =significant −coeff −flag,LAST =last −significant −coeff −flag.2)Group Bypass Coded Bins:Multiple bypass bins can be processed in the same cycle if they occur consecutively within the bitstream.Thus,bins should be reordered such that bypass coded bins are grouped together in order to increase the likelihood that multiple bins are processed per cycle [15]–[17].3)Group Bins With the Same Context:Processing multiple context coded bins in the same cycle often requires speculative calculations for context selection.The amount of speculative computations increases if bins using different contexts and context selection logic are interleaved,since various combina-tions and permutations must be accounted for.Thus,to reduce speculative computations,bins should be reordered such that bins with the same contexts and context selection logic are grouped together so that they are likely to be processed in the same cycle [18]–[20].This also reduces context switching resulting in fewer memory accesses,which also increases throughput and reduces power consumption.This technique was first introduced in [18]and referred to as parallel context processing (PCP)throughout the standardization process.4)Reduce Context Selection Dependencies:Speculative computations are required for multiple bins per cycle decoding due to the dependencies in the context selection.Reducing these dependencies simplifies the context selection logic and reduces the amount of speculative calculations required to process multiple bins in parallel [11],[21],[22].5)Reduce Total Number of Bins:In addition to increasing the throughput,it is desirable to reduce the workload itself by reducing the total number of bins that need to be processed.This can be achieved by changing binarization,inferring the value of some bins,and sending higher level flags to avoid signaling redundant bins [23],[24].6)Reduce Parsing Dependencies:As parsing with CABAC is already a tight bottleneck,it is important to minimize any dependency on other video coding modules,which could cause the CABAC to stall [25].Ideally,the parsing process should be decoupled from all other processing.7)Reduce Memory Requirements:Memory accesses often contribute to the critical path delay.Thus,reducing memory storage requirements is desirable as fewer memory accesses increases throughput as well as reduces implementation cost and power consumption [26],[27].V .Prediction Unit CodingThe PU syntax elements describe how the prediction is performed in order to reconstruct the pixels.For inter prediction,the motion data are described by merge flag(merge −flag),merge index (merge −idx),prediction direction (inter −pred −idc),reference index (ref −idx −l0,ref −idx −l1),motion vector predictor flag (mvp −l0−flag,mvp −l1−flag)and motion vector difference (abs −mvd −greater0−flag,abs −mvd −greater1−flag,abs −mvd −minus2,mvd −sign −flag).For intra prediction,the intra prediction mode is described by prediction flag (prev −intra −luma −pred −flag),most probable mode index (mpm −idx),remainder mode (rem −intra −luma −pred −mode)and intra prediction mode for chroma (intra −chroma −pred −mode).Coding efficiency improvements have been made in HEVC for both motion data coding and intra mode coding.While H.264/A VC uses a single motion vector predictor (unless direct mode is used)or most probable mode,HEVC uses multiple candidate predictors and an index or flag is signaled to select the predictor.This section will discuss how to avoid parsing dependencies for the various methods of prediction and other throughput improvements.A.Motion Data CodingIn HEVC,merge mode enables motion data (e.g.,predic-tion direction,reference index,and motion vectors)to be inherited from a spatial or temporal (co-located)neighbor.A list of merge candidates are generated from these neighbors.merge −flag is signaled to indicate whether merge is used in a given PU.If merge is used,then merge −idx is signaled to indi-cate from which candidate the motion data should be inherited.merge −idx is coded with truncated unary,which means that the bins are parsed until a nonzero is reached or when the number of bins is equal to the cMax,the max allowed number of bins.1)Removing Parsing Dependencies for Merge:Determin-ing how to set cMax involved evaluating the throughput and coding efficiency tradeoffs in a core experiment [28].For optimal coding efficiency,cMax should be set to equal the merge candidate list size of the PU.Furthermore,merge −flag should not be signaled if the list is empty.However,this makes parsing depend on list construction,which is needed to determine the list size.Constructing the list requires a large amount of computation since it involves reading from multiple locations (i.e.,fetching the co-located neighbor and spatial neighbors)and performing several comparisons to prune the list;thus,dependency on list construction would significantly degrade parsing throughput [25],[29].To decouple the list generation process from the parsing process such that they can operate in parallel in HEVC,cMax is signaled in the slice header and does not depend on list size.To compensate for the coding loss due to the fixed cMax,combined and zero merging candidates are added when the list size is less than cMax as described in[30].This ensures that the list is never empty and that merge−flag is always signaled [31].2)Removing Parsing Dependencies for Motion Vector Prediction:If merge mode is not used,then the motion vector is predicted from its neighboring blocks and the difference between motion vector prediction(mvp)and motion vector (mv),referred to as motion vector difference(mvd),is signaled asmvd=mv-mvp.In H.264/A VC,a single predictor is calculated for mvp from the median of the left,top,and top-right spatial4×4neighbors. In HEVC,advanced motion vector prediction(AMVP)is used,where several candidates for mvp are determined from spatial and temporal neighbors[32].A list of mvp candidates is generated from these neighbors,and the list is pruned to remove redundant candidates such that there is a maximum of2candidates.A syntax element called mvp−l0−flag(or mvp−l1−flag depending on the reference list)is used to indicate which candidate is used from the list as the mvp. To ensure that parsing is independent of list construction, mvp−l0−flag is signaled even if there is only one candidate in the list.The list is never empty as the zero vector is used as the default candidate.3)Reducing Context Coded Bins:In HEVC,improve-ments were also made on the coding process of mvd it-self.In H.264/A VC,thefirst9bins of mvd are context coded truncated unary bins,followed by bypass coded third-order Exp-Golomb bins.In HEVC,the number of context coded bins for mvd is significantly reduced[13].Only the first two bins are context coded(abs−mvd−greater0−flag, abs−mvd−greater1−flag),followed by bypass codedfirst-order Exp-Golomb bins(abs−mvd−minus2).4)Reducing Memory Requirements:In H.264/A VC,con-text selection for thefirst bin in mvd depends on whether the sum of the motion vectors of the top and left4×4 neighbors are greater than32(or less than3).This requires 5-b storage per neighboring motion vector,which accounts 24576of the30720-b CABAC line buffer needed to support a4k×2k sequence.[27]highlighted the need to reduce the line buffer size in HEVC by modifying the context selection logic.It proposed that the motion vector for each neighbor befirst compared to a threshold of16,and then use the sum of the comparison for context selection,which would reduce the storage to1-b per neighboring motion vector.This was further extended in[33]and[34],where all dependencies on the neighbors were removed and the context is selected based on the binIdx(i.e.,whether it is thefirst or second bin).5)Grouping Bypass Bins:To maximize the impact of fast bypass coding,the bypass coded bins for both the x and y components of mvd are grouped together in HEVC[16]. B.Intra Mode CodingSimilar to motion coding,a predictor mode(most probable mode)is calculated for intra mode coding.In H.264/A VC,the minimum mode of the top and left neighbors is used as theTABLE IIIDifferences Between PU Coding in HEVC and H.264/AVCProperties HEVC H.264/A VCIntra mode AMVP Merge Intra mode MVP Max number of32511 candidates in listSpatial neighbor Used Used Used Used Used Temporal co-located Not Used Used Not Not neighbor used used used Number of contexts2102620 Max context coded2122798 bins per PUmost probable mode.prev−intra4x4−pred−mode−flag (or prev−intra8x8−pred−mode−flag)is signaled to indicate whether the most probable mode is used.If the most probable mode is not used,the remainder mode rem−intra4x4−pred−mode−flag(or rem−intra8x8−pred−mode−flag)is signaled.In HEVC,additional most probable modes are used to improve coding efficiency.A candidate list of most probable modes with afixed length of three is constructed based on the left and top neighbors.The additional candidate modes (DC,planar,vertical,+1or−1angular mode)can be added if the left and top neighbors are the same or unavailable. prev−intra−pred−mode−flag is signaled to indicate whether one of the most probable modes is used.If a most probable mode is used,a most probable mode index(mpm−idx)is signaled to indicate which candidate to use.It should be noted that in HEVC,the order in which the coefficients of the residual are parsed(e.g.,diagonal,vertical,or horizontal) depends on the reconstructed intra mode(i.e.,the parsing of the TU data that follows depends on list construction and intra mode reconstruction).Thus,the candidate list size was limited to three for reduced computation to ensure that it would not affect entropy decoding throughput[35],[36].1)Reducing Context Coded Bins:The number of context coded bins was reduced for intra mode coding in HEVC.In H.264/A VC,the remainder mode is a7-bin value where the first bin is context coded,while in HEVC,the remainder mode is a5-bin value that is entirely bypass coded.The most proba-ble mode index(mpm−idx)is also entirely bypass coded.The number of contexts used to code intra−chroma−pred−mode is reduced from4to1.2)Grouping Bypass Bins:To maximize the impact of fast bypass coding,the bypass coded bins for intra mode within a CU are grouped together in HEVC[17].C.Summary of Differences Between HEVC and H.264/AVC The differences between H.264/A VC and HEVC are sum-marized in Table III.HEVC uses both spatial and temporal neighbors as predictors,while H.264/A VC only uses spatial neighbors(unless direct mode is enabled).In terms of the impact of the throughput improvement techniques,HEVC has8×fewer maximum context coded bins per PU than H.264/A VC.HEVC also requires1.8×fewer contexts for PU syntax elements than H.264/A VC.VI.Transform Unit CodingIn video coding,both intra and inter prediction are used to reduce the amount of data that needs to be transmitted. Rather than sending the pixels,the prediction error is trans-mitted.This prediction error is transformed from spatial to frequency domain to leverage energy compaction properties, and after quantization,it can be represented in terms of a few coefficients.The method of signaling the value and the frequency position of these coefficients is referred to as transform coefficient coding.For regions with many edges (e.g.,screen content coding),coding gains can be achieved by skipping the transform from spatial to frequency domain [37],[38];when transform is skipped,the prediction error is coded in the same manner as transform coefficient coding(i.e., the spatial error is coded as transform coefficients).Syntax elements of the transform unit account for a signif-icant portion of the bin workload as shown in Table IV.At the same time,the transform coefficients also account for a significant portion of the total bits of a compressed video,and as a result the compression of transform coefficients signifi-cantly impacts the overall coding efficiency.Thus,transform coefficient coding with CABAC must be carefully designed in order to balance coding efficiency and throughput demands. Accordingly,as part of the HEVC standardization process, a core experiment on coefficient scanning and coding was established to investigate tools related to transform coefficient coding[39].It is also important to note that HEVC supports more transform sizes than H.264/A VC;H.264/A VC uses4×4and 8×8transforms,where as HEVC uses4×4,8×8,16×16, and32×32transforms.While these larger transforms provide significant coding gains,they also have implications in terms of memory storage as this represents an increase of4×to 16×in the number of coefficients that need to be stored per transform unit(TU).In CABAC,the position of the coefficients is transmitted in the form of a significance map.Specifically,the significance map indicates the location of the nonzero coefficients.The coefficient level information is then only transmitted for the coefficients with values greater than one,while the coefficient sign is transmitted for all nonzero coefficients.This section describes how transform coefficient coding evolved from H.264/A VC to thefirst test model of HEVC (HM-1.0)to the Draft International Standard of HEVC(HM-8.0),and discusses the reasons behind design choices that were made.Many of the throughput improvement techniques were applied,and new tools for improved coding efficiency were simplified.As a reference for the beginning and end points of the development,Figs.3and4show examples of transform coefficient coding in H.264/A VC and HEVC(HM-8.0),respectively.A.Significance MapIn H.264/A VC,the significance map is signaled by transmit-ting a significant−coeff−flag(SCF)for each position to indi-cate whether the coefficient is nonzero.The positions are pro-cessed in an order based on a zig–zag scan.After eachnonzero Fig.3.Example of transform coefficient coding for a4×4TU in H.264/AVC.Fig.4.Example of transform coefficient coding for a4×4TU in HEVC (HM-8.0).SCF,an additionalflag called last−significant−coeff−flag (LSCF)is immediately sent to indicate whether it is the last nonzero SCF;this prevents unnecessary SCF from being signaled.Different contexts are used depending on the position within the4×4and8×8transform unit(TU),and whether the bin represents an SCF or LSCF.Since SCF and LSCF are interleaved,the context selection of the current bin depends on the immediate preceding bin.The dependency of LSCF on SCF results in a strong bin to bin dependency for context selection for significance map in the H.264/A VC as illustrated in Fig.2.1)significant−coeff−flag(SCF):In HM-1.0,additional dependencies were introduced in the context selection of SCF for16×16and32×32TU to improve coding efficiency.The context selection for SCF in these larger TU depended on the number of nonzero neighbors to give coding gains between 1.4%to2.8%[42].Specifically,the context of SCF depended on up to ten neighbors as shown in Fig.5(a)[42],[43].To reduce context selection dependencies,and storage costs,[21]proposed using fewer neighbors and showed that it could be done with minimal cost to coding efficiency.For。

2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。

Posterior probability intervals for wavelet thresholdingStuart Barber,Guy P.Nason,and Bernard W.SilvermanUniversity of Bristol,UK.AbstractWe use cumulants to derive Bayesian credible intervals for wavelet regression estimates.The first four cumulants of the posterior distribution of the estimates are expressed in terms of theobserved data and integer powers of the mother wavelet functions.These powers are closelyapproximated by linear combinations of wavelet scaling functions at an appropriatefiner scale.Hence,a suitable modification of the discrete wavelet transform allows the posterior cumulantsto be found efficiently for any given data set.Johnson transformations then yield the credibleintervals themselves.Simulations show that these intervals have good coverage rates,evenwhen the underlying function is inhomogeneous,where standard methods fail.In the casewhere the curve is smooth,the performance of our intervals remains competitive with establishednonparametric regression methods.Keywords:Bayes estimation;Cumulants;Curve estimation;Interval estimates;Johnson curves;Nonparametric regression;Powers of wavelets.1IntroductionConsider the estimation of a function from an observed data vector satisfyingwhere and the are independently distributed.There are many methods of estimating smooth functions,such as spline smoothing(Green and Silverman,1994),kernel estimation(Wand and Jones,1995),and local polynomial regression(Fan and Gijbels,1996).In most cases,such point estimates can be supplemented by interval estimates with some specified nominal coverage probability or significance level.A recent proposal for estimation of inhomogeneous is wavelet thresholding(Donoho and Johnstone1994,1995).The representation of in terms of a wavelet basis is typically sparse, concentrating most of the signal in the data into a few large coefficients,whilst the noise is spread “evenly”across the coefficients due to the orthonormality of the wavelet basis.The data is denoised by a thresholding rule of some sort to discard“small”coefficients and retain,possibly with some modification,those coefficients which are thought to contain the signal.Several authors have described Bayesian wavelet thresholding rules,placing prior distributions on the wavelet coefficients.We consider a means of approximating the posterior distribution of each ,using the same prior as the BayesThresh method of Abramovich,Sapatinas and Silverman (1998).Posterior probability intervals of any nominal coverage probability can then be calculated. Our approach can also be applied to other Bayesian wavelet thresholding rules,such as those surveyed by Chipman and Wolfson(1999),Abramovich and Sapatinas(1999),and Vidakovic(1998).We briefly review the wavelet thresholding approach to curve estimation in section2,including two Bayesian methods of wavelet thresholding.In section3,we derive our WaveBand method of estimating the posterior distribution of given the observed data.We present an example and simulation results in section4and make some concluding remarks in section5.2Wavelets and wavelet thresholding2.1WaveletsWavelets provide a variety of orthonormal bases of,the space of square integrable functions on;each basis is generated from a scaling function,denoted,and an associated wavelet,. The wavelet basis consists of dilations and translations of these functions.For,the wavelet at level and location is given by(1) with an analogous definition for.The scaling function is sometimes referred to as the father wavelet,but we avoid this terminology.A function can be represented as(2)with and.Daubechies(1992)derived two families of wavelet bases which give sparse representations of wide sets of functions.(Technically,by choosing a wavelet with suitable properties,we can generate an unconditional wavelet basis in a wide set of function spaces;for further details, see Abramovich et al.(1998).)Generally,smooth portions of are represented by a small number of coarse scale(low level)coefficients,while local inhomogeneous features such as high frequency events,cusps and discontinuities are represented by coefficients atfiner scales(higher levels).For our nonparametric regression problem,we have discrete data and hence consider the discrete wavelet transform(DWT).Given a vector,where,the DWT of is ,where is an orthonormal matrix and is a vector of the discrete scaling coefficient and discrete wavelet coefficients.These are analogous to the coefficients in(2),with.Our data are restricted to lie in,requiring boundary conditions;we assume that is periodic at the boundaries.Other boundary conditions include the assumption that is reflected at the boundaries,or the“wavelets on the interval”transform of Cohen,Daubechies and Vial(1993)can be used.The pyramid algorithm of Mallat(1989)computes in operations,provided. The algorithm iteratively computes the and from the.From the vector,the inverse DWT(IDWT)can be used to reconstruct the original data.The IDWT starts with the overall scaling and wavelet coefficients and and reconstructs the;it then proceeds iteratively tofiner levels,reconstructing the from the and.22.2Curve estimation by wavelet thresholdingSince the DWT is an orthonormal transformation,white noise in the data domain is transformed towhite noise in the wavelet domain.If is the DWT of,and thevector of empirical coefficients obtained by applying the DWT to the data,then,where is a vector of independent variates.Wavelet thresholding assumes implicitly that“large”and“small”represent signal and noise respectively.Various thresholding ruleshave been proposed to determine which coefficients are“large”and“small”;see Vidakovic(1999)or Abramovich,Bailey and Sapatinas(2000)for reviews.The true coefficients are estimated byapplying the thresholding rule to the empirical coefficients to obtain estimates,and the sampled function values are estimated by applying the IDWT to obtain where denotes the transpose of;symbolically,we can represent this IDWT as the sum(3)Confidence intervals for the resulting curve estimates have received some attention in the wavelet literature.Brillinger(1994)derived an estimate of var when the wavelet decomposition involved Haar wavelets,and Brillinger(1996)showed that is asymptotically normal under certain conditions. Bruce and Gao(1996)extended the estimation of var to the case of non-Haar wavelets,and gave approximate confidence intervals using the asymptotic normality of.Chipman, Kolaczyk and McCulloch(1997)presented approximate credible intervals for their adaptive Bayesian wavelet thresholding method,which we discuss in section2.3.2,while Picard and Tribouley(2000) derive bias corrected confidence intervals for wavelet thresholding estimators.2.3Bayesian wavelet regression2.3.1IntroductionSeveral authors have proposed Bayesian wavelet regression estimates,involving priors on the wavelet coefficients,which are updated by the observed coefficients to obtain posterior distributions .Point estimates can be computed from these posterior distributions and the IDWT employed to estimate in the usual fashion outlined above.Some proposals have included priors on ;we restrict ourselves to the situation where can be well estimated from the data.The majority of Bayesian wavelet shrinkage rules have employed mixture distributions as priors on the coefficients,to model the notion that a small proportion of coefficients contain substantial signal.Chipman et al.(1997)and Crouse,Nowak and Baraniuk(1998)considered mixtures of two normal distributions,while Abramovich et al.(1998),Clyde,Parmigiani and Vidakovic(1998)and Clyde and George(2000)used mixtures of a normal and a point mass.Other proposals include a mixture of a point mass and a-distribution used by Vidakovic(1998),and an infinite mixture of normals considered by Holmes and Denison(1999).More thorough reviews are given by Chipman and Wolfson(1999)and Abramovich and Sapatinas(1999).32.3.2Adaptive Bayesian wavelet shrinkageThe ABWS method of Chipman et al.(1997)places an independent prior on each:(4) where Bernoulli;hyperparameters,and are determined from the data by empirical Bayes methods.At level,the proportion of non-zero coefficients is represented by,while and represent the magnitude of negligible and non-negligible coefficients respectively.Given,the empirical coefficients are independently,so the posterior distribution is a mixture of two normal components independently for each. Chipman et al.(1997)use the mean of this mixture as their estimator,and similarly use the variance of to approximate the variance of their ABWS estimate of.Estimating each coefficient by the mean of its posterior distribution is the Bayes rule under the loss function.They plot uncertainty bands of sd.These bands are useful in representing the uncertainty in the estimate,but are based on an assumption of normality despite being a sum of random variables with mixture distributions.2.3.3BayesThreshThe BayesThresh method of Abramovich et al.(1998)also places independent priors on the coefficients:(5) where and is a probability mass at zero.This is a limiting case of the ABWS prior(4).The hyperparameters are assumed to be of the form and min for non-negative constants and chosen empirically from the data and and selected by the user. Abramovich et al.(1998)show that choices of and correspond to choosing priors within certain Besov spaces,incorporating prior knowledge about the smoothness of in the prior.Chipman and Wolfson(1999)also discuss the interpretation of and.In the absence of any such prior knowledge, Abramovich et al.(1998)show that the default choice,is robust to varying degrees of smoothness of.The prior specification is completed by placing a non-informative prior on the scaling coefficient,which thus has the posterior distribution,and is estimated by.The resulting posterior distribution of given the observed value of is again independent for each and is given by(6) where,withand.The BayesThresh approach minimises the loss in the wavelet domain by using the posterior median of as the point estimate;Abramovich et al.(1998)show4that this gives a level-dependent true thresholding rule.The BayesThresh method is implemented in the WaveThresh package for SPlus(Nason,1998).3WaveBand3.1Posterior cumulants of the regression curveWe now consider the posterior density of for each.From(3),we see that is the convolution of the posteriors of the wavelet coefficients and the scaling coefficient,(7)this is a complicated mixture,and is impractical to evaluate analytically.Direct simulation from the posterior is extremely time consuming.Instead we estimate thefirst four cumulants of(7)andfit a distribution which matches these values.Evaluating cumulants of requires the use of powers of wavelets for,and,which we discuss in section3.2.We thenfit a parametric distribution to in section3.3.If the moment generating function of a random variable is written,then the cumulant generating function is.We write for the th cumulant of,given by the th derivative of,evaluated at.Note that thefirst moments uniquely determine thefirst cumulants and vice-versa.Further details of cumulants and their properties and uses can be found in Barndorff-Nielsen and Cox(1989)or Stuart and Ord(1994,chapter3).Thefirst four cumulants each have a direct interpretation;and are the mean and variance of respectively,while is the skewness and is the kurtosis.If is normally distributed then both and are zero.We make use of two standard properties of cumulants.If and are independent random variables and and are real constants,then(8)and(9) Applying(8)and(9)to(7),we can see that the cumulants of are given by(10)Once the cumulants of the wavelet coefficients are known,this sum can be evaluated directly using the IDWT when,but for,and,the computation involves powers of wavelets.The posterior distributions(6)for the wavelet coefficients using BayesThresh are of the form ,where,,and is a point mass at zero.Then5so the moments of(6)are easily obtained.From these,we can derive the cumulants of:Since the scaling coefficient has a normal posterior distribution,thefirst two cumulants are and;all higher order cumulants are zero.3.2Powers of waveletsThe parallel between(10)and the sum(3)evaluated by the IDWT is clear,and we shall describe a means of taking advantage of the efficient IDWT algorithm to evaluate(10).For Haar wavelets, this is trivial;the Haar scaling function and mother wavelet are and,where is the indicator function,hence and.Moreover,,,and ,all terms which can be included in a modified version of the IDWT algorithm which incorporates scaling function coefficients.Since representing by scaling functions and wavelets works in the Haar case,we consider a similar approach for other wavelet bases.Following Herrick(2000,pp.69),we approximate a general wavelet,,by(11)for,where is a positive integer;the choice of is discussed below.We use scaling functions rather than wavelets as the span of the set of scaling functions at a given level is the same as that of the union of and wavelets at levels.Moreover,if scaling functionsare used to approximate some function,and both and have at least derivatives,then the mean squared error in the approximation is bounded by,where is some positive constant; see,for example,Vidakovic(1999,p.87).To approximate for somefixed,wefirst compute using the cascade algorithm (Daubechies,1992,pp.205),then take the DWT of and set the coefficients to be equal to the scaling function coefficients at level,where.Recall that the wavelets at level are simply shifts of each other;from(1),hence(12) As we are assuming periodic boundary conditions,the can be cycled periodically.6(a)0.00.20.40.60.8 1.0-0.100.00.1••••••••••(b)24680.00.20.40.60.8••••••••••(c)24680.00.20.40.60.81.0••••••••••(d)24680.00.20.40.60.8Approximation levelApproximation level Approximation levelM S E r a t i oM S E r a t i oM S E r a t i oFigure 1:Daubechies’extremal phase wavelet with two vanishing moments (panel a)and accuracy of estimating for by scaling functions at level .The mean square errors of the estimates,divided by the norm of ,are plotted against :panels (b),(c),and (d)show results for ,and respectively.The vertical lines are at level 3,the level at which exists.Owing to the localised nature of wavelets,the coefficientsused to approximatecan be found by inserting zeros into the vector of:Approximation (11)cannot be used for wavelets at the finest levels .Werepresent these wavelets by both scaling functions and wavelets at the finest level of detail,level,using the block-shifting technique outlined above to make the computations more efficient.In all the cases we have examined,has been sufficient for a highly accurate approximation;examples are shown in figures 1and 2.Consider approximating the powers of Daubechies’extremal phase wavelet with two vanishing moments;this wavelet is extremely non-smooth and so can be regarded as a near worst-case scenario for the approximation.Panel (a)of figure 1shows ,while panels (b)-(d)show the mean square error in our approximation divided by the norm of the function being approximated,for respectively.In each plot (b)-(d),the vertical line is at resolution level ,the level at which thewavelet whose power is being estimated exists.The approximation is excellent forin each case,with little improvement at level .70.00.20.40.60.8 1.00.00.040.080.00.20.40.60.8 1.00.00.040.080.120.00.20.40.60.8 1.00.00.040.080.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.00.0020.0060.0100.00.20.40.60.8 1.00.00.0040.0080.0120.00.20.40.60.8 1.00.0020.0060.010Figure 2:Approximations to powers of Daubechies’least asymmetric wavelet with eight vanishing moments;the powers are indicated at the top of each column.Solid lines are wavelet powers and dotted lines show approximations using scaling functions at level .From top to bottom,graphs show approximation at levels ,,and ;the original wavelet is at level .Figure 2shows approximations to powers of Daubechies’least asymmetric wavelet with eight vanishing moments as the approximation level increases.Again,the base wavelet is at level,and approximations are shown for (top row),,and(bottom row).In each case,the solid line is the wavelet power and the dotted line is the ing (12),we can now re-write (10)asfor suitable coefficients ,and use a modified version of the IDWT algorithm which incorporates scaling function coefficients to evaluate this sum.83.3Posterior distribution of the regression curveWe must now estimate from its cumulants.Edgeworth expansions give poor results in the tails of the distribution,where we require a good approximation.Saddlepoint expansions improve on this, but require the cumulant generating function,while we only have thefirst four cumulants. Therefore,we approximate by a suitable parametric distribution.A family of distributions is the set of transformations of the normal curve described by Johnson (1949).As well as the normal distribution,Johnson curves fall into three categories;(a)the lognormal,,with,(b)the unbounded,,and(c)the bounded,,with,to which Hill,Hill and Holder(1976)added a limiting case of curves whereand shown infigure3(solid line).Figure3also shows data formed by adding independent normally distributed noise to.The noise has mean zero and root signal to noise ratio(rsnr)3;the rsnr is defined to be the ratio of the standard deviation of the data points to the standard deviation of the noise,.Dotted lines infigure3mark upper and lower endpoints of99%credible intervals for for each calculated using our WaveBand method,using default parameters of,,and Daubechies’least asymmetric wavelet with eight vanishing moments.In this example,the credible intervals include the true value of in490of512cases,an empirical coverage rate of95.7%. The brief spikes which occur in the bands are typical of wavelet regression methods;they can be smoothed out by using different and,but this risks oversmoothing the data.9...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................0.00.20.40.60.8 1.00123Figure 3:Pointwise 99%WaveBand interval estimates (dotted line)for the piecewise polynomial signal (solid line).Dots indicate data on equally spaced points with the addition of independent normally distributed noise with mean zero and rsnr 3.Figure 4shows the mean,variance,skewness,and kurtosis of for each point .The mean is itself an estimate of and the variance is generally low except near the discontinuity at.We use the usual definitions of skewness and kurtosis,range from approximately -7.9to 7.5,and from approximately 1.7to almost 120,indicating that for some ,the posterior distribution has heavy tails.(For comparison the distribution has skewness 7.1and kurtosis 79.)The prior (5)has kurtosis ;note that in our example the largest values of kurtosis occur when the function is smooth;in these cases the majority of the wavelet coefficients are zero,and hence is small.4.2Simulation results4.2.1Inhomogeneous signalsWe investigated the performance of our WaveBand credible intervals by simulation on the piecewise polynomial example of Nason and Silverman (1994)(denoted “PPoly”)and the standard “Blocks”,“Bumps”,“Doppler”and “HeaviSine”test functions of Donoho and Johnstone (1994),shown in figure 5.For each test function,100simulated data sets of length were created with rsnr100.00.20.40.60.8 1.01230.00.20.40.60.8 1.00.00.040.080.120.00.20.40.60.8 1.0-550.00.20.40.60.8 1.0020*********M e a nV a r i a n c eS k e w n e s sK u r t o s i sFigure 4:Mean,variance,skewness and kurtosis for the piecewise polynomial data shown in figure 3.4and the WaveBand and ABWS credible intervals evaluated at each data point for nominal coverage probabilities 0.90,0.95,and 0.99.The default hyperparameters and were used for WaveBand and both methods used Daubechies’least asymmetric wavelet with eight vanishing moments.Table 1shows the coverage rates and interval widths averaged over all points and the 100replications,with standard error shown in brackets.The WaveBand intervals have higher empirical coverage rates in each case,although still below the nominal coverage probabilities.Average widths of the WaveBand credible intervals are always greater than those of the ABWS intervals;one reason is that the ABWS method typically has a lower estimated variance.Moreover,the WaveBand posterior of is typically heavier-tailed than the normal distribution,as we saw in the piecewise polynomial example.The performance of the WaveBand intervals improves as the nominal coverage rate increases.In part,this can be attributed to the kurtosis of the posterior distributions.As the nominal coverage rates increase,the limits of the credible intervals move out into the tails of the posterior distributions.With heavy-tailed distributions,a small increase in the nominal coverage rate can produce a substantially wider interval.Figure 6examines the empirical coverage rates of the nominal 99%credible intervals in more detail.Solid lines denote the empirical coverage rates of the WaveBand intervals for each ,and dotted lines give the equivalent results for the ABWS intervals.Coverage varies greatly across each signal;unsurprisingly,the coverage is much better where the signal is smoother and less variable.This can be seen most clearly in the results for the piecewise polynomial and HeaviSine test functions,110.00.20.40.60.8 1.001230.00.20.40.60.8 1.0-20240.00.20.40.60.8 1.00123450.00.20.40.60.8 1.0-0.40.00.40.00.20.40.60.8 1.0-6-4-2024P p o l yB l o c k sB u m p sH e a v i S i n eD o p p l e rFigure 5:The piecewise polynomial of Nason and Silverman (1994)and the test functions of Donoho and Johnstone (1994).12Simulation results comparing mean coverage rates(CR)and interval widths for ABWS and WaveBand(denoted WB)credible intervals on the piecewise polynomial,Blocks,Bumps,Doppler, and HeaviSine test functions.Each test function was evaluated on points,the rsnr was 4,and100replications were done in each case.Standard errors are given in brackets.All methods were employed with Daubechies’least asymmetric wavelet with8vanishing moments,and the default hyperparameters and were used for WaveBand.130.00.20.40.60.81.00.00.40.80.00.20.40.60.81.00.00.40.80.00.20.40.60.8 1.00.00.40.80.00.20.40.60.81.00.00.40.80.00.20.40.60.8 1.00.00.40.8C o v e r a g eC o v e r a g eC o v e r a g eC o v e r a g eC o v e r a g eFigure 6:Empirical coverage rates of nominal 99%interval estimates for the indicated test functions evalauted at equally spaced data points.In each case,100simulated data sets with a rsnr of 4were used.Solid and dotted lines indicate coverage rates for the WaveBand method and ABWS methods respectively.14with sharp drops in performance near the discontinuities,and in the excellent coverage in the lower-frequency portion of the Doppler signal and the long constant parts of the Bumps signal.4.2.2Smooth signalsThe major advantage of wavelet thresholding as a nonparametric regression technique is the ability to model inhomogeneous signals such as those considered in section4.2.1.However,wavelet thresholding can also be used successfully on smooth signals,and we now consider such an example, the function.Table2shows the performance of ABWS and WaveBand credible intervals and confidence intervals using smoothing splines for.The smoothing spline estimate of can be written spline,where is an matrix,so var spline.Hence we can construct an approximate confidence interval for as spline where,and consider the random variable,, where is a double exponential variate with density function.Given an observation of,the15RSNR =20.95CR Width CR Width 0.939(.008)0.300(.002)0.990(.003)0.471(.004)WB 00.600Nominal coverage probability0.900.99CR WidthWB0.850(.010)0.143(.002)0.981(.002)0.276(.002)Spline0.934(.008)0.159(.002)0.493(.016)0.078(.003)0.643(.017)0.122(.004)Table 2:Simulation results comparing the mean coverage rate (CR)and interval widths forWaveBand ,smoothing spline,and ABWS methods on the functionposterior probability that is,where is the density function of a standard normal random variable,not a scaling function,and denotes convolution.Write for the distribution function associated with,and let and;then isAcknowledgmentsThe authors are grateful for the support of the EPSRC(grant GR/M10229)and by Unilever Research; GPN was also supported by EPSRC Advanced Research Fellowship AF/001664.The authors wish to thank Eric Kolaczyk and Thomas Yee for programs that implement the ABWS and spline methods respectively.The authors are also grateful for the constructive comments of the Joint Editor and two referees.ReferencesAbramovich, F.,Bailey,T.C.and Sapatinas,T.(2000).Wavelet analysis and its statistical applications.The Statistician49,1–29.Abramovich,F.and Sapatinas,T.(1999).Bayesian approach to wavelet decomposition and shrinkage.In M¨u ller,P.and Vidakovic,B.,editors,Bayesian Inference in Wavelet Based Models,volume141 of Lecture Notes in Statistics,pages33–50.Springer-Verlag,New York.Abramovich,F.,Sapatinas,T.and Silverman,B.W.(1998).Wavelet thresholding via a Bayesian approach.J.R.Statist.Soc.B60,725–749.Barndorff-Nielsen,O.E.and Cox,D.R.(1989).Asymptotic Techniques for Use in Statistics.Chapman and Hall,London.Brillinger,D.R.(1994).Some river wavelets.Environmetrics5,211–220.Brillinger,D.R.(1996).Uses of cumulants in wavelet analysis.J.Nonparam.Statist.6,93–114. Bruce,A.G.and Gao,H.Y.(1996).Understanding WaveShrink:variance and bias estimation.Biometrika83,727–745.Chipman,H.,Kolaczyk,E.and McCulloch,R.(1997).Adaptive Bayesian wavelet shrinkage.J.Am.Statist.Ass.92,1413–1421.Chipman,H.A.and Wolfson,L.J.(1999).Prior elicitation in the wavelet domain.In M¨u ller,P.and Vidakovic,B.,editors,Bayesian Inference in Wavelet Based Models,volume141of Lecture Notes in Statistics.Springer-Verlag,New York.Clyde,M.and George,E.I.(2000).Flexible empirical Bayes estimation for wavelets.J.R.Statist.Soc.B62,681–698.Clyde,M.,Parmigiani,G.and Vidakovic,B.(1998).Multiple shrinkage and subset selection in wavelets.Biometrika85,391–402.Cohen,A.,Daubechies,I.and Vial,P.(1993).Wavelets on the interval and fast wavelet transforms.p.Harm.Analysis1,54–81.Crouse,M.,Nowak,R.and Baraniuk,R.(1998).Wavelet-based statistical signal processing using hidden Markov models.IEEE Trans.Signal Processing46,886–902.Daubechies,I.(1992).Ten Lectures on Wavelets.SIAM,Philadelphia.Donoho,D.L.and Johnstone,I.M.(1994).Ideal spatial adaptation by wavelet shrinkage.Biometrika 81,425–455.Donoho,D.L.and Johnstone,I.M.(1995).Adapting to unknown smoothness via wavelet shrinkage.J.Am.Statist.Ass.90,1200–1224.18。

华中师范大学物理学院物理学专业英语仅供内部学习参考！2014一、课程的任务和教学目的通过学习《物理学专业英语》，学生将掌握物理学领域使用频率较高的专业词汇和表达方法，进而具备基本的阅读理解物理学专业文献的能力。

通过分析《物理学专业英语》课程教材中的范文，学生还将从英语角度理解物理学中个学科的研究内容和主要思想，提高学生的专业英语能力和了解物理学研究前沿的能力。

培养专业英语阅读能力，了解科技英语的特点，提高专业外语的阅读质量和阅读速度；掌握一定量的本专业英文词汇，基本达到能够独立完成一般性本专业外文资料的阅读；达到一定的笔译水平。

要求译文通顺、准确和专业化。

要求译文通顺、准确和专业化。

二、课程内容课程内容包括以下章节：物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量（约1200~1500词/学时），要求正确理解原文。

2.泛读适量课外相关英文读物，要求基本理解原文主要内容。

3.掌握基本专业词汇（不少于200词）。

4.应具有流利阅读、翻译及赏析专业英语文献，并能简单地进行写作的能力。

四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明：蓝色Arial字体（例如energy）：已知的专业词汇蓝色Arial字体加下划线（例如electromagnetism）：新学的专业词汇黑色Times New Roman字体加下划线（例如postulate）：新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交，交叉interdisciplinary交叉学科的，跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注，讨论，考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作，处理，使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化，偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导，感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的，正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力，万有引力explicit 详细的，清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格，点阵，网格★Society社会，学会★microscopic微观的hyperfine splitting超精细分裂fission分裂，裂变fusion熔合，聚变constituents成分，组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像，核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合，核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造，建造spintronics自旋电子元件，自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流，扰动，骚动catastrophes突变，灾变，灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。

论㊀㊀著(临床研究)基于超声影像纹理分析鉴别诊断乳腺分叶状肿瘤和纤维腺瘤李卫民ꎬ贾㊀磊ꎬ高骐磊ꎬ吴文娟ꎬ朱束华ꎬ范晓芳㊀㊀[摘要]㊀目的㊀乳腺分叶状肿瘤(ＰＴＢ)和纤维腺瘤(ＦＢ)超声特征具有一定重合ꎮ文中探讨超声影像纹理分析鉴别诊断ＰＴＢ和ＦＢ的价值ꎮ㊀方法㊀选取５３例ＰＴＢ和１１４例ＦＢ患者的术前超声影像资料ꎮ将超声二维影像导入ＭａＺｄａ４.６软件中ꎬ手动勾画病变的感兴趣区(ＲＯＩ)ꎬ分别选择Ｆｉｓｈｅｒ系数㊁分类错误概率联合平均相关系数(ＰＯＥ＋ＡＣＣ)㊁交互信息(ＭＩ)以及联合３种方法(Ｆｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ＋ＭＩ)ꎮ选择最具鉴别价值的纹理特征参数ꎬ构建人工神经网络模型ꎬ比较ＰＴＢ和ＦＢ纹理特征的差异ꎬ并评估３种纹理分析方法和超声医师对ＰＴＢ和ＦＢ的误判率ꎮ㊀结果㊀３种纹理参数分析方法共选取的３０组纹理参数中ꎬ８组差异有统计学意义(Ｐ<０.０５)ꎮ在总误判率方面ꎬ３种方法联合分析的误判率最低ꎬ与Ｆｉｓｈｅｒ系数㊁ＰＯＥ＋ＡＣＣ㊁ＭＩ以及超声医师的误判率相比ꎬ差异均具有统计学意义(χ２＝３０.６８３㊁７.４６７㊁１２.３７１㊁４.１３８ꎬＰ<０.０５)ꎮ同时ꎬ超声医师对ＰＴＢ的误诊率明显高于ＦＢ(５４.７２％ｖｓ１７.５４％ꎬＰ<０.０５)ꎮ㊀结论㊀超声影像纹理分析可用于鉴别诊断ＰＴＢ和ＦＢꎮ㊀㊀[关键词]㊀超声ꎻ纹理分析ꎻ分叶状肿瘤ꎻ纤维腺瘤㊀㊀[中图分类号]㊀Ｒ７３７.９㊀㊀㊀[文献标志码]㊀Ａ㊀㊀㊀[文章编号]㊀１００８￣８１９９(２０２１)０３￣０２６８￣０５㊀㊀[ＤＯＩ]㊀１０.１６５７１/ｊ.ｃｎｋｉ.１００８￣８１９９.２０２１.０３.００９基金项目:无锡市妇幼健康适宜技术推广项目(ＦＹＴＧ２０１９０４)作者单位:２１４０６２无锡ꎬ江南大学附属医院超声科[李卫民(医学硕士)㊁贾㊀磊㊁高骐磊㊁吴文娟㊁朱束华㊁范晓芳]通信作者:范晓芳ꎬＥ－ｍａｉｌ:ｆａｎｘｉａｏａｌｌ＠１２６.ｃｏｍＴｈｅｕｌｔｒａｓｏｕｎｄｉｍａｇｅｔｅｘｔｕｒｅａｎａｌｙｓｉｓｆｏｒｐｈｙｌｌｏｄｅｓｔｕｍｏｒａｎｄｆｉｂｒｏａｄｅｎｏｍａｏｆｂｒｅａｓｔＬＩＷｅｉ￣ｍｉｎꎬＪＩＡＬｅｉꎬＧＡＯＱｉ￣ｌｅｉꎬＷＵＷｅｎ￣ｊｕａｎꎬＺＨＵＳｈｕ￣ｈｕａꎬＦＡＮＸｉａｏ￣ｆａｎｇ(ＤｅｐａｒｔｍｅｎｔｏｆＵｌｔｒａｓｏｕｎｄꎬＡｆｆｉｌｉａｔｅｄＨｏｓｐｉｔａｌｏｆＪｉａｎｇｎａｎＵｎｉｖｅｒｓｉｔｙꎬＷｕｘｉ２１４０６２ꎬＪｉａｎｇｓｕꎬＣｈｉｎａ)㊀㊀[Ａｂｓｔｒａｃｔ]㊀Ｏｂｊｅｃｔｉｖｅ㊀Ｔｏｉｎｖｅｓｔｉｇａｔｅｔｈｅｖａｌｕｅｏｆｕｌｔｒａｓｏｕｎｄｉｍａｇｅｔｅｘｔｕｒｅａｎａｌｙｓｉｓｆｏｒｔｈｅｄｉａｇｎｏｓｉｓｏｆｐｈｙｌｌｏｄｅｓｔｕｍｏｒａｎｄｆｉｂｒｏａｄｅｎｏｍａｏｆｂｒｅａｓｔ.㊀Ｍｅｔｈｏｄｓ㊀Ａｔｏｔａｌｏｆ５３ｐａｔｉｅｎｔｓｗｉｔｈｐｈｙｌｌｏｄｅｓｔｕｍｏｒｏｆｔｈｅｂｒｅａｓｔ(ＰＴＢ)ａｎｄｆｉｂｒｏａｄｅｎｏｍａｏｆｔｈｅｂｒｅａｓｔ(ＦＢ)ｗｅｒｅｅｎｒｏｌｌｅｄｉｎｔｈｉｓｓｔｕｄｙ.ＴｈｅｕｌｔｒａｓｏｕｎｄｉｍａｇｅｓｗｅｒｅｉｍｐｏｒｔｅｄｉｎｔｏＭａｚｄａ４.６ｓｏｆｔｗａｒｅａｎｄｒｅｇｉｏｎｓｏｆｔｈｅｉｎｔｅｒｅｓｔ(ＲＯＩ)ｗｅｒｅｍａｎｕａｌｌｙｄｒａｗｎ.ＴｏｂｕｉｌｄｔｈｅｍｏｄｅｌｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋꎬｔｈｅｏｐｔｉｍｕｍｔｅｘｔｕｒｅｐａｒａｍｅｔｅｒｓｗｅｒｅｓｅｌｅｃｔｅｄｒｅｓｐｅｃｔｉｖｅｌｙｆｒｏｍＦｉｓｈｅｒꎬｐｒｏｂａｂｉｌｉｔｙｏｆｃｌａｓｓｉｆｉｃａｔｉｏｎｅｒｒｏｒａｎｄａｖｅｒａｇｅｃｏｒｒｅｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔ(ＰＯＥ＋ＡＣＣ)ꎬｍｕｔｕａｌｉｎｆｏｒｍａｔｉｏｎ(ＭＩ)ａｎｄｔｈｅｃｏｍｂｉｎａｔｉｏｎｏｆｔｈｒｅｅｍｅｔｈｏｄｓ(Ｆｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ＋ＭＩ).ＴｈｅｄｉｆｆｅｒｅｎｃｅｓｏｆｔｈｅｕｌｔｒａｓｏｕｎｄｉｍａｇｅｔｅｘｔｕｒｅａｎａｌｙｓｉｓｆｏｒＰＴＢａｎｄＦＢｗｅｒｅｃｏｍｐａｒｅｄꎬａｎｄｔｈｅｍｉｓｄｉａｇｎｏｓｉｓｒａｔｅｓｏｆｔｈｅｆｏｕｒｔｅｘｔｕｒｅｐａｒａｍｅｔｅｒｓａｎｄｕｌｔｒａｓｏｕｎｄｄｏｃｔｏｒｓｗｅｒｅａｓｓｅｓｓｅｄ.㊀Ｒｅｓｕｌｔｓ㊀Ａｍｏｎｇｔｈｅｆｉｇｕｒｅｓｏｆ３０ｇｒｏｕｐｓｓｅｌｅｃｔｅｄｂｙｔｈｒｅｅｔｅｘｔｕｒｅｐａｒａｍｅｔｅｒｓꎬｔｈｅｒｅｗｅｒｅｓｔａｔｉｓｔｉｃａｌｄｉｆｆｅｒｅｎｃｅｓｉｎ８ｇｒｏｕｐｓ(Ｐ<０.０５).ＴｈｅｍｉｓｄｉａｇｎｏｓｉｓｒａｔｅｏｆｔｈｅｃｏｍｂｉｎａｔｉｏｎｏｆＦｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ＋ＭＩｗａｓｔｈｅｌｏｗｅｓｔꎬａｎｄｔｈｅｒｅｗｅｒｅｓｉｇｎｉｆｉｃａｎｔｄｉｆｆｅｒｅｎｃｅｓｃｏｍｐａｒｅｄｗｉｔｈＦｉｓｈｅｒｃｏｅｆｆｉｃｉｅｎｔꎬＰＯＥ＋ＡＣＣꎬＭＩａｎｄｕｌｔｒａｓｏｕｎｄｄｏｃｔｏｒｓ(χ２ｖａｌｕｅｓｗｅｒｅ３０.６８３ꎬ７.４６７ꎬ１２.３７１ꎬ４.１３８ꎬＰ<０.０５).ＭｅａｎｗｈｉｌｅꎬｔｈｅｍｉｓｄｉａｇｎｏｓｉｓｒａｔｅｏｆＰＴＢｏｆｕｌｔｒａｓｏｕｎｄｄｏｃ￣ｔｏｒｓｗａｓｓｉｇｎｉｆｉｃａｎｔｌｙｈｉｇｈｅｒｔｈａｎｔｈａｔｏｆＦＢ(Ｐ<０.０５).㊀ＣｏｎｃｌｕｓｉｏｎＵｌｔｒａｓｏｕｎｄｉｍａｇｅｔｅｘｔｕｒｅａｎａｌｙｓｉｓｃａｎｂｅｕｓｅｄｔｏｄｉａｇｎｏｓｅｐｈｙｌｌｏｄｅｓｔｕｍｏｒａｎｄｆｉｂｒｏａｄｅｎｏｍａｏｆｂｒｅａｓｔ.㊀㊀[Ｋｅｙｗｏｒｄｓ]㊀ｕｌｔｒａｓｏｕｎｄꎻｔｅｘｔｕｒｅａｎａｌｙｓｉｓꎻｐｈｙｌｌｏｄｅｓｔｕｍｏｒｏｆｔｈｅｂｒｅａｓｔꎻｆｉｂｒｏａｄｅｎｏｍａｏｆｂｒｅａｓｔ０㊀引㊀㊀言㊀㊀乳腺分叶状肿瘤(ｐｈｙｌｌｏｄｅｓｔｕｍｏｒｏｆｔｈｅｂｒｅａｓｔꎬＰＴＢ)是一种由乳腺上皮组织和纤维结缔组织组成的纤维上皮性肿瘤ꎬ占乳腺肿瘤的０.３％~１％ꎬ其病理成分与纤维腺瘤(ｆｉｂｒｏａｄｅｎｏｍａｏｆｂｒｅａｓｔꎬＦＢ)一致ꎬ穿刺病理往往难以准确与其鉴别[１]ꎮ同时ꎬ由于ＰＴＢ常采用扩大切除术ꎬ且第一次手术方式的选择与复发率和死亡率密切相关[２]ꎮ因此ꎬ术前对于ＰＴＢ和ＦＢ的准确鉴别具有重要意义ꎮ超声作为乳腺检查常用的影像学手段ꎬ具有简单方便的优点ꎮ然而ꎬＰＴＢ和ＦＢ的超声特征具有一定重合ꎬ这在一定程度上增加了ＰＴＢ与ＦＢ的超声鉴别难度ꎬ特别是体积较小的ＰＴＢ更易误诊为ＦＢ[３－４]ꎮ本研究通过对５３例ＰＴＢ和１１４例ＦＢ的超声影像资料进行纹理分析ꎬ提取常规超声无法观察的纹理特征参数ꎬ探讨其对ＰＴＢ和ＦＢ的鉴别价值ꎮ１㊀资料与方法１.１㊀研究对象㊀回顾性分析２０１８年１月至２０２０年４月间于江南大学附属医院就诊的ＰＴＢ患者５３例ꎬ均为女性ꎬ年龄３５~８２岁ꎬ平均(４６.６０ʃ１１.４５)岁ꎻ同时选取ＦＢ患者１１４例ꎬ均为女性ꎬ年龄１７~６５岁ꎬ平均(３５.５３ʃ７.４５)岁ꎮ纳入标准:①首次发现乳腺肿瘤ꎻ②经手术病理诊断ꎬ有明确的诊断结果ꎻ③超声影像资料完整㊁可靠ꎮ排除肿瘤体积过大ꎬ感兴趣区(ｒｅｇｉｏｎｏｆｉｎｔｅｒｅｓｔꎬＲＯＩ)无法进行勾画的肿块ꎮ１.２㊀仪器与检查方法㊀采用西门子ＡｃｕｓｏｎＡｎｔａｒｅｓＳ３０００彩色多普勒超声诊断仪ꎬ探头频率为７.５~１２.０ＭＨｚꎮ患者取仰卧位ꎬ充分暴露双侧乳房及腋窝ꎬ以乳头为中心ꎬ二维超声采用扇形扫查法扫查乳腺ꎬ对肿块进行多切面㊁多角度观察ꎮ在超声二维影像的基础上ꎬ行彩色多普勒超声检查ꎬ观察病灶内部及周边血流情况ꎬ超声影像资料的采集由具有１０年以上工作经验的超声医师进行ꎮ１.３㊀超声医师评估㊀超声影像资料的评估由２名具有１０年以上工作经验的副主任医师进行ꎮ根据相关研究结果将患者年龄较大㊁肿块>３ｃｍ㊁边缘呈分叶状㊁血供丰富等特征的乳腺肿块评估为ＰＴＢꎻ将患者年龄较轻ꎬ肿块体积<３ｃｍꎬ边缘光整ꎬ血供较少等特征的乳腺肿块评估为ＦＢ[５－７]ꎮ评估后将超声医师评估结果与术后病理结果进行对照ꎬ以获取超声医师对ＰＴＢ和ＦＢ的误判率ꎮ１.４㊀纹理分析㊀采用罗兹工业大学研制的纹理分析软件ＭａＺｄａ４.６ꎮ将超声二维影像以ｂｍｐ格式导入软件中ꎬ对超声影像进行归一化处理ꎮ采用多边形功能手动模式尽可能勾画病灶的全部区域ꎮ勾画完成后ꎬ分析病灶的纹理特征ꎬ并通过软件自带的纹理特征分析方法选择最具鉴别价值的纹理参数ꎬ包括Ｆｉｓｈｅｒ系数㊁分类错误概率联合平均相关系数(ｃｌａｓｓｉｆｉｃａｔｉｏｎｅｒｒｏｒｐｒｏｂａｂｉｌｉｔｙｃｏｍｂｉｎｅｄｗｉｔｈａｖｅｒａｇｅｃｏｒｒｅｌａｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｓꎬＰＯＥ＋ＡＣＣ)㊁交互信息(ｍｕｔｕ￣ａｌｉｎｆｏｒｍａｔｉｏｎꎬＭＩ)及３种方法联合(Ｆｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ＋ＭＩ)ꎮ前３种方法各提取１０项纹理参数ꎬＦｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ＋ＭＩ共提取３０项纹理特征参数ꎮ将简化后的纹理特征参数输入ＭａＺｄａ自带的Ｂ１１统计分析软件包中ꎬ构建人工神经网络(ａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋꎬＡＮＮ)模型ꎬ反复自动训练ꎬ将其与病理对比ꎬ得出纹理分析方法对ＰＴＢ和ＦＢ的误判率ꎮ１.５㊀统计学分析㊀采用ＳＰＳＳ１９.０统计分析软件ꎮ计量资料以(ｘʃｓ)表示ꎬ纹理参数的比较采用独立样本ｔ检验ꎻＰＴＢ与ＦＢ超声特征㊁超声医师的评估结果以及各种纹理分析方法误判等计数资料以ｎ(％)表示ꎬ组间比较采用c２检验㊁连续校正的c２检验或Ｆｉｓｈｅｒᶄｓ检验ꎮ以Ｐɤ０.０５为差异有统计学意义ꎮ２㊀结㊀㊀果２.１㊀ＰＴＢ和ＦＢ的超声特征比较㊀本组患者ＰＴＢ和ＦＢ的超声特征中ꎬ大小㊁边缘㊁内部回声㊁囊性变㊁血流分级等差异均有统计学意义(Ｐ<０.０５)ꎮ与病理结果比较ꎬ超声医师的总误判率为２９.３４％(４９/１６７)ꎬ其中对ＰＴＢ的误判率为５４.７２％(２９/５３)ꎬ对ＦＢ的误判率为１７.５４％(２０/１１４)ꎮ见表１ꎮ２.２㊀ＰＴＢ和ＦＢ超声影像ＲＯＩ标识及纹理特征统计㊀ＰＴＢ和ＦＢ患者ＲＯＩ标记前后的典型超声影像见图１㊁图２ꎮ４种纹理分析方法共选取３０项纹理参数ꎬ前１０组为Ｆｉｓｈｅｒ系数方法选取ꎬ中间１０组为ＰＯＥ＋ＡＣＣ选取ꎬ后１０组为ＭＩ选取的纹理参数ꎮ结果表明ꎬＦｉｓｈｅｒ系数选取的纹理参数中有３组差异有统计学意义(Ｐ<０.０５)ꎻＰＯＥ＋ＡＣＣ选取的纹理参数中４组差异有统计学意义(Ｐ<０.０５)ꎻＭＩ选取的纹理参数中仅有１组差异有统计学意义(Ｐ<０.０５)ꎻ３种方法联合选取的纹理参数共８组差异有统计学意义(Ｐ<０.０５)ꎮ见表２ꎮ表１㊀ＰＴＢ和ＦＢ的超声特征比较Ｔａｂｌｅ１㊀ＣｏｍｐａｒｉｓｏｎｏｆｕｌｔｒａｓｏｎｉｃｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＰＴＢａｎｄＦＢ病灶特征ＰＴＢ组(ｎ＝５３)ＦＢ组(ｎ＝１１４)ｔ/c ２值Ｐ值大小(ｘʃｓꎬｍｍ)３３.４３ʃ１０.５７１９.５９ʃ７.６３３３.４１６０.０００边界[ｎ(％)]㊀清晰４８(９０.５７)９７(８５.０９)０.９４９０.３３０㊀不清晰５(９.４３)１７(１４.９１)边缘呈分叶状[ｎ(％)]㊀是３７(６９.８１)１８(１５.７９)４７.８０３０.０００㊀否１６(３０.１９)９６(８４.２１)方位[ｎ(％)]㊀平行位５３(１００)１１２(９８.２５)０.９４１０.３３２㊀非平行位０(０)２(１.７５)内部回声[ｎ(％)]㊀均匀２４(４５.２８)７９(６９.３０)８.８２８０.００３㊀不均匀２９(５４.７２)３５(３０.７０)后方回声[ｎ(％)]㊀无改变５３(１００)１１１(９７.３７)１.４２００.２３３㊀衰减０(０)３(２.６３)囊性变[ｎ(％)]㊀有４(７.５５)０(０)８.８１５０.００３㊀无４９(９２.４５)１１４(１００)钙化[ｎ(％)]㊀有０(０)７(６.１４)３.３９７０.０６５㊀无５３(１００)１０７(９３.８６)血流[ｎ(％)]㊀０－Ｉ级２２(４１.５１)９５(８３.３３)３０.１７１０.０００㊀ＩＩ－ＩＩＩ级３１(５８.４９)１９(１６.６７)㊀㊀㊀ａ:标记ＲＯＩ前ꎻｂ:标记ＲＯＩ后图１㊀乳腺分叶状肿瘤ＲＯＩ标记前后超声影像Ｆｉｇｕｒｅ１㊀ＵｌｔｒａｓｏｎｉｃｉｍａｇｅｓｏｆｐｈｙｌｌｏｄｅｓｔｕｍｏｒｂｅｆｏｒｅａｎｄａｆｔｅｒＲＯＩｌａｂｅｌｉｎｇ㊀㊀㊀ａ:标记ＲＯＩ前ꎻｂ:标记ＲＯＩ后图２㊀乳腺纤维腺瘤ＲＯＩ标记前后超声影像Ｆｉｇｕｒｅ２㊀Ｕｌｔｒａｓｏｎｉｃｉｍａｇｅｓｏｆｆｉｂｒｏａｄｅｎｏｍａｂｅｆｏｒｅａｎｄａｆ￣ｔｅｒＲＯＩｌａｂｅｌｉｎｇ表２㊀ＰＴＢ和ＦＢ超声影像纹理特征参数比较(ｘʃｓ)Ｔａｂｌｅ２㊀Ｃｏｍｐａｒｉｓｏｎｏｆｕｌｔｒａｓｏｎｉｃｉｍａｇｅｔｅｘｔｕｒｅｐａｒａｍｅ￣ｔｅｒｓｂｅｔｗｅｅｎＰＴＢａｎｄＦＢ(ｘʃｓ)纹理参数ＰＴＢ组(ｎ＝５３)ＦＢ组(ｎ＝１１４)ｔ值Ｐ值Ｈｏｒｚｌ＿Ｆｒａｃｔｉｏｎ１.０９Ｅ２ʃ５０.８９１.２７Ｅ２ʃ３８.２２０.６４３０.５３８Ｓ(０ꎬ２)ＤｉｆＥｎｔｒｐ２.８０ʃ１.１６１.８３ʃ０.３２１.８０４０.１０９Ｓ(１ꎬ０)ＩｎｖＤｆＭｏｍ１.８４Ｅ２ʃ３９.５７１.４０Ｅ２ʃ３４.５４１.８８６０.０９６Ｓ(２ꎬ０)ＩｎｖＤｆＭｏｍ１.８３Ｅ２ʃ３９.８８１.３９Ｅ２ʃ３４.５４１.８９６０.０９４Ｓ(２ꎬ２)ＤｉｆＥｎｔｒｐ２.８４Ｅ２ʃ５９.８９１.３９Ｅ２ʃ３４.３９３.９１００.０２７Ｓ(２ꎬ－２)ＤｉｆＥｎｔｒｐ１.８４Ｅ２ʃ３９.８１１.３９Ｅ２ʃ３４.５２１.８９９０.０９４Ｐｅｒｃ.９０％０.６９ʃ０.２２０.７９ʃ０.２２０.７４８０.４７６Ｐｅｒｃ.９９％２.４５Ｅ２ʃ３８.９５１.４１Ｅ２ʃ３４.９３２.８８８０.０３１Ｓ(３ꎬ０)Ｃｏｎｔｒａｓｔ３.４３ʃ１.８６１.９７ʃ０.４２１.７０８０.１２６ＷａｖＥｎＨＬ＿ｓ￣６５.３８Ｅ４ʃ２４３０４.９４２.５７Ｅ４ʃ１４３９８.２６２.７２００.０３３１３５ｄｒ＿ＬｎｇＲＥｍｐｈ６.１９Ｅ２ʃ１８７.６６４.２７Ｅ２ʃ１２５.９９１.８９４０.０９５ＷａｖＥｎＬＨ＿ｓ￣２８８.２９ʃ２２.９４１.０２Ｅ２ʃ２７.０５０.８９１０.３９９４５ｄｇｒ＿ＬｎｇＲＥｍｐｈ６.２１Ｅ２ʃ１８８.５７４.２７Ｅ２ʃ１２８.６０１.８９７０.０９４４５ｄｇｒ＿ＲＬＮｏｎＵｎｉ８.５６Ｅ２ʃ２７７.２１４.６３Ｅ２ʃ１４０.５４２.９０１０.０２９Ｓ(２ꎬ０)ＳｕｍＯｆＳｑｓ１.８３Ｅ２ʃ４０.１６１.３９Ｅ２ʃ３４.１２１.８８００.０９７Ｔｅｔａ１５.１６Ｅ４ʃ２３５２３.２６２.４８Ｅ４ʃ１３９２３.０７２.３９３０.０４３∗Ｓ(３ꎬ０)ＳｕｍＯｆＳｑｓ２.８０ʃ１.１６１.８５ʃ０.３３１.７５８０.１１７Ｖｅｒｔｌ＿ＬｎｇＲＥｍｐｈ５.８０Ｅ４ʃ２４６７０.３２２.５８Ｅ４ʃ１４３６０.７４２.２１００.０４７Ｓ(５ꎬ－５)Ｃｏｎｔｒａｓｔ１.８１Ｅ２ʃ４１.２９１.３６Ｅ２ʃ３３.７２１.９０３０.０９４４５ｄｇｒ＿ＲＬＮｏｎＵｎｉ０.６２ʃ０.０５０.６５ʃ０.０８０.７３３０.４８４１３５ｄｒ＿ＲＬＮｏｎＵｎｉ１.０３ʃ０.７８１.０６ʃ０.１１０.４０２０.６９８Ｖｅｒｔｌ＿ＲＬＮｏｎＵｎｉ０.６１ʃ０.０６０.５８ʃ０.０７０.５４７０.５９９Ｈｏｒｚｌ＿ＲＬＮｏｎＵｎｉ０.４４ʃ０.０５０.４１ʃ０.０８０.７２７０.４８８Ｓ(１ꎬ１)ＳｕｍＯｆＳｑｓ１.０６ʃ０.０８１.０８ʃ０.１１０.３７２０.７１９Ｓ(２ꎬ２)ＳｕｍＯｆＳｑｓ１.０６ʃ０.０８１.０９ʃ０.１２０.４２００.６８５Ｓ(３ꎬ３)ＳｕｍＶａｒｎｃ７４.４０ʃ４２.５３６７.２０ʃ１６.１６０.３５４０.７３３Ｓ(０ꎬ１)ＳｕｍＯｆＳｑｓ１.１２Ｅ２ʃ５１.８７１.１１Ｅ２ʃ１７.６００.０３３０.９７５Ｓ(５ꎬ５)ＳｕｍＶａｒｎｃ４５.９３ʃ３２.５９３１.５１ʃ２４.２３３.３４３０.０１２Ｓ(１ꎬ－１)ＳｕｍＯｆＳｑｓ２.６２Ｅ２ʃ１２０.００２.５１Ｅ２ʃ６０.３８０.１９５０.８５０２.３㊀纹理分析和超声医师的误判率比较㊀对于所有ＰＴＢ和ＦＢ病灶ꎬＭＩ方法进行纹理分析的总误判率为４８.５０％(８１/１６７)ꎬＰＯＥ＋ＡＣＣ为３２.９３％(５５/１６７)ꎬＦｉｓｈｅｒ系数为３７.１３％(６２/１６７)ꎬ３种方法联合为１９.７６％(３３/１６７)ꎬ超声医师的误判率为２９.３４％(４９/１６７)ꎮ其中ꎬ３种方法联合分析的误判率最低ꎬ与ＭＩ㊁ＰＯＥ＋ＡＣＣ㊁Ｆｉｓｈｅｒ系数以及超声医师的评估结果比较ꎬ差异均具有统计学意义(c２值分别为３０.６８３㊁７.４６７㊁１２.３７１㊁４.１３８ꎬＰ<０.０５)ꎮ各种纹理分析方法在ＰＴＢ和ＦＢ２组患者之间的误诊率差异无统计学意义(Ｐ>０.０５)ꎮ超声医师对ＰＴＢ的误诊率明显高于ＦＢ的误诊率(５４.７２％ｖｓ１７.５４％ꎬＰ<０.０５)ꎮ见表３ꎮ表３㊀纹理分析ＰＴＢ和ＦＢ误诊率比较(％)Ｔａｂｌｅ３㊀ｍｉｓｄｉａｇｎｏｓｉｓｒａｔｅｏｆＰＴＢａｎｄＦＢｆｏｒｔｅｘｔｕｒｅａｎａｌｙ￣ｓｉｓ(％)项目ＰＴＢ组(ｎ＝５３)ＦＢ组(ｎ＝１１４)χ２值Ｐ值ＭＩ５０.９４４７.３７０.１８５０.６６７ＰＯＥ＋ＡＣＣ４３.４０２８.０７３.８４７０.０５Ｆｉｓｈｅｒ系数３５.８５３７.７２０.０５４０.８１６ＭＩ＋Ｆｉｓｈｅｒ＋ＰＯＥ＋ＡＣＣ２２.６４１８.４２０.４０６０.５２４超声医师５４.７２１７.５４２４.１１４０.０００３㊀讨㊀㊀论㊀㊀纹理分析作为人工智能的重要内容ꎬ可通过一定的图像处理技术提取出纹理特征ꎬ从而获得图像的定量或定性描述[８]ꎮ在影像学诊断方面ꎬ纹理分析通过提取肉眼难以发现的纹理特征ꎬ而更加细致地分析图像ꎬ这可为鉴别病灶的性质提供一定的依据[９]ꎮ本研究使用的ＭａＺｄａ软件提供了６种纹理分析方法和４种纹理选择方法ꎬ６种纹理分析方法包括:①灰度直方图ꎻ②灰度绝对梯度ꎻ③游程矩阵ꎻ④灰度共生矩阵ꎻ⑤自回归模型ꎻ⑤小波变换ꎮ４种纹理选择方法包括ＭＩ㊁ＰＯＥ＋ＡＣＣ㊁Ｆｉｓｈｅｒ系数以及三种方法的联合(ＭＩ＋ＰＯＥ＋ＡＣＣ＋Ｆｉｓｈｅｒ)ꎬ共提取３０种纹理参数信息ꎬ有利于增加诊断的准确性[１０－１２]ꎮ研究表明ꎬＸ线纹理分析可提高ＰＴＢ和ＦＢ诊断的准确率[１３]ꎮ这也为超声影像纹理分析鉴别诊断ＰＴＢ和ＦＢ奠定了一定的基础ꎮ本文的研究结果表明ꎬ超声影像纹理分析有助于鉴别诊断ＰＴＢ和ＦＢꎮ本研究选用的Ｍａｚｄａ纹理分析软件共提取了３０组纹理参数ꎬ其中ＭＩ中仅有１组纹理参数具有统计学差异ꎬＰＯＥ＋ＡＣＣ中有４组纹理参数具有统计学差异ꎬＦｉｓｈｅｒ系数中３组纹理参数有统计学差异ꎬ而有价值的纹理参数与肿块的纹理信息呈正相关ꎬ纹理参数越多ꎬ所提供具有鉴别价值的信息就越多ꎬ因此ꎬ在总误判率方面ꎬＭＩ>Ｆｉｓｈｅｒ系数>ＰＯＥ＋ＡＣＣꎮ而ＭＩ＋ＰＯＥ＋ＡＣＣ＋Ｆｉｓｈｅｒ是Ｆｉｓｈｅｒ系数㊁ＭＩ＋ＰＡ＋Ｆ及ＭＩ三种方法的结合ꎬ所包括的纹理参数较多ꎬ可弥补使用Ｆｉｓｈｅｒ系数㊁ＰＯＥ＋ＡＣＣ㊁ＭＩ这３种方法相对训练不足导致的缺陷ꎬ因而总误判率最低ꎬ本研究中ꎬＭＩ＋ＰＯＥ＋ＡＣＣ＋Ｆｉｓｈｅｒ的误判率为１９.７６％ꎬ均明显低于ＭＩ㊁ＰＯＥ＋ＡＣＣ㊁Ｆｉｓｈｅｒ３种方法ꎮ本研究通过对ＰＴＢ和ＦＢ两组的误判率分析发现ꎬ纹理分析在２组误判率之间的差异均不具有统计学意义ꎬ这说明纹理分析对将ＰＴＢ误诊为ＦＢꎬ以及将ＦＢ误诊为ＰＴＢ的比率无明显差异ꎮ相对于超声医师的评估结果ꎬ纹理分析方法中的３种方法联合评估的价值明显高于超声医师ꎬ而３种纹理分析方法均低于超声医师ꎮ３种方法联合评估共８组纹理参数具有统计学意义ꎬ与超声医师的评估相比ꎬ纹理分析所提取的信息可排除超声医师主观因素的干扰ꎮ超声医师对ＰＴＢ的评估主要根据病灶大小㊁边缘㊁内部回声㊁血流以及发病年龄等信息ꎮ本研究结果表明ꎬＰＴＢ和ＦＢ在大小㊁边缘㊁内部回声㊁血流分级等方面差异具有统计学意义ꎬ然而ꎬ两者超声特征均具有一定的重合ꎬ这与相关研究结果相同ꎬ这可能是本研究中超声医师评估出现误诊的主要原因[１４]ꎮ研究表明ꎬ交界性㊁恶性ＰＴＢ与ＦＢ的声像图特点差异较大ꎬ超声检查较易诊断ꎬ而良性ＰＴＢ与ＦＢ的超声鉴别难度较大[５]ꎬ这在一定程度上增加了超声医师的评估的主观性ꎬ从而将ＰＴＢ评估为ＦＢꎬ这也是本研究中超声医师对ＰＴＢ的误诊率高于ＦＢ的原因所在ꎮ而纹理分析可提取肉眼无法观察到的肿瘤信息ꎬ不受超声医师主观因素的影响ꎬ增加了纹理分析的准确性ꎮ综上所述ꎬ超声影像纹理分析可用于鉴别乳腺分叶肿瘤和ＦＢꎬ值得进一步推广ꎬ从而为精准的诊疗方案提供依据ꎮʌ参考文献ɔ[１]㊀ＯｓｓａＣＡꎬＨｅｒａｚｏＦꎬＧｉｌＭꎬｅｔａｌ.Ｐｈｙｌｌｏｄｅｓｔｕｍｏｒｏｆｔｈｅｂｒｅａｓｔ[Ｊ].ＣｏｌｏｍｂｉａＭéｄｉｃａＣｍꎬ２０１５ꎬ４６(３):１０４￣１０８. [２]㊀ＭｉｔｕｓＪＷꎬＢｌｅｃｈａｒｚＰꎬＪａｋｕｂｏｗｉｃｚＪꎬｅｔａｌ.Ｐｈｙｌｌｏｄｅｓｔｕｍｏｒｓｏｆｔｈｅｂｒｅａｓｔ.Ｔｈｅｔｒｅａｔｍｅｎｔｒｅｓｕｌｔｓｆｏｒ３４０ｐａｔｉｅｎｔｓｆｒｏｍａｓｉｎｇｌｅｃａｎｃｅｒｃｅｎｔｒｅ[Ｊ].Ｂｒｅａｓｔꎬ２０１９ꎬ４３:８５￣９０.[３]㊀ＳｔｏｆｆｅｌＥꎬＢｅｃｋｅｒＡＳꎬＷｕｒｎｉｇＭＣꎬｅｔａｌ.Ｄｉｓｔｉｎｃｔｉｏｎｂｅｔｗｅｅｎｐｈｙｌｌｏｄｅｓｔｕｍｏｒａｎｄｆｉｂｒｏａｄｅｎｏｍａｉｎｂｒｅａｓｔｕｌｔｒａｓｏｕｎｄｕｓｉｎｇｄｅｅｐｌｅａｒｎｉｎｇｉｍａｇｅａｎａｌｙｓｉｓ[Ｊ].ＥｕｒＪＲａｄｉｏｌＯｐｅｎꎬ２０１８ꎬ５:１６５￣１７０.[４]㊀王琳琳ꎬ方建强ꎬ李尔清.超声造影在乳腺叶状肿瘤与ＦＢ鉴别诊断中的价值[Ｊ].中华医学超声杂志(电子版)ꎬ２０２０ꎬ１７(０１):２９￣３２.[５]㊀赵㊀丹ꎬ董凤林ꎬ鄢英男ꎬ等.不同病理分型的乳腺叶状肿瘤与ＦＢ超声表现的对照分析[Ｊ].中国超声医学杂志ꎬ２０１９ꎬ３５(１０):８９０￣８９３.[６]㊀崔㊀岩ꎬ李子桢.乳腺ＦＢ与ＰＴＢ超声表现的对照分析[Ｊ].河北医学ꎬ２０１８ꎬ２４(３):４８５￣４８９.[７]㊀方建强ꎬ单世胜ꎬ赵维安ꎬ等.超声造影及常规超声在乳腺叶状肿瘤与ＦＢ鉴别诊断中的价值[Ｊ].肿瘤影像学ꎬ２０１８ꎬ２７(５):４２１￣４２５.[８]㊀ＫａｓｓｎｅｒＡꎬＴｈｏｒｎｈｉｌｌＲＥ.ＴｅｘｔｕｒｅＡｎａｌｙｓｉｓ:ＡＲｅｖｉｅｗｏｆＮｅｕ￣ｒｏｌｏｇｉｃＭＲＩｍａｇｉｎｇＡｐｐｌｉｃａｔｉｏｎｓ[Ｊ].ＡｍＪＮｅｕｒｏｒａｄｉｏｌꎬ２０１０ꎬ３１(５):８０９￣８１６.[９]㊀徐㊀琰ꎬ胡保全.浅谈人工智能在乳腺癌领域的应用进展[Ｊ].中华乳腺病杂志(电子版)ꎬ２０１７ꎬ１９(５):７￣１１. [１０]㊀ＨｏｕｓｓａｍｉＮꎬＬｅｅＣＩꎬＢｕｉｓｔＤＳＭꎬｅｔａｌ.Ａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅｆｏｒｂｒｅａｓｔｃａｎｃｅｒｓｃｒｅｅｎｉｎｇ:Ｏｐｐｏｒｔｕｎｉｔｙｏｒｈｙｐｅ[Ｊ].Ｂｒｅａｓｔꎬ２０１８ꎬ３６(１２):３１￣３３.[１１]㊀ＳｉｖａｒａｍａｋＲꎬＫｉｍｅｒｌｙＡＰꎬＭｉｃｈａｅｌＬＬꎬｅｔａｌ.Ｔｅｘｔｕｒｅａｎａｌｙｓｉｓｏｆｌｅｓｉｏｎｓｉｎｂｒｅａｓｔｕｌｔｒａｓｏｕｎｄｉｍａｇｅｓ[Ｊ].ＣｏｍＭｅｄＩｍａｇｉｎｇＧｒａｐｈ￣ｉｃｓꎬ２０１７ꎬ２６(５):３０３￣３０７.[１２]㊀种美玲ꎬ时白雪ꎬ张㊀禧ꎬ等.超声联合纹理分析对乳腺结节良恶性的诊断价值[Ｊ].中华医学超声杂志(电子版)ꎬ２０１９ꎬ１６(８):５８１￣５８５.[１３]㊀张锦超ꎬ胡汉金.Ｘ线纹理分析鉴别诊断乳腺叶状肿瘤与纤维腺瘤[Ｊ].中国医学影像技术ꎬ２０１９ꎬ３５(２):２１８￣２２１. [１４]㊀ＶｅｎｔｅｒＡＣꎬＲｏşｃａＥꎬＤａｉｎａＬＧꎬｅｔａｌ.Ｐｈｙｌｌｏｄｅｓｔｕｍｏｒ:ｄｉａｇ￣ｎｏｓｔｉｃｉｍａｇｉｎｇａｎｄｈｉｓｔｏｐａｔｈｏｌｏｇｙｆｉｎｄｉｎｇｓ[Ｊ].ＲｏｍＪＭｏｒｐｈｏｌＥｍｂｒｙｏｌꎬ２０１５ꎬ５６(４):１３９７￣１４０２.(收稿日期:２０２０￣０９￣０７ꎻ㊀修回日期:２０２１￣０１￣２３)(责任编辑:闻㊀浩ꎻ㊀英文编辑:周丽桃)。

3GPP TS 36.331 V13.2.0 (2016-06)Technical Specification3rd Generation Partnership Project;Technical Specification Group Radio Access Network;Evolved Universal Terrestrial Radio Access (E-UTRA);Radio Resource Control (RRC);Protocol specification(Release 13)The present document has been developed within the 3rd Generation Partnership Project (3GPP TM) and may be further elaborated for the purposes of 3GPP. The present document has not been subject to any approval process by the 3GPP Organizational Partners and shall not be implemented.This Specification is provided for future development work within 3GPP only. The Organizational Partners accept no liability for any use of this Specification. Specifications and reports for implementation of the 3GPP TM system should be obtained via the 3GPP Organizational Partners' Publications Offices.KeywordsUMTS, radio3GPPPostal address3GPP support office address650 Route des Lucioles - Sophia AntipolisValbonne - FRANCETel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16InternetCopyright NotificationNo part may be reproduced except as authorized by written permission.The copyright and the foregoing restriction extend to reproduction in all media.© 2016, 3GPP Organizational Partners (ARIB, ATIS, CCSA, ETSI, TSDSI, TTA, TTC).All rights reserved.UMTS™ is a Trade Mark of ETSI registered for the benefit of its members3GPP™ is a Trade Mark of ETSI registered for the benefit of its Members and of the 3GPP Organizational PartnersLTE™ is a Trade Mark of ETSI currently being registered for the benefit of its Members and of the 3GPP Organizational Partners GSM® and the GSM logo are registered and owned by the GSM AssociationBluetooth® is a Trade Mark of the Bluetooth SIG registered for the benefit of its membersContentsForeword (18)1Scope (19)2References (19)3Definitions, symbols and abbreviations (22)3.1Definitions (22)3.2Abbreviations (24)4General (27)4.1Introduction (27)4.2Architecture (28)4.2.1UE states and state transitions including inter RAT (28)4.2.2Signalling radio bearers (29)4.3Services (30)4.3.1Services provided to upper layers (30)4.3.2Services expected from lower layers (30)4.4Functions (30)5Procedures (32)5.1General (32)5.1.1Introduction (32)5.1.2General requirements (32)5.2System information (33)5.2.1Introduction (33)5.2.1.1General (33)5.2.1.2Scheduling (34)5.2.1.2a Scheduling for NB-IoT (34)5.2.1.3System information validity and notification of changes (35)5.2.1.4Indication of ETWS notification (36)5.2.1.5Indication of CMAS notification (37)5.2.1.6Notification of EAB parameters change (37)5.2.1.7Access Barring parameters change in NB-IoT (37)5.2.2System information acquisition (38)5.2.2.1General (38)5.2.2.2Initiation (38)5.2.2.3System information required by the UE (38)5.2.2.4System information acquisition by the UE (39)5.2.2.5Essential system information missing (42)5.2.2.6Actions upon reception of the MasterInformationBlock message (42)5.2.2.7Actions upon reception of the SystemInformationBlockType1 message (42)5.2.2.8Actions upon reception of SystemInformation messages (44)5.2.2.9Actions upon reception of SystemInformationBlockType2 (44)5.2.2.10Actions upon reception of SystemInformationBlockType3 (45)5.2.2.11Actions upon reception of SystemInformationBlockType4 (45)5.2.2.12Actions upon reception of SystemInformationBlockType5 (45)5.2.2.13Actions upon reception of SystemInformationBlockType6 (45)5.2.2.14Actions upon reception of SystemInformationBlockType7 (45)5.2.2.15Actions upon reception of SystemInformationBlockType8 (45)5.2.2.16Actions upon reception of SystemInformationBlockType9 (46)5.2.2.17Actions upon reception of SystemInformationBlockType10 (46)5.2.2.18Actions upon reception of SystemInformationBlockType11 (46)5.2.2.19Actions upon reception of SystemInformationBlockType12 (47)5.2.2.20Actions upon reception of SystemInformationBlockType13 (48)5.2.2.21Actions upon reception of SystemInformationBlockType14 (48)5.2.2.22Actions upon reception of SystemInformationBlockType15 (48)5.2.2.23Actions upon reception of SystemInformationBlockType16 (48)5.2.2.24Actions upon reception of SystemInformationBlockType17 (48)5.2.2.25Actions upon reception of SystemInformationBlockType18 (48)5.2.2.26Actions upon reception of SystemInformationBlockType19 (49)5.2.3Acquisition of an SI message (49)5.2.3a Acquisition of an SI message by BL UE or UE in CE or a NB-IoT UE (50)5.3Connection control (50)5.3.1Introduction (50)5.3.1.1RRC connection control (50)5.3.1.2Security (52)5.3.1.2a RN security (53)5.3.1.3Connected mode mobility (53)5.3.1.4Connection control in NB-IoT (54)5.3.2Paging (55)5.3.2.1General (55)5.3.2.2Initiation (55)5.3.2.3Reception of the Paging message by the UE (55)5.3.3RRC connection establishment (56)5.3.3.1General (56)5.3.3.1a Conditions for establishing RRC Connection for sidelink communication/ discovery (58)5.3.3.2Initiation (59)5.3.3.3Actions related to transmission of RRCConnectionRequest message (63)5.3.3.3a Actions related to transmission of RRCConnectionResumeRequest message (64)5.3.3.4Reception of the RRCConnectionSetup by the UE (64)5.3.3.4a Reception of the RRCConnectionResume by the UE (66)5.3.3.5Cell re-selection while T300, T302, T303, T305, T306, or T308 is running (68)5.3.3.6T300 expiry (68)5.3.3.7T302, T303, T305, T306, or T308 expiry or stop (69)5.3.3.8Reception of the RRCConnectionReject by the UE (70)5.3.3.9Abortion of RRC connection establishment (71)5.3.3.10Handling of SSAC related parameters (71)5.3.3.11Access barring check (72)5.3.3.12EAB check (73)5.3.3.13Access barring check for ACDC (73)5.3.3.14Access Barring check for NB-IoT (74)5.3.4Initial security activation (75)5.3.4.1General (75)5.3.4.2Initiation (76)5.3.4.3Reception of the SecurityModeCommand by the UE (76)5.3.5RRC connection reconfiguration (77)5.3.5.1General (77)5.3.5.2Initiation (77)5.3.5.3Reception of an RRCConnectionReconfiguration not including the mobilityControlInfo by theUE (77)5.3.5.4Reception of an RRCConnectionReconfiguration including the mobilityControlInfo by the UE(handover) (79)5.3.5.5Reconfiguration failure (83)5.3.5.6T304 expiry (handover failure) (83)5.3.5.7Void (84)5.3.5.7a T307 expiry (SCG change failure) (84)5.3.5.8Radio Configuration involving full configuration option (84)5.3.6Counter check (86)5.3.6.1General (86)5.3.6.2Initiation (86)5.3.6.3Reception of the CounterCheck message by the UE (86)5.3.7RRC connection re-establishment (87)5.3.7.1General (87)5.3.7.2Initiation (87)5.3.7.3Actions following cell selection while T311 is running (88)5.3.7.4Actions related to transmission of RRCConnectionReestablishmentRequest message (89)5.3.7.5Reception of the RRCConnectionReestablishment by the UE (89)5.3.7.6T311 expiry (91)5.3.7.7T301 expiry or selected cell no longer suitable (91)5.3.7.8Reception of RRCConnectionReestablishmentReject by the UE (91)5.3.8RRC connection release (92)5.3.8.1General (92)5.3.8.2Initiation (92)5.3.8.3Reception of the RRCConnectionRelease by the UE (92)5.3.8.4T320 expiry (93)5.3.9RRC connection release requested by upper layers (93)5.3.9.1General (93)5.3.9.2Initiation (93)5.3.10Radio resource configuration (93)5.3.10.0General (93)5.3.10.1SRB addition/ modification (94)5.3.10.2DRB release (95)5.3.10.3DRB addition/ modification (95)5.3.10.3a1DC specific DRB addition or reconfiguration (96)5.3.10.3a2LWA specific DRB addition or reconfiguration (98)5.3.10.3a3LWIP specific DRB addition or reconfiguration (98)5.3.10.3a SCell release (99)5.3.10.3b SCell addition/ modification (99)5.3.10.3c PSCell addition or modification (99)5.3.10.4MAC main reconfiguration (99)5.3.10.5Semi-persistent scheduling reconfiguration (100)5.3.10.6Physical channel reconfiguration (100)5.3.10.7Radio Link Failure Timers and Constants reconfiguration (101)5.3.10.8Time domain measurement resource restriction for serving cell (101)5.3.10.9Other configuration (102)5.3.10.10SCG reconfiguration (103)5.3.10.11SCG dedicated resource configuration (104)5.3.10.12Reconfiguration SCG or split DRB by drb-ToAddModList (105)5.3.10.13Neighbour cell information reconfiguration (105)5.3.10.14Void (105)5.3.10.15Sidelink dedicated configuration (105)5.3.10.16T370 expiry (106)5.3.11Radio link failure related actions (107)5.3.11.1Detection of physical layer problems in RRC_CONNECTED (107)5.3.11.2Recovery of physical layer problems (107)5.3.11.3Detection of radio link failure (107)5.3.12UE actions upon leaving RRC_CONNECTED (109)5.3.13UE actions upon PUCCH/ SRS release request (110)5.3.14Proximity indication (110)5.3.14.1General (110)5.3.14.2Initiation (111)5.3.14.3Actions related to transmission of ProximityIndication message (111)5.3.15Void (111)5.4Inter-RAT mobility (111)5.4.1Introduction (111)5.4.2Handover to E-UTRA (112)5.4.2.1General (112)5.4.2.2Initiation (112)5.4.2.3Reception of the RRCConnectionReconfiguration by the UE (112)5.4.2.4Reconfiguration failure (114)5.4.2.5T304 expiry (handover to E-UTRA failure) (114)5.4.3Mobility from E-UTRA (114)5.4.3.1General (114)5.4.3.2Initiation (115)5.4.3.3Reception of the MobilityFromEUTRACommand by the UE (115)5.4.3.4Successful completion of the mobility from E-UTRA (116)5.4.3.5Mobility from E-UTRA failure (117)5.4.4Handover from E-UTRA preparation request (CDMA2000) (117)5.4.4.1General (117)5.4.4.2Initiation (118)5.4.4.3Reception of the HandoverFromEUTRAPreparationRequest by the UE (118)5.4.5UL handover preparation transfer (CDMA2000) (118)5.4.5.1General (118)5.4.5.2Initiation (118)5.4.5.3Actions related to transmission of the ULHandoverPreparationTransfer message (119)5.4.5.4Failure to deliver the ULHandoverPreparationTransfer message (119)5.4.6Inter-RAT cell change order to E-UTRAN (119)5.4.6.1General (119)5.4.6.2Initiation (119)5.4.6.3UE fails to complete an inter-RAT cell change order (119)5.5Measurements (120)5.5.1Introduction (120)5.5.2Measurement configuration (121)5.5.2.1General (121)5.5.2.2Measurement identity removal (122)5.5.2.2a Measurement identity autonomous removal (122)5.5.2.3Measurement identity addition/ modification (123)5.5.2.4Measurement object removal (124)5.5.2.5Measurement object addition/ modification (124)5.5.2.6Reporting configuration removal (126)5.5.2.7Reporting configuration addition/ modification (127)5.5.2.8Quantity configuration (127)5.5.2.9Measurement gap configuration (127)5.5.2.10Discovery signals measurement timing configuration (128)5.5.2.11RSSI measurement timing configuration (128)5.5.3Performing measurements (128)5.5.3.1General (128)5.5.3.2Layer 3 filtering (131)5.5.4Measurement report triggering (131)5.5.4.1General (131)5.5.4.2Event A1 (Serving becomes better than threshold) (135)5.5.4.3Event A2 (Serving becomes worse than threshold) (136)5.5.4.4Event A3 (Neighbour becomes offset better than PCell/ PSCell) (136)5.5.4.5Event A4 (Neighbour becomes better than threshold) (137)5.5.4.6Event A5 (PCell/ PSCell becomes worse than threshold1 and neighbour becomes better thanthreshold2) (138)5.5.4.6a Event A6 (Neighbour becomes offset better than SCell) (139)5.5.4.7Event B1 (Inter RAT neighbour becomes better than threshold) (139)5.5.4.8Event B2 (PCell becomes worse than threshold1 and inter RAT neighbour becomes better thanthreshold2) (140)5.5.4.9Event C1 (CSI-RS resource becomes better than threshold) (141)5.5.4.10Event C2 (CSI-RS resource becomes offset better than reference CSI-RS resource) (141)5.5.4.11Event W1 (WLAN becomes better than a threshold) (142)5.5.4.12Event W2 (All WLAN inside WLAN mobility set becomes worse than threshold1 and a WLANoutside WLAN mobility set becomes better than threshold2) (142)5.5.4.13Event W3 (All WLAN inside WLAN mobility set becomes worse than a threshold) (143)5.5.5Measurement reporting (144)5.5.6Measurement related actions (148)5.5.6.1Actions upon handover and re-establishment (148)5.5.6.2Speed dependant scaling of measurement related parameters (149)5.5.7Inter-frequency RSTD measurement indication (149)5.5.7.1General (149)5.5.7.2Initiation (150)5.5.7.3Actions related to transmission of InterFreqRSTDMeasurementIndication message (150)5.6Other (150)5.6.0General (150)5.6.1DL information transfer (151)5.6.1.1General (151)5.6.1.2Initiation (151)5.6.1.3Reception of the DLInformationTransfer by the UE (151)5.6.2UL information transfer (151)5.6.2.1General (151)5.6.2.2Initiation (151)5.6.2.3Actions related to transmission of ULInformationTransfer message (152)5.6.2.4Failure to deliver ULInformationTransfer message (152)5.6.3UE capability transfer (152)5.6.3.1General (152)5.6.3.2Initiation (153)5.6.3.3Reception of the UECapabilityEnquiry by the UE (153)5.6.4CSFB to 1x Parameter transfer (157)5.6.4.1General (157)5.6.4.2Initiation (157)5.6.4.3Actions related to transmission of CSFBParametersRequestCDMA2000 message (157)5.6.4.4Reception of the CSFBParametersResponseCDMA2000 message (157)5.6.5UE Information (158)5.6.5.1General (158)5.6.5.2Initiation (158)5.6.5.3Reception of the UEInformationRequest message (158)5.6.6 Logged Measurement Configuration (159)5.6.6.1General (159)5.6.6.2Initiation (160)5.6.6.3Reception of the LoggedMeasurementConfiguration by the UE (160)5.6.6.4T330 expiry (160)5.6.7 Release of Logged Measurement Configuration (160)5.6.7.1General (160)5.6.7.2Initiation (160)5.6.8 Measurements logging (161)5.6.8.1General (161)5.6.8.2Initiation (161)5.6.9In-device coexistence indication (163)5.6.9.1General (163)5.6.9.2Initiation (164)5.6.9.3Actions related to transmission of InDeviceCoexIndication message (164)5.6.10UE Assistance Information (165)5.6.10.1General (165)5.6.10.2Initiation (166)5.6.10.3Actions related to transmission of UEAssistanceInformation message (166)5.6.11 Mobility history information (166)5.6.11.1General (166)5.6.11.2Initiation (166)5.6.12RAN-assisted WLAN interworking (167)5.6.12.1General (167)5.6.12.2Dedicated WLAN offload configuration (167)5.6.12.3WLAN offload RAN evaluation (167)5.6.12.4T350 expiry or stop (167)5.6.12.5Cell selection/ re-selection while T350 is running (168)5.6.13SCG failure information (168)5.6.13.1General (168)5.6.13.2Initiation (168)5.6.13.3Actions related to transmission of SCGFailureInformation message (168)5.6.14LTE-WLAN Aggregation (169)5.6.14.1Introduction (169)5.6.14.2Reception of LWA configuration (169)5.6.14.3Release of LWA configuration (170)5.6.15WLAN connection management (170)5.6.15.1Introduction (170)5.6.15.2WLAN connection status reporting (170)5.6.15.2.1General (170)5.6.15.2.2Initiation (171)5.6.15.2.3Actions related to transmission of WLANConnectionStatusReport message (171)5.6.15.3T351 Expiry (WLAN connection attempt timeout) (171)5.6.15.4WLAN status monitoring (171)5.6.16RAN controlled LTE-WLAN interworking (172)5.6.16.1General (172)5.6.16.2WLAN traffic steering command (172)5.6.17LTE-WLAN aggregation with IPsec tunnel (173)5.6.17.1General (173)5.7Generic error handling (174)5.7.1General (174)5.7.2ASN.1 violation or encoding error (174)5.7.3Field set to a not comprehended value (174)5.7.4Mandatory field missing (174)5.7.5Not comprehended field (176)5.8MBMS (176)5.8.1Introduction (176)5.8.1.1General (176)5.8.1.2Scheduling (176)5.8.1.3MCCH information validity and notification of changes (176)5.8.2MCCH information acquisition (178)5.8.2.1General (178)5.8.2.2Initiation (178)5.8.2.3MCCH information acquisition by the UE (178)5.8.2.4Actions upon reception of the MBSFNAreaConfiguration message (178)5.8.2.5Actions upon reception of the MBMSCountingRequest message (179)5.8.3MBMS PTM radio bearer configuration (179)5.8.3.1General (179)5.8.3.2Initiation (179)5.8.3.3MRB establishment (179)5.8.3.4MRB release (179)5.8.4MBMS Counting Procedure (179)5.8.4.1General (179)5.8.4.2Initiation (180)5.8.4.3Reception of the MBMSCountingRequest message by the UE (180)5.8.5MBMS interest indication (181)5.8.5.1General (181)5.8.5.2Initiation (181)5.8.5.3Determine MBMS frequencies of interest (182)5.8.5.4Actions related to transmission of MBMSInterestIndication message (183)5.8a SC-PTM (183)5.8a.1Introduction (183)5.8a.1.1General (183)5.8a.1.2SC-MCCH scheduling (183)5.8a.1.3SC-MCCH information validity and notification of changes (183)5.8a.1.4Procedures (184)5.8a.2SC-MCCH information acquisition (184)5.8a.2.1General (184)5.8a.2.2Initiation (184)5.8a.2.3SC-MCCH information acquisition by the UE (184)5.8a.2.4Actions upon reception of the SCPTMConfiguration message (185)5.8a.3SC-PTM radio bearer configuration (185)5.8a.3.1General (185)5.8a.3.2Initiation (185)5.8a.3.3SC-MRB establishment (185)5.8a.3.4SC-MRB release (185)5.9RN procedures (186)5.9.1RN reconfiguration (186)5.9.1.1General (186)5.9.1.2Initiation (186)5.9.1.3Reception of the RNReconfiguration by the RN (186)5.10Sidelink (186)5.10.1Introduction (186)5.10.1a Conditions for sidelink communication operation (187)5.10.2Sidelink UE information (188)5.10.2.1General (188)5.10.2.2Initiation (189)5.10.2.3Actions related to transmission of SidelinkUEInformation message (193)5.10.3Sidelink communication monitoring (195)5.10.6Sidelink discovery announcement (198)5.10.6a Sidelink discovery announcement pool selection (201)5.10.6b Sidelink discovery announcement reference carrier selection (201)5.10.7Sidelink synchronisation information transmission (202)5.10.7.1General (202)5.10.7.2Initiation (203)5.10.7.3Transmission of SLSS (204)5.10.7.4Transmission of MasterInformationBlock-SL message (205)5.10.7.5Void (206)5.10.8Sidelink synchronisation reference (206)5.10.8.1General (206)5.10.8.2Selection and reselection of synchronisation reference UE (SyncRef UE) (206)5.10.9Sidelink common control information (207)5.10.9.1General (207)5.10.9.2Actions related to reception of MasterInformationBlock-SL message (207)5.10.10Sidelink relay UE operation (207)5.10.10.1General (207)5.10.10.2AS-conditions for relay related sidelink communication transmission by sidelink relay UE (207)5.10.10.3AS-conditions for relay PS related sidelink discovery transmission by sidelink relay UE (208)5.10.10.4Sidelink relay UE threshold conditions (208)5.10.11Sidelink remote UE operation (208)5.10.11.1General (208)5.10.11.2AS-conditions for relay related sidelink communication transmission by sidelink remote UE (208)5.10.11.3AS-conditions for relay PS related sidelink discovery transmission by sidelink remote UE (209)5.10.11.4Selection and reselection of sidelink relay UE (209)5.10.11.5Sidelink remote UE threshold conditions (210)6Protocol data units, formats and parameters (tabular & ASN.1) (210)6.1General (210)6.2RRC messages (212)6.2.1General message structure (212)–EUTRA-RRC-Definitions (212)–BCCH-BCH-Message (212)–BCCH-DL-SCH-Message (212)–BCCH-DL-SCH-Message-BR (213)–MCCH-Message (213)–PCCH-Message (213)–DL-CCCH-Message (214)–DL-DCCH-Message (214)–UL-CCCH-Message (214)–UL-DCCH-Message (215)–SC-MCCH-Message (215)6.2.2Message definitions (216)–CounterCheck (216)–CounterCheckResponse (217)–CSFBParametersRequestCDMA2000 (217)–CSFBParametersResponseCDMA2000 (218)–DLInformationTransfer (218)–HandoverFromEUTRAPreparationRequest (CDMA2000) (219)–InDeviceCoexIndication (220)–InterFreqRSTDMeasurementIndication (222)–LoggedMeasurementConfiguration (223)–MasterInformationBlock (225)–MBMSCountingRequest (226)–MBMSCountingResponse (226)–MBMSInterestIndication (227)–MBSFNAreaConfiguration (228)–MeasurementReport (228)–MobilityFromEUTRACommand (229)–Paging (232)–ProximityIndication (233)–RNReconfiguration (234)–RNReconfigurationComplete (234)–RRCConnectionReconfiguration (235)–RRCConnectionReconfigurationComplete (240)–RRCConnectionReestablishment (241)–RRCConnectionReestablishmentComplete (241)–RRCConnectionReestablishmentReject (242)–RRCConnectionReestablishmentRequest (243)–RRCConnectionReject (243)–RRCConnectionRelease (244)–RRCConnectionResume (248)–RRCConnectionResumeComplete (249)–RRCConnectionResumeRequest (250)–RRCConnectionRequest (250)–RRCConnectionSetup (251)–RRCConnectionSetupComplete (252)–SCGFailureInformation (253)–SCPTMConfiguration (254)–SecurityModeCommand (255)–SecurityModeComplete (255)–SecurityModeFailure (256)–SidelinkUEInformation (256)–SystemInformation (258)–SystemInformationBlockType1 (259)–UEAssistanceInformation (264)–UECapabilityEnquiry (265)–UECapabilityInformation (266)–UEInformationRequest (267)–UEInformationResponse (267)–ULHandoverPreparationTransfer (CDMA2000) (273)–ULInformationTransfer (274)–WLANConnectionStatusReport (274)6.3RRC information elements (275)6.3.1System information blocks (275)–SystemInformationBlockType2 (275)–SystemInformationBlockType3 (279)–SystemInformationBlockType4 (282)–SystemInformationBlockType5 (283)–SystemInformationBlockType6 (287)–SystemInformationBlockType7 (289)–SystemInformationBlockType8 (290)–SystemInformationBlockType9 (295)–SystemInformationBlockType10 (295)–SystemInformationBlockType11 (296)–SystemInformationBlockType12 (297)–SystemInformationBlockType13 (297)–SystemInformationBlockType14 (298)–SystemInformationBlockType15 (298)–SystemInformationBlockType16 (299)–SystemInformationBlockType17 (300)–SystemInformationBlockType18 (301)–SystemInformationBlockType19 (301)–SystemInformationBlockType20 (304)6.3.2Radio resource control information elements (304)–AntennaInfo (304)–AntennaInfoUL (306)–CQI-ReportConfig (307)–CQI-ReportPeriodicProcExtId (314)–CrossCarrierSchedulingConfig (314)–CSI-IM-Config (315)–CSI-IM-ConfigId (315)–CSI-RS-Config (317)–CSI-RS-ConfigEMIMO (318)–CSI-RS-ConfigNZP (319)–CSI-RS-ConfigNZPId (320)–CSI-RS-ConfigZP (321)–CSI-RS-ConfigZPId (321)–DMRS-Config (321)–DRB-Identity (322)–EPDCCH-Config (322)–EIMTA-MainConfig (324)–LogicalChannelConfig (325)–LWA-Configuration (326)–LWIP-Configuration (326)–RCLWI-Configuration (327)–MAC-MainConfig (327)–P-C-AndCBSR (332)–PDCCH-ConfigSCell (333)–PDCP-Config (334)–PDSCH-Config (337)–PDSCH-RE-MappingQCL-ConfigId (339)–PHICH-Config (339)–PhysicalConfigDedicated (339)–P-Max (344)–PRACH-Config (344)–PresenceAntennaPort1 (346)–PUCCH-Config (347)–PUSCH-Config (351)–RACH-ConfigCommon (355)–RACH-ConfigDedicated (357)–RadioResourceConfigCommon (358)–RadioResourceConfigDedicated (362)–RLC-Config (367)–RLF-TimersAndConstants (369)–RN-SubframeConfig (370)–SchedulingRequestConfig (371)–SoundingRS-UL-Config (372)–SPS-Config (375)–TDD-Config (376)–TimeAlignmentTimer (377)–TPC-PDCCH-Config (377)–TunnelConfigLWIP (378)–UplinkPowerControl (379)–WLAN-Id-List (382)–WLAN-MobilityConfig (382)6.3.3Security control information elements (382)–NextHopChainingCount (382)–SecurityAlgorithmConfig (383)–ShortMAC-I (383)6.3.4Mobility control information elements (383)–AdditionalSpectrumEmission (383)–ARFCN-ValueCDMA2000 (383)–ARFCN-ValueEUTRA (384)–ARFCN-ValueGERAN (384)–ARFCN-ValueUTRA (384)–BandclassCDMA2000 (384)–BandIndicatorGERAN (385)–CarrierFreqCDMA2000 (385)–CarrierFreqGERAN (385)–CellIndexList (387)–CellReselectionPriority (387)–CellSelectionInfoCE (387)–CellReselectionSubPriority (388)–CSFB-RegistrationParam1XRTT (388)–CellGlobalIdEUTRA (389)–CellGlobalIdUTRA (389)–CellGlobalIdGERAN (390)–CellGlobalIdCDMA2000 (390)–CellSelectionInfoNFreq (391)–CSG-Identity (391)–FreqBandIndicator (391)–MobilityControlInfo (391)–MobilityParametersCDMA2000 (1xRTT) (393)–MobilityStateParameters (394)–MultiBandInfoList (394)–NS-PmaxList (394)–PhysCellId (395)–PhysCellIdRange (395)–PhysCellIdRangeUTRA-FDDList (395)–PhysCellIdCDMA2000 (396)–PhysCellIdGERAN (396)–PhysCellIdUTRA-FDD (396)–PhysCellIdUTRA-TDD (396)–PLMN-Identity (397)–PLMN-IdentityList3 (397)–PreRegistrationInfoHRPD (397)–Q-QualMin (398)–Q-RxLevMin (398)–Q-OffsetRange (398)–Q-OffsetRangeInterRAT (399)–ReselectionThreshold (399)–ReselectionThresholdQ (399)–SCellIndex (399)–ServCellIndex (400)–SpeedStateScaleFactors (400)–SystemInfoListGERAN (400)–SystemTimeInfoCDMA2000 (401)–TrackingAreaCode (401)–T-Reselection (402)–T-ReselectionEUTRA-CE (402)6.3.5Measurement information elements (402)–AllowedMeasBandwidth (402)–CSI-RSRP-Range (402)–Hysteresis (402)–LocationInfo (403)–MBSFN-RSRQ-Range (403)–MeasConfig (404)–MeasDS-Config (405)–MeasGapConfig (406)–MeasId (407)–MeasIdToAddModList (407)–MeasObjectCDMA2000 (408)–MeasObjectEUTRA (408)–MeasObjectGERAN (412)–MeasObjectId (412)–MeasObjectToAddModList (412)–MeasObjectUTRA (413)–ReportConfigEUTRA (422)–ReportConfigId (425)–ReportConfigInterRAT (425)–ReportConfigToAddModList (428)–ReportInterval (429)–RSRP-Range (429)–RSRQ-Range (430)–RSRQ-Type (430)–RS-SINR-Range (430)–RSSI-Range-r13 (431)–TimeToTrigger (431)–UL-DelayConfig (431)–WLAN-CarrierInfo (431)–WLAN-RSSI-Range (432)–WLAN-Status (432)6.3.6Other information elements (433)–AbsoluteTimeInfo (433)–AreaConfiguration (433)–C-RNTI (433)–DedicatedInfoCDMA2000 (434)–DedicatedInfoNAS (434)–FilterCoefficient (434)–LoggingDuration (434)–LoggingInterval (435)–MeasSubframePattern (435)–MMEC (435)–NeighCellConfig (435)–OtherConfig (436)–RAND-CDMA2000 (1xRTT) (437)–RAT-Type (437)–ResumeIdentity (437)–RRC-TransactionIdentifier (438)–S-TMSI (438)–TraceReference (438)–UE-CapabilityRAT-ContainerList (438)–UE-EUTRA-Capability (439)–UE-RadioPagingInfo (469)–UE-TimersAndConstants (469)–VisitedCellInfoList (470)–WLAN-OffloadConfig (470)6.3.7MBMS information elements (472)–MBMS-NotificationConfig (472)–MBMS-ServiceList (473)–MBSFN-AreaId (473)–MBSFN-AreaInfoList (473)–MBSFN-SubframeConfig (474)–PMCH-InfoList (475)6.3.7a SC-PTM information elements (476)–SC-MTCH-InfoList (476)–SCPTM-NeighbourCellList (478)6.3.8Sidelink information elements (478)–SL-CommConfig (478)–SL-CommResourcePool (479)–SL-CP-Len (480)–SL-DiscConfig (481)–SL-DiscResourcePool (483)–SL-DiscTxPowerInfo (485)–SL-GapConfig (485)。

Multiscale simulation of phonon transport in superlattices P.K.Schelling a)Materials Science Division,Argonne National Laboratory,Argonne,Illinois60439and Institutefor Nanotechnology,Forschungszentrum Karlsruhe,76021Karlsruhe,GermanyS.R.PhillpotMaterials Science Division,Argonne National Laboratory,Argonne,Illinois60439͑Received3June2002;accepted28January2003͒A particle-based model for phonon transport and the scattering of phonon wave packets at interfacesis developed.The model,which incorporates the interference effects associated with the wave nature of phonons,is parametrized with frequency-dependent scattering rates obtained from molecular-dynamics simulations of the interaction of phonon wave packets with a single interface.From simulations of scattering of phonon wave packets from superlattices,wefind that when the interference effects are not included there is qualitative disagreement between the molecular-dynamics and particle simulations.Moreover,we show that such interference effects tend to result in a larger amount of energy being transmitted through a superlattice.©2003American Institute of Physics.͓DOI:10.1063/1.1561601͔I.INTRODUCTIONRecent experiments have shown that semiconductor su-perlattices exhibit very low thermal conductivities1–3open-ing up potential applications for semiconductor superlatticesin thermoelectric devices,where very low lattice thermalconductivity is required to achieve high efficiency.1A de-tailed theoretical understanding of the thermal-transportproperties of semiconductor superlattices is,thus,highly de-sirable.There are three important length scales involved in ther-mal transport in superlattices:the phonon wavelength␭,thephonon mean free path l,and the superlattice layer thicknessL.The mean free path l can vary as a result of changes insystem temperature or the presence of defects and impurities.The standard approach to transport theory,which uses a par-ticle picture with the particles representing wave packets,4requires another length scale␰that is defined to be the spatial extent of a wave packet.There are several constraints onthese length scales.First,to correctly describe propagation ofa wave packet with a dominant wavelength␭,we must have ␰Ͼ␭.Second,in order for a phonon to move in a coherent manner in between scattering events,we only need considerthe regime where lϾ␭.Finally,for a wave packet descrip-tion of transport to apply,we also require that lϾ␰.All of these considerations taken together result in the requirement that lϾ␰Ͼ␭.The presence of a superlattice structure results in twodistinct regimes:lϾL and lϽL.In the regime where lϽL,aphonon that has scattered from an interface typically scattersoff another phonon before encountering another interface.With the considerations of the previous paragraph,we there-fore require the wave packets to be defined by␰ϽL.Since a wave packet with␰ϽL is confined within a single layer of the superlattice,its properties are described by the bulk prop-erties of the layers.4,5In the other limit,lϾL,a phonon wave packet typically does not undergo a collision between scat-tering events at neighboring interfaces.In this regime,inter-ference effects are known to be important,and it is usually thought that the correct description of wave packet propaga-tion requires that we choose␰ϾL.In this limit,wave pack-ets propagate in a manner determined by the phonon spec-trum of the superlattice,and not the phonon spectrum of the bulk superlattice layers.6We are thus led to the conclusion that the existing approaches to treating different phonon dy-namics in superlattices apply only in two essentially non-overlapping regimes.In this article,we will show that it is possible to con-struct a particle model that incorporates key wave aspects, resulting in a wider range of applicability than existing ap-proaches.In our interfering particle model͑IPM͒,we use wave packets with␰ϽL,and therefore we can describe the regime where lϽL.However,because we include interfer-ence effects not usually included in particle models of this type,we can also describe the regime lϾL.We therefore find that our IPM is valid over the entire range of wave-lengths and mean free paths,with the exception of modes with␭ϾL,in which a full wave picture is still necessary.We will prove the viability of this particle-based method under the conditions in which the conventional particle picture fails most spectacularly;namely when the mean free path is infi-nite.Our IPM allows us to examine the phonon dynamics of superlattices containing rather large numbers of layers.In particular we identify the very important role played by the coherent wave-like interference at the interfaces that is omit-ted in the conventional particle picture.The rest of the article is organized as follows.In the next section we describe the IPM and show how it may be param-etrized from the results of molecular dynamics͑MD͒simu-lations.In Sec.III,using short-period superlattices as a prov-ing ground,we demonstrate quantitative agreement in the phonon transport properties calculated from MD and thea͒Electronic mail:schelling@JOURNAL OF APPLIED PHYSICS VOLUME93,NUMBER91MAY200353770021-8979/2003/93(9)/5377/11/$20.00©2003American Institute of PhysicsIPM.Moreover,we use the IPM to show that,due to inter-ference effects,the transmission coefficient through superlat-tices is almost independent of the number of superlattice layers.In Sec.IV we address the effect of varying the spatial extent of a wave packet.There,using the results of MD simulation and analytical calculations of a model one-dimensional lattice,we will see that the transmission minima and maxima seen in experiment for a superlattice depend strongly on the degree of localization of the incidence pho-non wave packet.As a result,we show here that the IPM canonly correctly describe transport under the assumption that the wave packets themselves are spatially localized within one layer of the superlattice structure.In Sec.V,we show that in a superlattice made from layers of various thick-nesses,interference effects are diminished.Finally,we con-clude with an analysis of the importance of these results to our understanding of thermal transport in superlattice struc-tures and an outline of possible further developments of the IPM.II.DESCRIPTION AND PARAMETRIZATIONOF THE IPMThe use of particle-based methods to describe transport problems is well established,including their use in describ-ing thermal transport,in which the particles represent pho-non wave packets.4The advantage of these methods lies in their ability to describe very large systems for long simula-tion times,with the results being understandable in an intui-tive way.There are two key features to particle-based mod-els.First,it is necessary to define rules by which the particles interact with each other and with the microstructure.The physical processes that are described by these rules includ-ing,e.g.,phonon–phonon interactions,phonon–point-defect interactions,and phonon–interface interactions,are typically incorporated in the form of scattering rates.The second key input is the materials parameters,which include the phonon group velocity.4,5The key to a successful model is the defi-nition of rules that most closely reproduce the true physics of the system͑under the constraint of maintaining computa-tional efficiency͒and the use of realistic values for the key parameters.A fundamental assumption of previous particle models for phonons has been that the particles͑i.e.,phonons͒do not interfere with each other;thus the wave nature of phonon transport is neglected.4,5In this section,we describe how wave effects can be incorporated into a particle model in a natural and intuitively appealing way.In addition,we show how MD simulations of the interactions of phonon wave packets with interfaces can provide parameters and physical insights to the particle model.As a nontrivial but tractable model system,we consider a coherent interface created by joining materials A and B, each having perfect͗001͘-oriented diamond lattices differing only in their atomic masses,as shown in Fig.1.We define material A to be Si with a mass M AϭM Si ͑28.09amu͒.The atoms in material B have mass M B ϭ4M Si.For our MD simulations,we use the Stillinger–Weber͑SW͒model for silicon to describe all of the interactions.7For a particle model of phonon transport,wefirst need a description of how a particle propagates.Because the par-ticles represent phonon wave packets,the particle velocity should be equal to the group velocity of the corresponding phonon wave packet.Therefore,to describe particle propa-gation in materials A and B,we use results for the group velocity that are obtained from the bulk phonon dispersion curves for SW Si.In Fig.2we show the phonon frequencies and phonon group velocities for wave vectors directedalong FIG.1.Schematic of the system studied with MD to provide transmission coefficients for single-interface scattering results.For material A,the mass of an atom is M AϭM Si͑28.09amu͒;for material B,atoms have mass M B ϭ4M Si.FIG.2.Results of lattice-dynamic calculations for phonons with wave vec-tors along a͓001͔direction for Stillinger–Weber silicon:͑a͒frequency vs wave vector and͑b͒group velocity vs wave vector.These results correspond to a phonon in material A͑see Fig.1͒.For a phonon in material B,the frequencies and group velocities are reduced by a factor of2.͓001͔in the diamond lattice.In the following analyses,we will consider particles that correspond to wave packets in the longitudinal acoustic͑LA͒,longitudinal optical͑LO͒,and transverse acoustic͑TA͒branches of the spectrum.We do not consider transverse optical͑TO͒modes here because these modes are completely reflected from the interface considered here.8We treat particle propagation in the IPM in the following way.We assign to a particle,m,an amplitude A m,wave-vector k m,and phonon branch␭m.We determine the par-ticle frequency␯m from the phonon dispersions curves for the appropriate wave vector and branch͓Fig.2͑a͔͒.If the particle m propagates in material A͑see Fig.1͒,it will have velocity v A(k m,␭m),given by the group velocities for the SW model shown in Fig.2͑b͒.If it propagates in material B, its velocity is given by v B(k m,␭m).Because the mass of the atoms in material B is four times that of the atoms in material A,for a given phonon branch␭m and wave vector k m,the group velocities are related by v B(k m,␭m)ϭv A(k m,␭m)/2.The particle velocities thus obtained de-scribe how particles move through the crystals between in-terfacial scattering events.The key difference between our model and the standard Boltzman transport equation͑BTE͒approaches is in the treatment of the particle dynamics in terms of the particle amplitude as opposed to the particle energy.When particle m of amplitude A m and frequency␯m encounters an interface, we remove the incident particle and create in its place two particles representing the transmitted and reflected wave packets.We assume that the frequencies of the transmitted and reflected particles are equal to the frequency␯m of the incident particle,i.e.,the scattering process is purely elastic. Using the phonon dispersions for the SW model of Si,this permits us to assign k vectors and group velocities to the transmitted and reflected particles.The amplitudes of the transmitted and reflected particles are given in terms of the fraction of energy transmitted through the interface␣(␯m) and the amplitude A m of the incident particle.The amplitude of the transmitted particle is͓␣(␯m)͔1/2A m.If particle m in material B is incident on an interface with material A,the amplitude of the reflected particle is͓1Ϫ␣(␯m)͔1/2A m. However,when a particle in material A is reflected from an interface with material B,we must also include the180°phase shift that occurs;in this case,the amplitude of the reflected particle is equal toϪ͓1Ϫ␣(␯m)͔1/2A m.The energy of the particles is proportional to the square of their ampli-tude,assuring that␣(␯m)represents the fraction of transmit-ted energy.Our previous letter8demonstrated the importance of polarization for TA scattering;hence,in the case of inci-dent particles that represent TA wave packets,we assign a polarization to the particle and use the value␣(␯m)that cor-responds to the chosen polarization.The characterization of the particles in terms of their amplitude also allows us to define rules for particle–particle interactions.When two particles corresponding to the same phonon branch␭and of the same wave vector k arrive at the same point in space at the same time,we consider a collision to have occurred.In practice,we consider a collision to have occurred when the two particles are closer than their wave-length;our results were found to be essentially independent of the precise choice of this distance.Whenever a collision occurs,we remove the two colliding particles and replace them with a new particle whose amplitude is equal to the sum of the amplitudes of the colliding particles.If the two particles have the same phase,the interference is construc-tive;if they have opposite phases,the interference is destruc-tive.To parametrize interfacial scattering events within the IPM,we use our previous MD results6for wave-packet scat-tering at the interface shown in Fig.1.The wave packets themselves are created from linear combinations of the vi-brational normal modes of the SW perfect crystal according tou in␮ϭA␧i␮␭͑k0͒exp͓ik0͑z nϪz0͔͒exp͓Ϫ͑z nϪz0͒2/␰2͔.͑1͒Here u in␮is the␮th component of the displacement for atom i in the unit cell labeled by n.The phonon branch is labeled by␭.The wave packet has amplitude A and polarization ␧i␮␭(k0);z n is the z coordinate of the unit cell n.Equation ͑1͒generates a Gaussian wave packet centered in real spacearound z0of infinite extent in the x and y directions.To generate the initial velocities of the atoms,wefind the normal-mode components required for the displacements given by Eq.͑1͒.We then add time-dependence to these normal modes in the usual manner,and then differentiate with respect to time to obtain the initial velocities.By allowing the wave packet to propagate and scatter from the interface we can compute the amount of energy that is transmitted and reflected.In Fig.3we show the results from our previous paper6for the energy transmission coeffi-cient␣(␯)of LA wave packets incident at the interface shown in Fig.1as a function of the mean frequency␯of the phonons in the packet.The situation is more complicated for incident TA wave packets because the polarization of the incident wave is also important.8The results shown in Fig.4 FIG.3.Energy-transmission coefficient␣(␯)vs phonon frequency␯,ob-tained by MD simulation for LA modes at the interface shown in Fig.1.for the maximum,minimum,and average values of ␣(␯)for incident TA wave packets were obtained by varying the po-larization of the incident wave.8Since we can parametrize the IPM using MD results as described above,it should be an exact description of wave-packet propagation and scattering in the system shown in Fig.1.In principle,the IPM can now be applied to more complex systems with multiple interfaces.In the next sec-tion,by comparing results of the IPM to MD results,we show that our particle model very accurately describes super-lattice phonon transport as long as the wavelength of the phonons that make up the wave packet is less than the su-perlattice spacing.In addition,we demonstrate that the inclu-sion of interference effects within the particle model is es-sential to obtaining correct results.III.PHONON TRANSPORT THROUGH SUPERLATTICESIn this section we analyze in detail phonon transport through ͓001͔-oriented superlattices with various numbers of layers using the MD simulation and the IPM.We first verify that the IPM can quantitatively reproduce the results of MD simulations for superlattices containing only a few layers.We then use the IPM to investigate phonon transport in su-perlattices with large numbers of layers,a regime not ame-nable to even large-scale parallel MD simulations.We consider superlattice structures like the one shown in Fig.5,in which the N layers of the superlattice,alternating between materials A and B,are sandwiched between thick layers of A and B on the left and right,respectively.The properties of material A and material B are the same as in the previous section,so that each interface in the superlattice is identical to the single interface used in the last section to parametrize the IPM.To verify the correctness of the IPM,we begin by com-paring with MD results of energy transmission through su-perlattices containing N ϭ2and N ϭ4layers.For the MD wave-packet simulations,the ͗001͘-oriented simulation cell is chosen to be 2000unit cells long in the z direction ͑i.e.,1086nm for the Si lattice parameter a 0ϭ0.543nm),and 2ϫ2unit cells in the transverse directions.Each layer of the superlattice is 50unit cells ͑27.15nm ͒thick.We first studied a long wavelength LA wave packet of the form given by Eq.͑1͒.We chose a wave vector in mate-rial A of k 0ϭ0.05(2␲/a 0)which corresponds to a frequency of 0.73THz;the value of ␰2was chosen to be 250a 02,result-ing in wave packets with a width of ϳ30unit cells,i.e.,spatially localized within one layer of the superlattice.The contribution of the different k values to create this wave packet is shown in Fig.6.Shown in the inset to Fig.6are the corresponding atomic displacements as a function of the z coordinate of the atoms;because this is an LA phonon,all of these displacements lie along the z axis.According to the results shown in Fig.3,this wave packet has an energy trans-mission coefficient of 0.88800.In Fig.7we show two snapshots (t ϭ0and t ϭ53ps)from an MD simulation of the N ϭ4superlattice.The super-lattice itself is located between z ϭ0and z ϭ200a 0,with interfaces at every 50a 0.Whenever a wave packetencoun-FIG.4.Energy-transmission coefficient ␣(␯)vs phonon frequency ␯,ob-tained by MD simulation,for TA modes at the interface shown in Fig.1.Since the results are polarization dependent,we show the maximum ͑squares ͒,minimum ͑triangles ͒,and average ͑circles ͒values of ␣.FIG.5.Schematic of superlattice.Atoms in layers labeled A have mass M A ,while atoms in layers labeled B have mass M B .The particular case shown here is for N ϭ10layers.FIG.6.Contribution of different k values required to generate an LA wave packet with k 0ϭ0.05(2␲/a 0)and ␰2ϭ0.004/a 02͓see Eq.͑1͔͒.Inset:Atomic displacements of the resulting wave packet.The atomic displacements are generated from Eq.͑1͒and are used in an MD simulation to study scattering from a superlattice.ters an interface it is scattered into a transmitted and reflected wave packet,each of lower amplitude than the incident wave packet.Ultimately,the reflected and transmitted wave pack-ets emerge from the superlattice structure.Shown in Tables I and II are the times at which the center of the transmitted wave packet is coincident with the last interface (z ϭ100for N ϭ2and z ϭ200for N ϭ4).Here,we take t ϭ0to be the time that the center of the incident wave packet is locateddirectly at the first interface at z ϭ0.All times are given in terms of t 0ϭt A ϩt B ,which is defined to be the total time required for a wave packet to pass through a layer of material A (t A )and a layer of material B (t B ).Since the atoms in material A have one-fourth the mass of the atoms in material B,the group velocity of a phonon in material B should be approximately one-half that in material A.From the phonon group velocities shown in Fig.2,we find that the ratio of the wave packet velocities for this frequency is actually v B /v A ϭ0.498,where the small deviation from 0.5arises from the fact that the wave vectors excited in materials A and B are different and the LA phonon branch exhibits some dispersion ͑see Fig.2͒.By computing the group velocity for the wave packets used here,we have determined that t 0ϭ10.13ps.Also shown in Tables I and II is the amount of energy con-tained in each of these transmitted pulses.We have carried out IPM simulations for the same N ϭ2and N ϭ4superlattices.We define the incident particle as the LA wave packet with k 0ϭ0.05(2␲/a 0)used for the above MD simulations.For the transmission coefficient at a single interface,we use the value ␣ϭ0.88800obtained from Fig.3.The calculated energy content of each of the four first transmitted pulses are also shown in Tables I and II for both the MD and IPM models.There is near exact agreement in the amount of energy contained in each transmitted pulse.Moreover,the total fraction of incident energy transmitted in these first four pulses is 0.7250͑MD ͒versus 0.7248͑IPM ͒for N ϭ2,and 0.6499͑MD ͒versus 0.6502͑IPM ͒for N ϭ4,again showing excellent agreement.The agreement shown in Tables I and II depends criti-cally on the interference of different particle trajectories be-ing treated correctly.To demonstrate this,we also show in Tables I and II the results obtained using the same particle model,except that particle collisions and hence wave-interference effects are not included.For N ϭ2,the first two emitted wave packets contain the same amount of energy in both the noninterfering and the interfering models,while the third and fourth wave packets do not.The basic idea is that if all of the energy emitted at a particular time arises from a single unique trajectory through the superlattice,then there will be no interference effects.To illustrate this,consider the particle trajectories that contribute to these four peaks.To describe the different trajectories,A will represent a particle propagating in the forward direction through a layer of ma-terial A.Likewise,B will represent a particle propagating in the forward direction through a layer of material B.To de-scribe paths that include reflections,let A¯͑B ¯͒denote a par-ticle propagating in material A ͑B ͒in the backward direction.Thus,for an N ϭ2superlattice,the wave packet emergingatFIG.7.Atomic displacements determined by MD at ͑a ͒t ϭ0and ͑b ͒t ϭ53ps for the N ϭ4superlattice.As the initial wave packet is scattered from the interfaces,many wave packets with smaller amplitude are created.TABLE I.Fraction of incident energy (E /E 0)transmitted through an N ϭ2superlattice in the first four wave packets.The times at which these packets emerge are given in terms of t 0,which is the time required to pass through a layer of material A and a layer of material B.Wave packet Time ͓t 0͔E /E 0MD E /E 0particles with interferenceE /E 0particles without interference1 1.000.700150.700230.700232 1.670.008800.008780.008783 2.330.010830.010860.0088943.000.005050.005120.00704TABLE II.Same as Table I but for the N ϭ4superlattice.Wave packet Time ͓t 0͔E /E 0MD E /E 0particles with interferenceE /E 0particles without interference1 2.000.552060.552160.552162 2.670.027700.027710.013853 3.330.037660.037800.0139444.000.032510.032500.01665tϭ1.00has been transmitted through the superlattice without reflection,and we represent this trajectory by BϪA.We note that in this case,the energy of the transmitted wave packet will be equal to␣3due to the fact that the wave packet hasbeen transmitted through three interfaces.For the wave packet emerging at tϭ1.67,there is also only one corre-sponding trajectory denoted by BϪAϪA¯ϪA,with the en-ergy of the wave packet in this case equal to␣3(1Ϫ␣)2.Forthe packets emerging at tϭ2.33and tϭ3.0,there are mul-tiple trajectories resulting in the same transmission time,and hence we see from Table I that the results from the IPM differ from the results obtained when interference effects are neglected.For example,the wave packet emerging at t ϭ2.33results from paths denoted by BϪB¯ϪBϪA and B ϪAϪA¯ϪAϪA¯ϪA.The amplitude of the trajectory BϪB¯ϪBϪA is proportional to T1ϭ␣3/2(1Ϫ␣),and the ampli-tude of the trajectory BϪAϪA¯ϪAϪA¯ϪA is proportional to T2ϭ␣3/2(1Ϫ␣)2.For the IPM,the transmitted particle is a result of the interference of these two trajectories,and hence the amount of transmitted energy is proportional to(T1ϩT2)2.If interference effects are neglected,the amount of energy arriving at tϭ2.33is less,being in the case given by T12ϩT22.For the packet emerging at time tϭ3.0,there are three corresponding trajectories denoted by BϪAϪA¯ϪB¯ϪBϪA,BϪB¯ϪBϪAϪA¯ϪA,and BϪAϪA¯ϪAϪA¯ϪA ϪA¯ϪA,with amplitudes T1ϭϪ␣5/2(1Ϫ␣),T2ϭ␣3/2(1Ϫ␣)2,and T3ϭ␣3/2(1Ϫ␣)3,respectively.The energy trans-mitted for the IPM is(T1ϩT2ϩT3)2,compared to the result for noninterfering particles of T12ϩT22ϩT32.In this particular case,the amount of energy transmitted for noninterfering particles is greater than for interfering particles because of the phase shift that occurs for the trajectory BϪAϪA¯ϪB¯ϪBϪA,resulting in T1having the opposite sign from T2 and T3.To establish that this quantitative agreement is not lim-ited to low k0,we have also simulated an LA mode with a relatively large wave vector of k0ϭ0.300(2␲/a0),corre-sponding to a frequency of␯ϭ4.39THz and wavelength of 3.33a0,which is short enough that lattice discreteness ef-fects could be significant.Again extracting the group veloci-ties from Fig.2,we determine that v B/v Aϭ0.441.The value of␣for a single interface in this case was determined using MD simulation to be0.85549.For the Nϭ4superlattice,we find that0.574of the initial energy is transmitted within the first4t0using the IPM compared with0.571in the MD simulation.We have also studied a low-frequency TA wave packet with k0ϭ0.05(2␲/a0),corresponding to a frequency of0.44 THz.Since our previous results showed that interfacial scat-tering is only weakly dependent on the polarization of the TA mode in the low-frequency regime͑i.e.,below about1.5 THz͒,there was no need to define the polarization of this wave packet.8For this value of k0,we determined that␣ϭ0.88913for a single interface8and v B/v Aϭ0.498.The MD simulation resulted in0.654of the initial energy being transmitted in a time4t0,very close to the IPM result of 0.652.For high-frequency TA modes͑i.e.,above about 1.5THz͒,the energy transmission coefficient for a single inter-face depends strongly on the polarization of the incidentwave packet͑see Fig.4͒.8We showed in an earlier letter that,because of the strongly anisotropic covalent bonding in sili-con,when the polarization is along a͓11¯0͔direction,thevalue of␣is maximized,whereas if the polarization lies along a͓110͔direction,␣is minimized.8If a wave packet is formed from an arbitrary mixture of these two polarizationdirections,each transmission or reflection event will changethe properties of the wave packet,including the value of␣for a single interface.To compare the MD and IPM results,itis therefore necessary to choose a polarization that corre-sponds either to a maximum or a minimum of␣(␯).For a wave vector k0ϭ0.300(2␲/a0),which corresponds to␯ϭ2.67THz,we therefore studied two orthogonal TA wave packets corresponding to maximum and minimum energytransmission at a single interface.In each case,for the IPMwe used v B/v Aϭ0.375as obtained from the group velocities in Fig.2.The choice of polarization along a͓11¯0͔direction corresponds to a maximum value of␣ϭ0.97326for a single interface.For this choice of polarization,the IPM predicts 0.883of the energy is transmitted within a time of4t0 through the Nϭ4superlattice,which compares well to the MD result of0.884.The other choice of polarization results in͓110͔displacements and corresponds to a minimum value of␣ϭ0.74144.The IPM in this case predicts that0.375of the initial energy is transmitted within a time of4t0,again very close to the MD result of0.376.Finally,we have studied the transmission of an LO modethrough an Nϭ4superlattice.If we create an optical mode inmaterial A,it will be completely reflected from the superlat-tice(␣ϭ0).Thus,in this case,we perform a simulation in which the incident optical wave packet is launched in mate-rial B.For the incident wave packet,we chose k0ϭ0.900(2␲/a0)which corresponds to␯ϭ6.96THz,for which v B/v Aϭ3.10and␣ϭ0.75876.From the IPM wefind that0.402of the incident energy is transmitted in the IPM within4t0,compared with0.401in the MD simulations.The above results for the three phonon branches that canlead to scattering in the superlattice demonstrate that the IPMquantitatively reproduces the MD results.The advantage ofthe IPM lies,of course,it its low computational load com-pared to MD,and its consequent ability to simulate consid-erably larger systems for considerably longer times.Having established the correctness of the IPM,we maynow use it to analyze in some detail the transport of phononsthrough superlattices.Wefirst determine the net energytransmission coefficient through a superlattice␣N.This is a quantity that is quite difficult to determine by MD,even using our efficient parallel code,because of the very long simulation time required for a high fraction of the energy to be transmitted.We have studied the N dependence using the IPM and the values of k0used above to study Nϭ2and N ϭ4superlattices for the LA and LO modes͑i.e.,␣ϭ0.88800,␣ϭ0.85549,and␣ϭ0.75876).The results are shown as the closed symbols in Fig.8.While there is a sharp decrease in the net transmission coefficient for NϽ10,for。

Sep. 2011, Volume 5, No. 9 (Serial No. 46), pp. 856-859Journal of Civil Engineering and Architecture, ISSN 1934-7359, USAStudy of the Functions of Wavelet Packet Transform (WPT) and Continues Wavelet Transform (CWT) in Recognizing the Damage SpecificationMahdi Koohdaragh1, M. A. Lotfollahi Yaghin2, S. Sepehr3 and F. Hosseyni41. Young Researchers Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran2. Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran3. Faculty of Civil Engineering, Islamic Azad University, Urmia Branch, Iran4. Faculty of Mechanic Engineering, Islamic Azad University, Maragheh Branch, IranAbstract: Modern and efficient methods focus on signal analysis and have drawn researchers’ attention to it in recent years. These methods mainly include Continuous Wavelet and Wavelet Packet transforms. The main advantage of the application of these Wavelets is their capacity to analyze the signal position in different occasions and places. However, in sites with high frequencies its resolution becomes much more difficult. Wavelet packet transform is a more advanced form of continuous wavelets and can make a perfect level by level resolution for each signal. Although very few studies have been done in the field. In order to do this, in the present study, first there was an attempt to do a modal analysis on the structure by the ANSYS finite elements software, then using MATLAB, the wavelet was investigated through a continuous wavelet analysis. Finally the results were displayed in 2-D location-coefficient figures. In the second form, transient-dynamic analysis was done on the structure to find out the characteristics of the damage and the wavelet packet energy rate index was suggested. The results indicate that suggested index in the second form is both practical and applicable, and also this index is sensitive to the intensity of the damage.Key words: Wavelet packet transform, continues wavelet transform, dynamic analysis, energy rate index.1. IntroductionDamages may occur suddenly like ruptures in one element due to seismic loadings or may be developing damages like stiffness reduction happened as a result of damage growth. So there is a great need to find ways to identify hidden damages. To do so, Structural Health Monitoring (SHM) methods have been widely under research recently. There have been a lot of efforts to develop reliable and optimized methods of SHM in recent years. These methods should be able to meet the needs like identifying location of damages.Shancog Zhong and Olutunde Oyadiji presented a new approach for damage detection in beam-likeCorresponding author:Mahdi Koohdaragh, PhD, research fields: dynamic of structure and concrete and structural helth monitoring.E-mail:********************.structures when damage is relatively small [1]. This approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. Maosen Cao and Pizhong Qiao proposed a new technique (so-called “integrated wavelet transform (IWT)”) of taking synergistic advantages of the stationary wavelet transform (SWT) and the continuous wavelet transform (CWT) that this technique improved the robustness of abnormality analysis of mode shapes in damage detection [2].The present study aims to investigate continuous wavelets and wavelet packet changes thoroughly and offer a comprehensive study in the field. On the other hand it attempts to study the differences between them.Also it tries to devise a method of identifying thel Rights Reserved.Study of the Functions of Wavelet Packet Transform (WPT) and Continues Wavelet Transform (CWT) in Recognizing the Damage Specification857damage in a more applicable and practical way. Since the damage identification methods use continuous wavelet transforms based on the modal analysis, so in practice this analysis can be very hard and in some cases impossible, and these methods cannot be considered practical. Hence in the second form a wavelet packet energy rate index is suggested, and the advantages of the suggested method are investigated over other ones.2. The Theoretical Domains of the Continuous Wavelet TransformWavelet transform (WT) is a useful and new method to analyse the signals. The functions of the wavelet are combinations of series of basic functions that can separate a signal in time and frequency. So, the wavelet transforms are able to determine most unknown aspectsof the information that the other methods of signalanalysis couldn't clarify. These specifications areuseful in finding the damages. Most of the researchershave used the wavelet transforms to find damages instructural frames. But one of the disadvantages ofwavelet transform is the weak frequency separation inareas with high frequency [3-7].Considering the high capability of wavelet transform in analysing the signal of the vibration or staticresponse of a structure providing the specification ofany kinds of discontinuity or nonconformity, and fromthe graph of wavelet coefficients we can identify it inform of one or some close points with non-uniformamounts with the other points. The wavelet transform of a signal is defined as follows. dt a bt t x aa b W x )(.)(),(*2/1-=⎰+∞∞--ψ(1) 3. The Theoretical Domains of WaveletPacket TransformThe wavelet packet transform (WPT) is an extension of the CWT, which provides a complete level-by-level decomposition of signal. This transform is formed by the linear combination of the wavelet. Finally theWPERI index is proposed as follows to identify the location and intensity of the damage∑=-=∆ji ji ji jj i af af b f f E E E E 21)()()()( (2)where a f i jE )( is the component signal energy i jf E at jlevel without damage.b f i jE )(is the component signal energy i jf E at jlevel with some damage.First the measured oscillator signals from thestructure are decomposed to wavelet packet components by MATLAB and then the energy rateindex of wavelet packet is gained which is gained later using the statistic analysis of damage sill for different points of the structure: )(n Z UL WPERI WPERI WPERI δμαα+= (3)n : The number of signal draws off pointsWPERI μ: Average amountWPERI ∆: Standard deviationZ α: The amount of normal distribution with the average of Zero and unit variance increasing with theprobability of 100(1-α)% [8]. 4. Modeling Beams To model a beam we used a 3-meter span beamwhich can be seen in (Fig. 1). Elastic module and thedensity of the structure is 2.11*1011 Pa and 7850Kg/m 3. Area and moment of inertia in the crosssectional of the element are 24 cm 2 and 32 cm 4.l Rights Reserved.Study of the Functions of Wavelet Packet Transform (WPT) and Continues Wavelet Transform (CWT) inRecognizing the Damage Specification8585. Modal Analysis and the Process of Identifying Damages Using Continuous Wavelet TransformIn order to do this, one safe specimen along withother two damaged ones were chosen. Their characteristics are presented in Table 1. Beside this, to model the damages, stiffness reduction method was applied in the location of the damage. So considering the depth of the damage in its location, a cut is made and the stiffness is reduced. Then the damage is modelled. These specimens are studied in the 0-100 frequency range under modal analysis.Table 1 Characteristics of local and depth of damages in all simulated specimens.SpecimenLocation ofDamagesNumber ofElementsDepth of DamagesS1 Safe - -S2 C (20, 21) 35%S3A, B, C (9,10),(16,17), (20,21)10%, 50%,25%After doing a modal analysis on the structure, the results of the displacements were derived from 207 spots on it. In order to make the damage identification possible, the derived results were probed using a continuous wavelet packet analysis. The results are shown in Figs. 2-3.Disorders between spots number 160 and 180 are shown in Fig. 2. Using this method helps to identify thedamage position clearly. On the other hand the disorders’ length correspond the length of the damagesin the structure. Fig. 3 shows countless numbers of disorders which exists on the beam and this makes the identification process of these damages harder. Thus it can be concluded that it is impossible to identify multiple damages.6. Dynamic Analysis and the Process of Identifying Damages Using Wavelet PacketIn order to model impulse load, which is in the form of a triangular load with 10 ton magnitudes, force-time history is applied in different distances from the left support. Acceleration- time is calculated using transient dynamic analysis in ANSYS software [9]. The specimens were stimulated applying the impulse load in the points 0.5, 1.5 and 2.0 and for each individual loading, a different energy rate index in the same 25 points which is shown in Fig. 1 was derived and finally they are summed up cumulatively. So, for every damaged beam, the histogram can be drawn when theWPERI ULvalue is subtracted from the WPERI values. The location of the damage can beclearly shown in histograms. These histograms are shown in Figs. 4-5.Fig. 2 Location-coefficient diagram of specimen (S2).Fig. 3 Location-coefficient diagram of specimen (S3). l Rights Reserved.Study of the Functions of Wavelet Packet Transform (WPT) and Continues Wavelet Transform (CWT) inRecognizing the Damage Specification859Fig. 4 Histogram after considering damage threshold (S2).Fig. 5 Histogram after considering damage threshold (S3).As it can be seen in the figures, the damage threshold is clearly visible and in damage-free positions this index is zero. For instance in Fig. 4 wavelet packet energy rate index between the 20th and 21st nod (element C in specimen S2) shows the exact position of the damage.7. ConclusionsAlthough the continuous wavelet transform method makes individual damages’ identification possible, deriving the results of modal analysis is nearly impossible in practice. Since in the continuous wavelet transform method extraction of 207 data is not an easy and cheap task, this method cannot be practical and economical.Stimulation of the structure using impulse loads and extraction of 25 data from the structure is practical using wavelet packet transform and since these computation are rather fast and less time-consuming; they are applicable in real structures.Considering these results, the cumulative index suggested by the researcher is efficient enough to identify the damages in the structure. And the main point about this research is that using this method, it’s possible to identify all damages in every point of the beam and this method can be implemented for seismic retrofitting structures to increase life service of structure.References[1]S. Zhong and S. O. Oyadiji, Crack detection in simplysupported beams without baseline modal parameters bystationary wavelet transform, Mechanical Systems andSignal Processing 21 (4) (2007) 1853-1884.[2] C. Maosen and Q. P. Zhong, Integrated wavelet transformand its application to vibration mode shapes for thedamage detection of beam-type structures, Smart Materials and Structures 17 (5) (2008).[3]Z. Hou, R. Amand, Wavelet-based approach for structuraldamage detection, J. Structural Engineering 12 (7) (2000)677-383.[4]Y. Kitada, Identification of nonlinear structural dynamicsystems using wavelets, J. Engineering Mechanics 124 (10)(1998) 1059-1066.[5]Q. Wang and X. Deng, Damage detection with spatialwavelets, International Journal of Solids and Structures 36(23) (1999) 3443-3468.[6]W. J. Wang and P. D. McFadden, Application of waveletsto gearbox vibration signals for fault detection, J. Soundand Vibration 192 (5) (1996) 927-939.[7]Z. Sun and C. C. Chang, Structural damage assessmentbased on wavelet packet transform, J. Structural Engineering 128 (10) (2002) 1354-1361.[8]J. G. Han, W. X. Ren and Z. S. Sun., Wavelet packetbased damage identification of beam structures, International Journal of Solids and Structures 42 (2005)6610-6627.[9]ANSYS, Users’ Manual, revision 5.6. Swanson AnalysisSystem, USA, 1999.l Rights Reserved.。

光纤通信中常用英文简写光纤通信中常用英文缩写Acronymsac alternating current 交变电流交流AM amplitude modulation 幅度调制AON all-optical network 全光网络APD avalanche photodiode 雪崩二极管ASE amplified spontaneous emission 放大自发辐射ASK amplitude shift keying 幅移键控ATM asynchronous transfer mode 异步转移模式BER bit error rate 误码率BH buried heterostructure 掩埋异质结BPF band pass filter 带通滤波器C3 cleaved-coupled cavity 解理耦合腔CATV common antenna cable television 有线电视CDM code division multiplexing 码分复用CNR carrier to noise ratio 载噪比CSO Composite second order 复合二阶CPFSK continuous-phase frequency-shift keying 连续相位频移键控CVD chemical vapour deposition 化学汽相沉积CW continuous wave 连续波DBR distributed Bragg reflector 分布布拉格反射DFB distributed feedback 分布反馈dc direct current 直流DCF dispersion compensating fiber 色散补偿光纤DSF dispersion shift fiber 色散位移光纤DIP dual in line package 双列直插DPSK differential phase-shift keying 差分相移键控EDFA erbium doped fiber amplifier 掺铒光纤激光器FDDI fiber distributed data interface 光纤数据分配接口FDM frequency division multiplexing 频分复用FET field effect transistor 场效应管FM frequency modulation 频率调制FP Fabry Perot 法布里里-珀落FSK frequency-shift keying 频移键控FWHM full width at half maximum 半高全宽FWM four-wave mixing 四波混频GVD group-velocity dispersion 群速度色散HBT heterojunction-bipolar transistor 异质结双极晶体管HDTV high definition television 高清晰度电视HFC hybrid fiber-coaxial 混合光纤纤/电缆IC integrated circuit 集成电路IMD intermodulation distortion 交互调制失真IM/DD intensity modulation with direct detection 强度调制直接探测ISDN integrated services digital network 综合业务数字网ISI intersymbol interference 码间干扰LAN local-area network 局域网LED light emitting diode 发光二极管L-I light current 光电关系LPE liquid phase epitaxy 液相外延MAN metropolitan-area network 城域网MBE molecular beam epitaxy 分子束外延MOCVD metal-organic chemical vapor deposition金属有机物化学汽相沉积MCVD Modified chemical vapor deposition改进的化学汽相沉积MONET Multiwavelength optical network 多波长光网络MPEG motion-picture entertainment group 视频动画专家小组MPN mode-partition noise 模式分配噪声MQW multiquantum well 多量子阱MSK minimum-shift keying 最小频偏键控MSR mode-suppression ratio 模式分配噪声MZ mach-Zehnder 马赫泽德NA numerical aperture 数值孔径NF noise figure 噪声指数NEP noise-equivalent power 等效噪声功率NRZ non-return to zero 非归零NSE nonlinear Schrodinger equation 非线性薛定额方程OC optical carrier 光载波OEIC opto-electronic integrated circuit 光电集成电路OOK on-off keying 开关键控OPC optical phase conjugation 光相位共轭OTDM optical time-division multiplexing 光时分复用OVD outside-vapor deposition 轴外汽相沉积OXC optical cross-connect 光交叉连接PCM pulse-code modulation 脉冲编码调制PDF probability density function 概率密度函数PDM polarization-division multiplexing 偏振复用PON passive optical network 无源接入网PSK phase-shift keying 相移键控RIN relative intensity noise 相对强度噪声RMS root-mean-square 均方根RZ return-to-zero 归零RA raman amplifier 喇曼放大器SAGCM separate absorption, grading, charge, and multiplication 吸收渐变电荷倍增区分离APD 的一种SAGM separate absorption and multiplication吸收渐变倍增区分离APD 的一种SAM separate absorption and multiplication吸收倍增区分离APD 的一种SBS stimulated Brillouin scattering 受激布里渊散射SCM subcarrier multiplexing 副载波复用SDH synchronous digital hierarchy 同步数字体系SLA/SOA semiconductor laser/optical amplifier 半导体光放大器SLM single longitudinal mode 单纵模SNR signal-to-noise ratio 信噪比SONET synchronized optical network 同步光网络SPM self-phase modulation 自相位调制SRS stimulated Raman scattering 受激喇曼散射STM synchronous transport module 同步转移模块STS synchronous transport signal 同步转移信号TCP/IP transmission control protocol/internet protocol传输控制协议议/互联网协议TDM time-division multiplexing 时分复用TE transverse electric 横电模TM transverse magnetic 横磁TW traveling wave 行波VAD vapor-axial epitaxy 轴向汽相沉积VCSEL vertical-cavity surface-emitting laser垂直腔表面发射激光器VPE vapor-phase epitaxy 汽相沉积VSB vestigial sideband 残留边带WAN wide-area network 广域网WDMA wavelength-division multiple access 波分复用接入系统WGA waveguide-grating router 波导光栅路由器XPM cross-phase modulation 交叉相位调制YIG yttrium iron garnet 钇铁石榴石晶体DWDM dense wavelength division multiplexing/multiplexer密集波分复用用/器FBG fiber-bragg grating 光纤布拉格光栅AWG arrayed-waveguide grating 阵列波导光栅LD laser diode 激光二极管AOTF acousto optic tunable filter 声光调制器AR coatings antireflection coatings 抗反膜SIOF step index optical fiber 阶跃折射率分布GIOF graded index optical fiber 渐变折射率分布光纤通信技术课程常用词汇Cross-talk 串音Passive component 无源器件Active component 有源器件Soliton 孤子Jitter 抖动Heterodyne 外差Homodyne 零差Transmitter 发射机Receiver 接收机Transceiver module 收发模块Birefringence 双折射Chirp 啁啾Binary 二进制Chromatic dispersion 色度色散Cladding 包层Jacket 涂层Core cladding interface 纤芯包层界面Gain-guided semiconductor laser 增益波导半导体激光器Index-guide semiconductor laser 折射率波导半导体激光器Damping constant 阻尼常数Threshold 阈值Power penalty 功率代价Dispersion 色散Attenuation 衰减Nonlinear optical effect 非线性效应Polarization 偏振Double heterojunction 双异质结Electron-hole recombination 电子空穴复合Linewidth 线宽Preamplifer 前置放大器Inline amplifier 在线放大器Power amplifier 功率放大器Extinction ratio 消光比Eye diagram 眼图Fermi level 费米能级Multimode fiber 多模光纤Higher-order dispersion 高阶色散Dispersion slope 色散斜率Block diagram 原理图Quantum limited 量子极限Intermode dispersion 模间色散Intramode dispersion 模内色散Filter 滤波器Directional coupler 定向耦合器Isolator 隔离器Circulator 环形器Detector 探测器Laser 激光器Polarization controller 偏振控制器Attenuator 衰减器Modulator 调制器Optical switch 光开关Lowpass filter 低通滤波器Highpass filter 高通滤波器Bandpass filter 带通滤波器Longitudinal mode 纵模Transverse mode 横模Lateral mode 侧模Sensitivity 灵敏度Linewidth enhancement factor 线宽增强因子Packet switch 分组交换Quantum efficiency 量子效率White noise 白噪声Responsibility 响应度Waveguide dispersion 波导色散Stripe geometry semiconductor laser 条形激光器Ridge waveguide 脊波导Zero-dispersion wavelength 零色散波长Free spectral range 自由光谱范围Surface emitting LED 表面发射LEDEdge emitting LED 边发射LEDEthernet 以太网Shot noise 散粒噪声Thermal noise 热噪声Quantum limit 量子极限Sensitivity degradation 灵敏度劣化Intensity noise 强度噪声Timing jitter 时间抖动Front end 前端Packaging 封装Maxwell’s equations 麦克斯韦方程组Material dispersion 材料色散Rayleigh scattering 瑞利散射Nonradiative recombination 非辐射复合Driving circuit 驱动电路ADM Add Drop Multiplexer 分插复用器:AON Active Optical Network 有源光网络:APON ATM Passive Optical Network ATM无源光网络: ADSL Asymmetric Digital Subscriber Line 非对称数字用户线: AA Adaptive Antenna 自适应天线:ADPCM Adaptive Differential Pulse Code Modulation 自适应脉冲编码调制: ADFE Automatic Decree Feedback Equalizer自适应判决反馈均衡器:AMI Alternate Mark Inversion 信号交替反转码:AON All Optical Net 全光网AOWC All Optical Wave Converter 全光波长转换器:ASK Amplitude Shift Keying 振幅键控:ATPC Automatic Transfer Power Control自动发信功率控制:AWF All Wave Fiber 全波光纤:AU Administrative Unit 管理单元:AUG Administrative Unit Group 管理单元组:APD Avalanche Diode 雪崩光电二极管:BA Booster(power) Amplifier 光功率放大器:BBER Background Block Error Ratio 背景误块比:BR Basic Rate Access 基本速率接入:Bluetooth 蓝牙:C Band C波带:Chirp 啁啾:C Container C 容器:CSMA/CD Carrier Sense Multiple Access with Collision Detection 载波侦听多址接入/碰撞检测协议:CSMA/CA Carrier Sense Multiple Access with Collision Avoidance 载波侦听多址接入/避免冲撞协议:CNR Carrier to Noise Ratio 载噪比:CP Cross polarization 交叉极化:DCF Dispersion Compensating Fiber色散补偿单模光纤DFF Dispersion-flattened Fiber色散平坦光纤:DR Diversity Receiver 分集接收DPT Dynamic Packet Transport动态包传输技术:ODM Optical Division ltiplexer 光分用器:DSF Dispersion-Shifted Fiber 色散移位光纤:DTM Dynamic Synchronous Transfer Mode 动态同步传送模式: DWDM Dense Wavelength Division Multiplexing 密集波分复用: DLC Digital loop carrier 数字环路载波:DXC Digital cross connect equipment 数字交叉连接器:EA Electricity Absorb Modulation电吸收调制器:EB Error Block 误块:ECC Embedded Control Channel 嵌入控制通路:EDFA Erbium-doped Fiber Amplifier 掺铒光纤放大器EDFL Erbium-doped Fiber Laser掺铒光纤激光器:ES Errored Second 误块秒:ESR Errored Second Ratio 误块秒比:FEC Forward Error Correction 前向纠错:FWM Four-wave Mixing 四波混频:FDMA Frequency Division Multiple Access 频分多址: FTTB Fiber to the Building 光纤到大楼:FTTC Fiber to the Curb 光纤到路边FTTH Fiber to the Home 光纤到户:FA Frequency agility 频率捷变:CSMF Common Single Mode Fiber 单模光纤:DSF Dispersion-Shifted Fiber 色散位移光纤:GE Gigabit Ethernet 千兆以太网技术:GIF Graded Index Fiber 渐变型多模光纤:GS-EDFA Gain Shifted Erbium-doped Fiber Amplifier增益平移掺饵光纤放大器: GVD Group Velocity Dispersion 群速度色散:HPF High Pass Filter 高通滤波器:HRDS Hypothetical Reference Digital Section 假设参考数字段:IDLC Integrated DLC 综合数字环路载波:IDEN Integrated Digital Enhanced Networks 数字集群调度专网:IEEE 802.3: CSMA/CD局域网，即以太网标准。

10447 Mercedes-Benz MBN Company Standard Date published: 2010-05Folder: 22Supersedes: A212 000 18 99Total no. of pages (including Annex): 49Person in charge: Matthias GeigerPlant 050; Dept.: MBC/QEEDate of Translation: 2010-11 Phone: +49 7031 90 49 400Quality Management StandardElectrics/Electronicsfor Mercedes-Benz CarsQualitätsmanagement-Norm Elektrik/Elektronik für Mercedes-Benz CarsForewordThis Quality Management Standard Electrics/Electronics for Mercedes-Benz Cars describes therequirements specified by Daimler AG for suppliers of electrical/electronic components and electri-cal/electronic control units for Mercedes-Benz Cars.This Standard is applicable in addition to the component requirement specifications for the devel-opment, manufacture and series production of this component by a contractor of Daimler AG.ChangesFirst editionNOTE: This translation is for information purposes only.The German version shall prevail above all others.Copyright Daimler AG 2010Contents1Scope (5)2Normative references (6)3Terms and definitions (7)3.1List of abbreviations (7)3.2Nomenclature (8)4General requirements (9)4.1Contacts at Daimler AG (9)4.2Contacts at the supplier and its sub-suppliers (10)4.3Key processes (10)5Preventive maturity level management (11)5.1Start of preventive maturity level management (11)5.2Scope (11)5.3Tracking of sub-supplier maturity level (12)5.4Changes following start of production (12)5.4.1Process and sub-process relocation (12)5.4.2Replacement or exchange of machines or equipment (12)5.4.3Change of a sub-supplier (13)6Detection of anomalies (14)7Process capability and product reliability (15)7.1Proof of machine and process capability for SMT processes (15)7.1.1Machine and process capability of paste printer (15)7.1.2Machine capability placement machines (15)7.1.3Verification of solder profile (16)7.2Proof of reliability of the assembly and connection technology (16)7.3Proof of reliability of the devices used (16)7.4Board bending test (17)7.5Requalification (18)7.5.1Complete repeat of the environmental and life tests (18)7.5.2Q-Review Environment E/E (18)8Manufacturing processes for electronic components (20)8.1Storage (20)8.1.1Moisture sensitive devices (20)8.2Printed circuit board magazines (21)8.3Transportation of devices and components (21)8.4Soldering paste printing (21)8.4.1Initial part approval during series production (21)8.4.2Soldering paste (21)8.4.3Paste printer (22)8.4.4Cleaning of the stencil (22)8.4.5Cleaning of circuit boards following soldering paste printing (22)8.4.6Mechanical stress in double-sided PCB assembly (23)8.5PCB assembly (23)8.5.1Initial part approval (23)8.5.2Reel change (23)8.5.3Mechanical stress (23)8.5.4Process control (23)8.5.5Maintenance (23)8.6Assembly and connection technology (24)8.6.1Reflow soldering (24)8.6.1.1Machine malfunctions (25)8.6.1.2Temperature profile (25)8.6.2Press-fit technology (25)8.6.3Selective soldering with mini-wave (26)8.6.3.1Flux (26)8.6.3.2Temperature pretreatment and temperature gradient (26)8.6.3.3Temperature monitoring (27)8.6.3.4Machine malfunctions (27)8.6.3.5Solder residue (27)8.6.3.6Solder bath (27)8.6.3.7Solder filling level (27)9Rework (28)10Test technology in series production (29)10.1Inspection of soldered joints (29)10.1.1Inspection of paste printing (29)10.1.2Inspections after reflow soldering (29)10.1.3Inspections after selective soldering (30)10.1.4Manual visual inspections (30)10.2In-circuit test (30)10.3Contacting of components (31)10.4End-of-line test (31)10.5Test parameters (32)10.6Mechanical interfaces (32)10.7Product audit (32)10.7.1Temperature cycle test (33)10.7.2Additional component-specific tests (33)10.7.3Changes (34)10.8Early defect detection (34)10.8.1Realization of early defect detection (34)10.8.2Active run-in (34)10.9Test coverage analysis (35)10.10Evaluation and reporting of internal test results (36)10.11Haptic measurements (36)10.12Testing of function, switch and controls illumination (37)10.13Noise testing (37)10.14Process documentation and process records (38)10.14.1Soldering paste printing (38)10.14.2Placement machines (38)10.14.3Reflow soldering (38)10.14.4Selective soldering with mini-wave (38)10.14.5Rework (39)10.14.6Test parameters (39)11Mechanical manufacturing processes (40)11.1Circuit board separation (40)11.1.1Milling (40)11.1.2Punching (V-cutting) (40)11.1.3Sawing (40)11.1.4Laser cutting (41)11.2Assembly and screw-fastening processes (41)11.3Zero Insertion Force (ZIF) connectors (41)11.3.1Manual joining of zero insertion force connectors (42)11.3.2Semi or fully automatic joining of zero insertion force connectors (42)11.3.3Testing of the connection of zero insertion force connectors (42)11.3.4Opening of the plug connection of zero insertion force connectors (42)12Traceabilty of devices and components (43)12.1Incoming goods (43)12.2PCB assembly (43)12.3Tests (44)12.4End-of-line test (44)12.5Outgoing goods (44)12.6Rework (44)13ESD (45)13.1ESD protection measures in electronics production (45)13.2Personnel grounding (45)13.3Rework (45)14Flashing of components (46)14.1Handling (46)14.2Contacting and flashing (46)14.3Testing and traceability of flashed components (46)14.4Capacity of the flashing process (47)15Failure analysis (48)15.1Analysis reports (48)15.2Priority failures (48)15.3NTF failures (complaints) (48)15.4Failure analysis on site (48)16On-site support (49)16.1Professional requirements for staff (49)16.2Time-related requirements (49)16.3Other requirements (49)1 ScopeThis Quality Management Standard Electrics/Electronics applies irrespective of the model to all electri-cal/electronic components in general.2 Normative referencesMB Special Terms Mercedes Benz Special Termsof Electronic AssembliesANSI/IPC-A-610D AcceptabilityIPC/JEDEC J-STD-033B.1 Handling, Packing, Shipping and Use of Moisture/ReflowSensitive Surface Mount DevicesDIN EN ISO 9453 Soft Solder Alloys – Chemical Compositions and FormsA2110039899 Design Rules for E/E ComponentsDIN EN 61340-5-1 Protection of Electronic Devices from Electrostatic Phenom-ena — General RequirementsIEC/TR 61340-5-2 Protection of Electronic Devices from Electrostatic Phenom-ena – User GuideDIN EN 61340-4-5 Standard Test Methods for Specific Applications – Methodsfor Characterising the Electrostatic Protection of Footwearand Flooring in Combination with a PersonDIN EN 61340-4-3 Standard Test Methods for Specific Applications – Footwear AEC-Q100 Stress Qualification for Integrated CircuitsAEC-Q101 Stress Test Qualification for Discrete SemiconductorsAEC-Q200 Stress Test Qualification for Passive ComponentsAEC-Q004 Zero Defects Guideline (Draft version)ANSI/IPC J-STD-001D Requirements for Soldered Electrical and Electronic Assem-bliesMBN 10448 Field Failure Analysis3 Terms and definitions3.1 List of abbreviationsTwo-dimensional2DThree-dimensional3DAEC Automotive Electronic Council (body for quality standards in the automotive indus-try)InspectionOpticalAutomatedAOI(Ausführungsvorschrift)regulationAVImplementationBGA Ball Grid Array componentsBR Vehicle model series (Baureihe)cmk Short-term process capabilitycapabilityprocessLong-termcpksupplyspecification (Liefervorschrift)Daimler-BenzDBLDS Identification and documentation of safety relevancedocumentation of certification relevanceandIdentificationDZE/E component Electrical/electronic componentProgrammable Read-Only MemoryEEPROM ElectricallyErasableX-rayspectroscopyEnergy-dispersiveEDXEOL End Of Line testOverStressEOSElectricalDischargeElectroStaticESDFMEA Failure Mode and Effects AnalysisLevelingAirHotHALHIL Hardware In the LoopHardWareHWStandardizationISOforOrganisationInternationalCircuitsIC IntegratedIn-Circuit-TestICTspecifications (Komponentenlastenheft)requirementComponentKLHMBN Mercedes-Benz standard (Mercedes-Benz Norm)SystemDevelopmentMercedes-BenzMDSInterfaceMan-MachineMMIMSD Moisture Sensitive DeviceLevelSensitiveMSLMoistureSystemProductionMercedes-BenzMPSMTTF Mean Time To FailureNTF No Trouble Foundprocess and product approvalPPAProductioncapabilityprocessPreliminaryppkPRG Product maturity level (Produkt-Reifegrad)GateQGQualityQualityManagementQMStatusQ-Status QualityMemoryAccessRandomRAMMemoryOnlyReadROMTemperatureRoomRTUnitControlCUMountedTechnologySurfaceSMTSOP Start of ProductionSoftWareSWTechnologyHoleThroughTHT3.2 NomenclatureBelow, electrical/electronic components and electrical/electronic control units are termed "components" for the reader’s convenience.Below, the contractor of Daimler AG is termed "supplier".Below, the sub-components of components such as circuit boards, electronic devices (e.g. controllers, transceivers, micromechanical semiconductors) and mechanical units (e.g. housings) are termed "de-vices" for the reader’s convenience.Below, requirements for documentation and the recording of data are specified. In this context, "docu-ment" refers to instructions and specifications (e.g. work instructions, process descriptions, etc). The term "record" refers to evidential data (e.g. completed checklists, audit evidence, etc).4 GeneralrequirementsFor safety requirements, homologation and quality, the existing statutory requirements and laws shall be complied with. In addition, the relevant requirements of Daimler AG apply.All materials, procedures, processes, components, and systems shall conform to the current regulatory (governmental) requirements regarding regulated substances and recyclability.This Quality Management Standard Electrics/Electronics makes reference to applicable laws, standards and regulations etc. The supplier shall be responsible for compliance with all laws, standards and regula-tions and for the development and production of the component in line with the state of the art. In this con-text, due consideration shall be given to the fact that the vehicles of Daimler AG containing this compo-nent are sold worldwide.This Quality Management Standard Electrics/Electronics makes reference to other applicable documents of the component requirement specifications (KLH) (specifications, test methods, implementation regula-tions, instructions of Daimler AG). Where this Quality Management Standard Electrics/Electronics contains deviating or contradictory information compared with other standards, specifications or implementation regulations, the more severe specification shall apply. In case of doubt, clarifying agreements following discussions with Daimler AG Quality Management shall be set down in writing.The supplier shall supply conforming products to Daimler AG, and the supplier shall maintain the zero-defect target.If the supplier is aware of measures or alternatives serving to increase quality or reliability, the supplier shall notify these to Daimler AG Quality Management.All information and documents associated with the development, manufacture and production of the com-ponent shall be treated confidentially.4.1 Contacts at Daimler AGThe responsible component developer and other contacts at Daimler AG are listed in the component re-quirement specifications (KLH).Mercedes-Benz Cars Quality Management is divided into two units:- Preventive Quality Management (Prevention) and- Quality Management Production in the worldwide Daimler assembly, body, paintwork and stamp-ing plants (e.g. Sindelfingen, Bremen, Tuscaloosa, South Africa etc.).During the development phase (requirement specification phase up to the launch of the component in production), a staff member from Prevention is the responsible quality contact for the supplier. Together with the responsible staff member from Prevention, the supplier shall hold coordination discussions re-garding quality management requirements. The supplier shall seek approval from the responsible staff member from Prevention for any deviations from these quality management requirements.During the production phase (launch of component in production up to discontinuation of production), a Quality Management staff member from each assembly, body, paintwork and stamping plant is the re-sponsible quality contact for the supplier. The supplier shall seek approval for all changes to the compo-nent or production process during the production phase from the responsible Quality Management staff member from the assembly, body, paintwork and stamping plants. In the event of deviations from the re-lease status of the component, the supplier shall present appropriate measures and samples and have any changes approved.Any deviation from the requirements of this Quality Management Standard Electrics/Electronics are sub-ject to the written approval of Daimler AG Quality Management.4.2 Contacts at the supplier and its sub-suppliersThe supplier shall submit an organizational diagram to Daimler AG Quality Management showing all per-sons responsible for the project and their functions.The supplier shall reveal the complete supply chain of devices for the project to Daimler AG Quality Man-agement. In this process, the supplier shall document the scope of supply and supplier name of each de-vice.4.3 Key processesTo facilitate the successful implementation of the project, the supplier shall provide evidence of docu-mented process structures for the following key processes during the concept presentation:1. Requirements analysis process2. Test strategy process3. Configuration and change management process4. Problem analysis process5. Project management5 Preventive maturity level managementThe objective of preventive maturity level management is to recognize quality-related problems and defi-cits concerning the product and/or production process as early as during the development phase of the component and to be able to initiate countermeasures. Timely completion of the project and defect-free implementation of all specified functions are the top priorities for Daimler AG.The supplier shall document and maintain a preventive maturity level management system. As part of this system, the supplier shall determine and record characteristic data (metrics, process capability indices, inspections, etc.).In this context, all company units of the supplier involved with the product creation process shall be sub-ject to the maturity level management system.Assessment of the maturity level shall be based on the specified quality targets and quality criteria throughout the product and process development process.The supplier shall document compliance with and fulfillment of all requirements from the component re-quirement specifications (KLH) and this Standard.To track all activities during development, the supplier shall maintain a list of open issues, and grant Daim-ler AG Quality Management access to this list on request.The supplier shall submit regular reports to Daimler AG Quality Management regarding maturity level pro-gress. The supplier shall document maturity level reports in writing. The supplier shall record the maturity level reports for the Quality Gates (according to MDS) and submission of A, B, C, D and PPF samples in writing.5.1 Start of preventive maturity level managementThe supplier shall initiate preventive maturity level management at the time of project start - immediately following the commencement of hardware and software development and the start of the production proc-ess.5.2 ScopeThe supplier shall coordinate and document the scope of preventive maturity level management with Daimler AG Quality Management.The preventive maturity level tracking during the product creation process includes the monitoring of the degree of fulfillment of all requirements. In this context, the supplier shall document and record the (func-tional and non-functional) requirements for the component and the production process during the devel-opment phase of the component.The supplier shall carry out an assessment on the basis of the degree of implementation of the require-ments at the relevant project date. The maturity level is divided into four stages:- Requirement not implemented by the deadline- Requirement is in the process of being implemented- Requirement has been implemented by the deadline- Requirement has been implemented and tested successfully by the deadline5.3 Tracking of sub-supplier maturity levelThe supplier shall document and implement a preventive maturity level management system at all sub-supplier companies involved in the project (Tier 2, Tier 3, …).The supplier shall inform Daimler AG Quality Management of the status of the preventive maturity level management if there is a risk of the sub-suppliers involved in the project failing to reach the project objec-tive.On request, the supplier shall grant Daimler AG Quality Management access to records concerning the maturity level management of the sub-suppliers involved in the project.5.4 Changes following start of productionAny changes to the component or an existing manufacturing process shall be subject to the approval of Daimler AG Quality Management and be approved using a PPA process.The supplier shall qualify any change, e.g. in the event of changes to devices (material or manufacturing process of the device) or in the manufacturing process of the component. The supplier shall provide evi-dence of and document qualification in accordance with the component requirement specifications.Deviations from a complete qualification by the supplier shall be subject to the approval of Daimler AG Quality Management.Qualification shall be carried out using components manufactured on the production equipment at the se-rial production location.The documentation of changes shall be coordinated with Daimler AG Quality Management.The supplier shall adhere to a previously defined time frame for pre-advice to Daimler AG Quality Man-agement.In the cases indicated below, the supplier shall inform the following Daimler AG units: Quality Manage-ment, Development, Purchasing and Logistics.5.4.1 Process and sub-process relocationIn the case of any type of process and sub-process relocation, the supplier shall inform Daimler AG Qual-ity Management no later than 9 months before the intended implementation of the change. The supplier shall submit a relocation scenario and seek the approval of Daimler AG Quality Management for such scenario.This time frame also applies to the outsourcing of processes or sub-processes to sub-suppliers.5.4.2 Replacement or exchange of machines or equipmentIn the case of the replacement or exchange of machines or equipment or other systems, the supplier shall inform Daimler AG Quality Management no later than 3 months before the intended implementation of the change.5.4.3 Change of a sub-supplierIn the case of a change of a sub-supplier or manufacturer of a device of the component, the supplier shall submit a change scenario to Daimler AG Quality Management and seek the approval of Daimler AG Qual-ity Management for such scenario. The supplier should inform Daimler AG Quality Management no later than 6 months before the intended implementation of the change.6 Detection of anomaliesThe statistical detection of anomalies is intended for the detection of unusual features in the functionality or measurement parameters. These may be anomalies which lie within the specification limits provided, but are unusual compared to other components. The anomalies may point towards pre-damage to the component.In order to ensure the process capability and product reliability, the supplier shall document and use a method for the detection of anomalies, and provide evidence by means of records.To verify the process capability and product reliability, the supplier shall use this method, starting with the manufacture of initial samples, and create records. Evidence shall be provided no later than at the time of submission of the initial sample documentation.7 Process capability and product reliabilityIn accordance with VDA 2, the supplier shall provide evidence of the process capabilities for its production processes.For the deadline and the required values for the process capabilities, refer to MBST.At the time of submission of the initial samples, the supplier shall document the final evidence of the proc-ess capabilities and product reliabilities required.The initial samples shall be manufactured on production equipment and selected randomly.The supplier shall have any deviations from these specifications approved by Daimler AG Quality Man-agement.7.1 Proof of machine and process capability for SMT processesWithin the framework of the zero-defects strategy in relation to the customer, the supplier shall make every effort to prevent and detect nonconformances. From the point of view of customer satisfaction and with a view to ensuring the quality of the components, it is essential that nonconformances are detected as early as possible and eliminated. The focus shall therefore be on the process capability of the supplier's manufacturing process. This includes the determination of the ongoing process capability, the control of the production process and continuous process improvement.The supplier shall supply regular evidence of the process capabilities of production as a whole and each production process and maintain the appropriate records.7.1.1 Machine and process capability of paste printerThe supplier shall check the machine capability once every year and maintain the pertinent records.Evidence of the machine capability of the paste printer can be provided by means of a reference stencil. The relevant parameters for this purpose are the positioning accuracy in the x and y direction of the solder deposit.The supplier shall check the process capability of the paste printer with the product-specific original stencil and maintain appropriate records. During this process, the supplier shall document reference points and determine their positioning accuracies in x and y position as well as the volume. To do so, the supplier may use the paste AOI provided that the AOI measuring data can be analyzed.7.1.2 Machine capability placement machinesThe supplier shall check the machine capability every other year and maintain the pertinent records.The supplier shall check the machine capability using a glass board and glass devices or ceramic pads and maintain appropriate records. To prove capability, the supplier shall document the critical SMD shapes and test these.7.1.3 Verification of solder profileThe supplier shall verify that the solder profile determined allows each solder joint to reach the required soldering temperature and the required temperature profile. The supplier shall maintain appropriate re-cords.The supplier shall verify that "thermally critical" devices on the circuit board are not overheated. The sup-plier shall maintain appropriate records.The supplier shall observe the specifications of the board, device and soldering paste manufacturers, and provide evidence of compliance. The temperature profile shall therefore be recorded with the printed com-ponent circuit board.7.2 Proof of reliability of the assembly and connection technologyThe supplier shall document the development progress at the time of each delivery of sample parts.At the time of submission of the initial samples, the supplier shall perform a full qualification on the basis of the requirements of the KLH and provide the appropriate evidence.The supplier shall coordinate the number and scope of the tests with Development and Daimler AG Qual-ity Management and document the results.In order to allow the impact of changes on the component to be assessed, the supplier shall document a comparison of measuring results before and after the intended change.Qualification shall be carried out using components manufactured on the series production equipment. 7.3 Proof of reliability of the devices usedOn delivery, the supplier shall provide evidence of device qualification.For ICs, the supplier shall provide evidence of the device qualification in accordance with AEC-Q100, for discrete components in accordance with AEC-Q101, and for passive components in accordance with AEC-Q200.To achieve the zero-defects strategy, the supplier shall document the methods as per AEC-Q004 and provide evidence of the records to Daimler AG Quality Management.The supplier shall have any deviations from these specifications approved by Daimler AG Quality Man-agement.7.4 Board bending testThe supplier shall ensure that soldered circuit boards or devices cannot be damaged as a result of me-chanical stresses. Excessive mechanical stresses result in the danger of the board or devices becoming pre-damaged due to microcracks. The supplier shall support the PCB boards using an appropriate fixture.By means of a board bending test, the mechanical stress to which a soldered circuit board is exposed during the production process can be determined.The supplier shall perform a bending test for the following production steps on the component-specific board and maintain the relevant records:- Paste printer (only for double-sided boards)- SMD placement machines- ICTseparatorboard- Circuit- Press-fit process for contacts- Press-fit and assembly fixtures and jigs for installing boards in a housing- Transport systems, including gripping devices.The supplier shall repeat the board bending test at regular time intervals and record the relevant results.The supplier shall use the bending test for fault finding in the event of failures of devices (e.g. damage, microcracks on ceramic capacitors). The supplier shall record the results and submit them to Daimler AG Quality Management on request.The supplier shall use an appropriate measurement procedure for carrying out the board bending test.The maximum critical bending of boards depends on the individual circuit board or the devices used. The supplier shall take care to ensure that the sensors are positioned on the board at the point of maximum bending.The supplier shall take care to ensure that circuit board is assembled and soldered in line with the relevant process step to be examined.During the processing of ceramic capacitors, the supplier shall ensure that the specifications ofAV A2110039899 "Design Rules for E/E Components“ are complied with for all manufactured compo-nents.7.5 RequalificationThe supplier shall check at least once every year whether its deliveries conform to the specifications of Daimler AG.As a minimum requirement, the test scope shall include evidence that the specifications with regard to dimensional, material, reliability, environmental, process and statutory rules have been complied with.The supplier shall coordinate and document the test scopes with Daimler AG Quality Management. This coordination shall be based on the environmental and lifetime tests specified in the component require-ment specifications (KLH) as well as other specifications such as DBL, MBN, AV, etc.The supplier can choose between the following methods to prove compliance with the specifications of the environmental and life tests required in KLH:- complete annual repeat of the of the environmental and life tests specified in KLH- annual execution of a so-called "Q-Review Environment E/E“.7.5.1 Complete repeat of the environmental and life testsThe supplier shall record the results of the repeat and submit them to Daimler AG Quality Management on request.The supplier shall notify Daimler AG Quality Management of any deviations from the specification without delay.The supplier shall supply regular evidence of the process capabilities of production as a whole and each production process and maintain the appropriate records.If the tests show that the required cp or cpk values are not achieved and that the equipment requires read-justment, the supplier shall shorten the test interval.7.5.2 Q-Review Environment E/ETo perform a "Q-Review Environment E/E“, the supplier is required to comply with the following conditions: The environmental and life tests specified in the KLH have been performed once successfully, and the relevant results recorded.Another condition for the execution of a "Q-Review Environment E/E“ is that the following requirements have been fulfilled during the previous 12 months:- The supplier has used a statistical method for the early detection of faults in production. This method has ensured that 100% of the manufactured parts have been covered, the results recorded and evaluated regularly. All measures defined as part of the early fault detection system during the previous 12 months must have been effectively implemented.- The required qualification tests shall have been passed successfully with regard to any changes to the component or the production process.- All failures during the tests in production have been determined, and the relevant results recorded and regularly evaluated. All measures defined during the previous 12 months shall have been effectively im-plemented.- All measures defined during internal and external audits during the previous 12 months shall have been effectively implemented.- All 0-km failures and field failures during the previous 12 months shall have been analyzed and evalu-ated. Any resulting measures shall have been implemented effectively.。