Comparison of Measurements and Simulations of RingOscillators Fabricated in InPInGaAs HBT T

Sediment Transport Modeling Review—Current andFuture DevelopmentsAthanasios N.͑Thanos ͒PapanicolaouAssociate Professor,Univ.of Iowa,IIHR-Hydroscience and Engineering,Dept.of Civil and Environmental Engineering,Iowa City,IA 52241.E-mail:apapanic@Mohamed ElhakeemResearch Associate Engineer,Univ.of Iowa,IIHR-Hydroscience and En-gineering,Dept.of Civil and Environmental Engineering,Iowa City,IA 52241.E-mail:melhakee@George KrallisERM Inc.,Exton,PA.E-mail:george.krallis@Shwet PrakashERM Inc.,Exton,PAJohn EdingerFaculty Research Associate,Bryn Mawr College,Dept.of Geology.E-mail:jeedgr@IntroductionThe use of computational models for solving sediment transport and fate problems is relatively recent compared with the use of physical models.Several considerations govern the choice be-tween physical and computational models;namely,the nature of the problem that needs to be solved,the available resources,and the overall cost associated with the problem solution.In some specific problems,a combination of physical and computational models can be used to obtain a better understanding of the pro-cesses under investigation ͑de Vries 1973͒.Using computational hydrodynamic/sediment transport models,in general,involves the numerical solution of one or more of the governing differential equations of continuity,momentum,and energy of fluid,along with the differential equation for sediment continuity.An advan-tage of computational models is that they can be adapted to dif-ferent physical domains more easily than physical models,which are typically constructed to represent site-specific conditions.An-other advantage of computational models is that they are not sub-ject to distortion effects of physical models when a solution can be obtained for the same flow conditions ͑identical Reynolds and Froude numbers,same length scale in the three directions,etc.͒as those present in the field.With the rapid developments in numerical methods for fluid mechanics,computational modeling has become an attractive tool for studying flow/sediment transport and associated pollutant fate processes in such different environments as rivers,lakes,and coastal areas.Representative processes in these environments in-clude bed aggradation and degradation,bank failure,local scour around structures,formation of river bends,fining,coarsening and armoring of streambeds,transport of point source and nonpointsource pollutant attached to sediments,such sediment exchange processes as settling,deposition,and self-weight consolidation;coastal sedimentation;and beach processes under tidal currents and wave action.Over the past three decades,a large number of computational hydrodynamic/sediment transport models have been developed ͑Fan 1988;Rodi 2006͒.Extensive reviews of different hydrodynamic/sediment transport models can be found in Nicollet ͑1988͒,Nakato ͑1989͒,Onishi ͑1994͒,Przedwojski et al.͑1995͒,Spasojevic and Holly ͑2000͒,and the ASCE Sedimentation Engi-neering Manual no.110͑2007͒.Broadly speaking,these models can be classified on the basis of the range of their applications ͑e.g.,suspended load versus bed-load;physical versus chemical transport ͒;and their formulation in the spatial and temporal con-tinua ͑e.g.,one-dimensional model ͑1D ͒;two-dimensional model ͑2D ͒;or three-dimensional model ͑3D ͒;and steady versus un-steady ͒.The choice of a certain model for solving a specific prob-lem depends on the nature and complexity of the problem itself,the chosen model capabilities to simulate the problem adequately,data availability for model calibration,data availability for model verification,and overall available time and budget for solving the problem.The objectives of this article are twofold.First,the article aims to trace the developmental stages of current representative ͑1D,2D,and 3D ͒models and describe their main applications,strengths,and limitations.The article is intended as a first guide to readers interested in immersing themselves in modeling and at the same time sets the stage for discussing current limitations and future needs.Second,the article provides insight about future trends and needs with respect to hydrodynamic/sediment transport models.In preparing this article,the authors may have uninten-tionally omitted some models,since including all the available models found in the literature is impossible.Finally,this article is mainly focused on multidimensional computational models ͑2D and 3D models ͒;however,a brief overview of the 1D models is also included for providing a rational comparison of the 1D model features with the main features of the 2D and 3D models.Description of ModelsThis section provides information about the model formulation,the spatial and temporal characteristics,the coupling/linkage of the hydrodynamic and sediment components,and the model’s predictive capabilities.Tables 1–3complement this description by providing useful information about the model capabilities to handle unsteady flows,bed load and suspended load,sediment exchange processes,type of sediment ͑cohesive versus cohesion-less ͒,and multifractional sediment rmation about model acronyms,language,availability,and distribution is also provided in Tables 1–3.Tables 4–6summarize examples of the different model applications.The reader can use these case stud-JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008/1D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .ies as a reference guide for model setup,calibration,and verifi-cation.One-Dimensional ModelsSince the early 1980s,1D models have been used with some success in research and engineering practice.Most of the 1D models are formulated in a rectilinear coordinate system and solve the differential conservation equations of mass and momen-tum of flow ͑the St.Venant flow equations ͒along with the sedi-ment mass continuity equation ͑the Exner equation ͒by using finite-difference schemes.Some representative models that are developed on the basis of the previously mentioned equations include MOBED by Krishnappan ͑1981͒,IALLUVIAL by Karim and Kennedy ͑1982͒,CHARIMA by Holly et al.͑1990͒,SEDI-COUP by Holly and Rahuel ͑1990͒,3ST1D by Papanicolaou et al.͑2004͒.The HEC-6formulation by Thomas and Prashum ͑1977͒is also presented in a rectilinear coordinate and is dis-cretized by using finite-difference schemes;but it solves the differential conservation equation of energy instead of the mo-mentum equation.Among other 1D models that use different coordinate systems,equations or schemes of solution are FLUVIAL 11by Chang ͑1984͒,GSTARS by Molinas and Yang ͑1986͒,and OTIS by Runkel and Broshears ͑1991͒.Chang ͑1984͒used a curvilinear coordinate system to solve the governing equations of his model.Molinas and Yang ͑1986͒implemented the theory of minimum stream power to determine the optimum channel width and ge-ometry for a given set of hydraulic and sediment conditions.Runkel and Broshears ͑1991͒modified the 1D advection-diffusion equation with additional terms to account for lateral inflow,first-order decay,sorption of nonconservative solutes,and transient storage of these solutes.Most of the 1D models that are presented here can predict the basic parameters of a particular channel,including the bulk-velocity,water surface elevation,bed-elevation variation,and sediment transport load.All of them,except OTIS,can also pre-dict the total sediment load and grain size distribution of nonuni-form sediment.3ST1D by Papanicolaou et al.͑2004͒cannot differentiate the total sediment load into bed load and suspended load.HEC-6by Thomas and Prashum ͑1977͒and IALLUVIAL by Karim and Kennedy ͑1982͒are not applicable to unsteady flow conditions.Table 1contains the complete model reference and acronym explanation and summarizes the main features for each model.Some of these 1D models have additional specific features.HEC-6by Thomas and Prashum ͑1977͒,for example,decom-poses energy losses into form loss and skin friction loss.MOBED by Krishnappan ͑1981͒can predict the sediment characteristics of a streambed as a function of time and distance for different flow hydrographs.FLUVIAL 11by Chang ͑1984͒accounts for the presence of secondary currents in a curved channel by adjusting the magnitude of the streamwise velocity.The same model can predict changes in the channel bed profile,width,and lateral mi-gration in channel bends.CHARIMA by Holly et al.͑1990͒andHEC-6:Hydraulic Engineering Center;Thomas and Prashum ͑1977͒V .4.2͑2004͒Steady Yes Yes Yes No Entrainment and deposition PDPDF77MOBED:MObile BED;Krishnappan ͑1981͒—Unsteady Yes Yes Yes No Entrainment and deposition C C F90IALLUVIAL:Iowa ALLUVIAL;Karim and Kennedy ͑1982͒—Quasi-steady Yes Yes Yes No Entrainment and deposition C C FIV FLUVIAL 11;Chang ͑1984͒—Unsteady Yes Yes Yes No Entrainment and deposition C P FIV GSTARS:Generalized sediment transport models for alluvial River simulation͑Molinas and Yang,1986͒V .3͑2002͒Unsteady Yes Yes Yes No Entrainment and deposition PDPDF90/95CHARIMA:Acronym of the word CHARiage which means bedload in FrenchHolly et al.͑1990͒—Unsteady Yes Yes Yes Yes Entrainment and deposition C C F 77SEDICOUP:SEDIment COUPled;Holly and Rahuel ͑1990͒—Unsteady Yes Yes Yes No Entrainment and deposition C C F77OTIS:One-dimensional transport with inflow and storage;Runkel and Broshears ͑1991͒V .OTIS-P ͑1998͒Unsteady No Yes No No Advection-diffusion PDPDF 77EFDC1D:Environmental fluid dynamics code;Hamrick ͑2001͒—Unsteady Yes Yes Yes Yes Entrainment anddeposition PD PD F773STD1,steep stream sediment Transport 1D model;Papanicolaou et al.͑2004͒—Unsteady a Yes aYes Yes No Entrainmentand deposition C P F90Note:V ϭversion;C ϭcopyrighted;LD ϭlimited distribution;P ϭproprietary;PD ϭpublic domain;and F ϭFORTRAN.aTreated as a total load without separation.2/JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .OTIS by Runkel and Broshears ͑1991͒can treat transport and fate of conservative contaminants and heat.EFDC1D by Hamrick ͑2001͒can be applied to stream networks.3ST1D by Papanico-laou et al.͑2004͒is capable of capturing hydraulic jumps and simulating supercritical flows;therefore,it is applicable to un-steady flow conditions that occur over transcritical flow stream reaches,such as flows over step-pool sequences in mountain streams.Because of their low data,central processor unit ͑CPU ͒re-quirements,and simplicity of use,1D models remain useful pre-dictive tools even today,especially in consulting,for rivers and stream ecological applications where 2D or 3D models may not be needed and are computationally expensive.Table 4presents examples of different 1D model applications.Two-Dimensional ModelsSince the early 1990s,there has been a shift in computational research toward 2D models.Most of the 2D models are currently available to the hydraulic engineering community as interface-based software to allow easy data input and visualization of re-sults.This added capability has made these models user-friendly and popular.2D models are depth-averaged models that can pro-vide spatially varied information about water depth and bed elevation within rivers,lakes,and estuaries,as well as the mag-nitude of depth-averaged streamwise and transverse velocity com-ponents.Most 2-D models solve the depth-averaged continuity and Navier-Stokes equations along with the sediment mass bal-ance equation with the methods of finite difference,finite element,or finite volume.Table 2shows the complete model reference and explanation of the model acronym and summarizes the characteristics of selected 2D hydrodynamic/sediment trans-port models.The main specific features of each model are de-scribed below:SERATRA:A finite-element sediment-contaminant transport model developed by Onishi and Wise ͑1982͒.The model includes general advection-diffusion equations and incorporates sink/source terms.The model can predict overland ͑terrestrial ͒and in-stream pesticide migration and fate to assess the potential short-and long-term impacts on aquatic biota in receiving streams.SUTRENCH-2D:A finite-volume hydrodynamic and sediment transport model developed by van Rijn and Tan ͑1985͒for simu-SERATRA:SEdiment and RAdionuclide TRAnsport;Onishi and Wise ͑1982͒—Unsteadya Yes a Yes No Yes Advection-diffusion CC/LDFIVSUTRENCH-2D:SUspended sediment transport in TRENCHes;van Rijn and Tan ͑1985͒—Quasisteadya Yes a Yes No No Advection-diffusion C LD F90TABS-2;Thomas and McAnally ͑1985͒—Unsteadya Yes a Yes No Yes Entrainment and deposition C C F77MOBED2:MObile BED;Spasojevic and Holly ͑1990a ͒—Unsteady Yes Yes Yes No Entrainment and depositionC C F77ADCIRC:ADvanced CIRCulation;Luettich et al.͑1992͒—Unsteady a Yes aYes No Yes Advection-diffusionC/LD C/LD F90MIKE 21:Danish acronym of the word microcomputer;Danish Hydraulic Institute ͑1993͒—Unsteady a Yes aYes No Yes Entrainment and deposition CPF90UNIBEST-TC:UNIform BEach Sediment Transport—Transport Cross-shore;Bosboom et al.͑1997͒—Quasi-steadya Yes a Yes No No Entrainment and advection C LD F90USTARS:Unsteady Sediment Transport models for Alluvial Rivers Simulations;Lee et al.͑1997͒—Unsteady Yes Yes Yes No Entrainment and deposition P P F90FAST2D:Flow Analysis Simulation Tool;Minh Duc et al.͑1998͒—Unsteady Yes Yes No No Entrainment and deposition LD P F90FLUVIAL 12;Chang ͑1998͒—Unsteady Yes Yes Yes No Entrainment and deposition C P F77Delft 2D;Walstra et al.͑1998͒—Unsteady Yes Yes No Yes Advection-diffusion C LD F90CCHE2D:The National Center for Computational Hydroscience and Engineering;Jia and Wang ͑1999͒V .2.1͑2001͒Unsteady Yes Yes Yes No Advection-diffusion PD/CLDF77/F90Note:V ϭversion;C ϭcopyrighted;LD ϭlimited distribution;P ϭproprietary;PD ϭpublic domain;F ϭFORTRAN.aTreated as a total load without separation.JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008/3D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .lating sediment transport and associated bed level change under conditions of combined quasi-steady currents and wind-induced waves over a sediment bed.The model solves the general advection-diffusion equations by incorporating a lag coefficient to account for the settling of sediments.TABS-2:A group of finite-element based hydrodynamic and sediment transport computer codes developed by the USACE Wa-terways Experimental Station ͑Thomas and McAnally 1985͒that currently operates by using the SMS v.9.0windows interface.These codes are applicable to rivers,reservoirs,and estuaries.The main components of TABS-2are the hydrodynamic component,RMA2;the sediment transport component,SED2D ͑formally STUDH ͒;and the water quality component,RMA4.MOBED2:A finite-difference hydrodynamic and sediment transport model used in a curvilinear coordinate system,devel-oped by Spasojevic and Holly ͑1990a ͒.The model can simulate water flow,sediment transport,and bed evolution in natural wa-terways such as reservoirs,estuaries,and coastal environments where depth averaging is appropriate.ADCIRC-2D:A finite-element hydrodynamic and sediment transport model developed by Luettich et al.͑1992͒in a rectilin-ear coordinate system for simulating large-scale domains ͑e.g.,the entire East Coast of the United States ͒by using 2D equationsfor the “external mode”but using the “internal mode”for obtain-ing detailed velocity and stress at localized areas.The internal mode is achieved by specifying the momentum dispersion and the bottom shear stress in terms of the vertical velocity profile.The wave-continuity formulation of the shallow-water equations is used to solve the time-dependent,free-surface circulation and transport processes.MIKE2:A finite-difference model in a rectilinear coordinate system developed by the Danish Hydraulic Institute ͑1993͒for simulating transport and fate of dissolved and suspended loads discharged or accidentally spilled in lakes,estuaries,coastal areas,or in the open sea.The system consists of four main model groups ͑modules ͒,namely,the hydrodynamic and wave models,the sediment process model,and the environmental hydrody-namic model groups.The hydrodynamic and wave models are relevant to the types of physical processes considered in flood-plain mapping.The sediment process models are used to simulate shoreline change and sand transport,whereas the environmental hydrodynamic models are used to examine water quality issues.UNIBEST-TC2:A finite-difference hydrodynamic and sedi-ment transport model in a rectilinear coordinate system to de-scribe the hydrodynamic processes of waves and currents in the cross-shore direction by assuming the presence of uniform meanECOMSED:Estuarine,Coastal,and Ocean Model—SEDiment transport;Blumberg and Mellor ͑1987͒V .1.3͑2002͒Unsteady aYesaYes No YesEntrainment and deposition PDPDF77RMA-10:Resource Management Associates;King ͑1988͒—Unsteady aYesaYes No Yes Entrainment and deposition C P F77GBTOXe:Green Bay TOXic enhancement;Bierman et al.͑1992͒—Unsteady No Yes No Yes Entrainment and deposition NA NA F77EFDC3D:Environmental Fluid Dynamics code;Hamrick ͑1992͒—Unsteady Yes Yes Yes Yes Entrainment and deposition PD P F77ROMS:Regional Ocean Modeling System;Song and Haidvogel ͑1994͒V .1.7.2͑2002͒Unsteady Yes Yes Yes No Entrainment and deposition LD LD F77CH3D-SED:Computational Hydraulics 3D-SEDiment;Spasojevic and Holly ͑1994͒—Unsteady Yes Yes Yes Yes Entrainment and deposition C C F90SSIIM:Sediment Simulation In Intakes with Multiblock options;Olsen ͑1994͒V .2.0͑2006͒Steady Yes Yes Yes No Advection-diffusion PD P C-Langua.MIKE 3:Danish acronym of the word Microcomputer;Jacobsen and Rasmussen ͑1997͒—Unsteady aYesaYes No Yes Entrainment and deposition C P F90FAST3D:Flow Analysis Simulation Tool;Landsberg et al.͑1998͒V .Beta-1.1͑1998͒Unsteady Yes Yes No No Entrainment and depositionLD P F90Delft 3D;Delft Hydraulics ͑1999͒V .3.25.00͑2005͒Unsteady Yes Yes No Yes Entrainment anddepositionC LD F77TELEMAC;Hervouet and Bates ͑2000͒—Unsteady a Yes a Yes No Yes Entrainment anddepositionC P F90Zeng et al.͑2005͒—UnsteadyYes Yes No No Entrainment anddepositionPPF90Note:V ϭversion;C ϭcopyrighted;LD ϭlimited distribution;P ϭproprietary;PD ϭpublic domain;F ϭFORTRAN.aTreated as a total load without separation.4/JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .longshore currents along the beach ͑Bosboom et al.1997͒.The bed load and suspended load transport processes are modeled by assuming local equilibrium conditions ͑no lag effects are consid-ered between flow and sediment ͒.USTARS:A modified form of ͑GSTARS ͒that is also based on the stream tube concept ͑Lee et al.1997͒.The hydrodynamic and sediment equations are solved with a finite-difference scheme in a rectilinear coordinate system.As in GSTARS,the theory of mini-mum stream power is used here to determine the optimum chan-nel width and geometry for a given set of hydraulic,geomorpho-logic,sediment,and man-made constraints.FAST2D:A finite-volume hydrodynamic and sediment model with boundary-fitted grids in a curvilinear coordinate system to simulate sediment transport and morphodynamic problems in al-luvial channels ͑Minh Duc et al.1998͒.The model accounts in-directly for secondary effects attributed to the complexity of the domain.FLUVIAL 12:A finite-difference hydrodynamic and sediment model in a curvilinear coordinate system developed by Chang ͑1998͒.The combined effects of flow hydraulics,sediment trans-port,and river channel changes can be simulated for a given flow period.The model is a mobile-bed model and simulates changes in the channel-bed profile,width,and sediment bed composition induced by the channel curvature.DELFT-2D:A finite-difference hydrodynamic and sediment transport model simulating waves and currents ͑Walstra et al.1998͒.The model couples the hydrodynamics with computed bot-tom morphological changes in a time-dependent way.The model can simulate bed-load and suspended load transport by using ei-ther a local equilibrium or a nonequilibrium ͑i.e.,the lag effects between flow and sediment ͒approach.The model can also show the effects of wave motion on transport magnitude and HE2D:A finite-element hydrodynamic and sediment model developed by Jia and Wang ͑1999͒.The model simulates the sus-pended sediment by solving the advection-diffusion equation and the bed-load transport by empirical functions ͑e.g.,Yalin 1972;van Rijn 1993͒.The model accounts for the secondary flow effect in curved channels.All the aforementioned models are applicable to unsteady flow conditions,except SUTRENCH-2D by van Rijn and Tan ͑1985͒and UNIBEST-TC2by Bosboom et al.͑1997͒.All models can predict the total sediment transport load;but only MOBED2,USTARS,FLUVIAL 12,and CCHE2D can handle multifrac-tional sediment transport and can decompose the total sediment load into bedload and suspended load.DELFT-2D and FAST2D can also separate the total sediment load into bedload and sus-HEC-6;Thomas and Prashum ͑1977͒Prediction of the flow and sediment transport along with the bed level change of the Saskatchewan River below Gardiner Dam,Canada ͑Krishnappan 1985͒Prediction of the bed profile for the eroded and redeposited delta sediment upstream from Glines Canyon Dam,Washington ͑U.S.Department of Interior,Bureau of Reclamation 1996͒MOBED;Krishnappan ͑1981͒Comparison of MOBED results with HEC-6results for the flow and sediment transport along with the bed-level change for the Saskatchewan River below Gardiner Dam,Canada ͑Krishnappan 1985͒Prediction of fine sediment transport under ice cover in the Hay River in Northwest Territories,Canada IALLUVIAL;Karim and Kennedy ͑1982͒Simulation of flow and sediment processes in the Missouri River,Nebraska ͑Karim and Kennedy 1982͒Simulation of flow and sediment processes downstream of the Gavins Point Dam on the Missouri River,Nebraska ͑Karim 1985͒FLUVIAL 11;Chang ͑1984͒Simulation of flow and sediment processes of the San Dieguito River,Southern California ͑Chang 1984͒Simulation of flow and sediment processes of the San Lorenzo River,Northern California ͑Chang 1985͒GSTARS;Molinas and Yang ͑1986͒Prediction of the scour depth and pattern at the Lock and Dam No.26replacement site on the Mississippi River,Illinois ͑Yang et al.1989͒Prediction of the variation in channel geometry for the unlined spillway downstream Lake Mescalero Reservoir,New Mexico ͑Yang and Simões 2000͒CHARIMA;Holly et al.͑1990͒Mobile-bed dynamics in the Missouri River from Ft.Randall to Gavins Point Dam,South Dakota ͑Corps of Engineers ͒Mobile-bed dynamics in the Missouri River from Gavins Point Dam to Rulo,Nebraska ͑National Science Foundation ͒SEDICOUP;Holly and Rahuel ͑1990͒Modeling of long-term effects of rehabilitation measures on bed-load transport at the Lower Salzach River,Germany ͑Otto 1999͒Long-term modeling of the morphology of the Danube River,Germany ͑Belleudy 1992͒OTIS;Runkel and Broshears ͑1991͒Simulation of field experiments conducted by Bencala and Walters ͑1983͒for the change in chloride concentration of the Uvas Creek,California.Estimation of the travel times and mixing characteristics of the Clackamas River,Oregon,using the slug of rhodamine data of Laenen and Risley ͑1997͒EFDC1D;Hamrick ͑2001͒Simulation of the flow and sediment transport processes in the Duwamish River and Elliott Bay,Washington ͑Schock et al.1998͒Development of a water quality model for the Christina River,Delaware ͑USEPA 2000͒3STD1;Papanicolaou et al.͑2004͒Prediction of the grain size distribution and bed morphology of the Cocorotico River,Venezuela ͑Papanicolaou et al.2004͒.Prediction of the grain size distribution and bed-load rate of the Alec River,Alaska ͑Papanicolaou et al.2006͒JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008/5D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .pended load,but they are limited to uniform sediment sizes.Ex-amples of the different 2D model applications are summarized in Table 5.Three-Dimensional ModelsIn many hydraulic engineering applications,one has to resort to 3D models when 2D models are not suitable for describing cer-tain hydrodynamic/sediment transport processes.Flows in the vi-cinity of piers and near hydraulic structures are examples in which 3D flow structures are ubiquitous and in which 2D models do not adequately represent the physics.With the latest develop-ments in computing technology—such as computational speed,parallel computing,and data storage classification—3D hydrodynamic/sediment transport models have become much more attractive to use.Most 3D models solve the continuity and the Navier-Stokes equations,along with the sediment mass bal-ance equation through the methods of finite difference,finite ele-ment,or finite-volume.The Reynolds average Navier-Stokes ͑RANS ͒approach has been employed to solve the governing equations.The RANS models can be separated into hydrostatic and non-hydrostatic models.The hydrostatic models ͑e.g.,Gessler et al.1999͒are not able to accurately predict flow and transport phe-nomena in regions where the flow is strongly 3D and where large adverse pressure gradients or massive separation are present ͑e.g.,river bends containing hydraulic structures ͒.On the contrary,non-hydrostatic RANS models have been shown to adequately de-scribe intricate features of secondary flows in complex domains ͑e.g.,Wu et al.2000;Ruther and Olsen 2005͒.Table 3shows the complete model reference and explanation of the acronym and summarizes the characteristics of 12selected 3D hydrodynamic/sediment transport models.The main specific features of each model are described below:ECOMSED:A fully integrated 3D finite-difference hydrody-namic,wave,and sediment transport model in an orthogonal cur-SERATRA;Onishi and Wise ͑1982͒Investigation of the effects of sediment on the transport of radionuclides in Cattaraugus and Buttermilk Creeks,New York ͑Walters et al.1982͒Simulation of the hydrogeochemical behavior of radionuclides released to the Pripyat and Dnieper rivers from the Chernobyl Nuclear Power Plant in Ukraine ͑V oitsekhovitch et al.1994͒SUTRENCH-2D;van Rijn and Tan ͑1985͒Simulation of sand transport processes and associated bed-level changes along dredged pits and trenches at the lower Dutch coast,The Netherlands ͑Walstra et al.1998͒Modeling sediment transport and coastline development along the Iranian coast,Caspian Sea ͑Niyyati and Maraghei 2002͒TABS-2;Thomas and McAnally ͑1985͒Simulation of the flow and sediment transport processes in the Black Lake,Alaska ͑Papanicolaou et al.2006͒Evaluation of the hydraulic performance of different structures found in the Missouri River for creating new shallow water habitat ͑Papanicolaou and Elhakeem 2006͒MOBED2;Spasojevic and Holly ͑1990a ͒Simulation of mobile-bed dynamics in the Coralville Reservoir on the Iowa River,Iowa ͑Spasojevic and Holly 1990b ͒ADCIRC;Luettich et al.͑1992͒Simulation of the flow and sediment transport processes of the natural cap in the Matagorda Bay,Texas ͑Edge 2004͒Simulation of sand transport processes at Scheveningen Trial Trench,The Netherlands ͑Edge 2004͒MIKE 21;Danish Hydraulic Institute ͑1993͒Prediction of the spreading of dredged spoils in the Øresund Link,Denmark-Sweden Prediction of sediment transport rate at ebb flow in a tidal inlet,Grådyb,Denmark UNIBEST-TC;Bosboom et al.͑1997͒Coastal study for the impacts of constructing Kelantan Harbor,MalaysiaCoastal study for shoreline protection of Texel region,The NetherlandsUSTARS;Lee et al.͑1997͒Simulation of sand transport processes and associated bed-level changes of a reach in the Keelung River,Taiwan ͑Lee et al.1997͒Routing of flow and sediment of the Shiemen Reservoir,upstream Tan-Hsui River,Taiwan ͑Lee et al.1997͒FAST2D;Minh Duc et al.͑1998͒Simulation of sediment transport processes and associated bed level changes of a reach in the Bavarian Danube River,Germany ͑Minh Duc et al.1998͒Flood analysis and mitigation on the Orlice River,Poland ͑Beck et al.2003͒FLUVIAL 12;Chang ͑1998͒Simulation of flow and sediment processes of the San Dieguito River,Southern California ͑Chang 1994͒Simulation of flow and sediment processes of the Feather River,Northern California ͑Chang et al.1996͒Delft 2D;Walstra et al.͑1998͒Simulation of sand transport processes and associated bed-level changes along dredged pits and trenches at the lower Dutch coast,The Netherlands ͑Walstra et al.1998͒Simulation of the flow field and sediment transport processes of the Pannerdense Kop and IJssel Kop bifurcations in the Rhine River,The Netherlands ͑Sloff 2004͒CCHE2D;Jia and Wang ͑1999͒Investigation of the effects of the rock pile and the submerged dikes downstream of the Lock and Dam No.2of the Red River Waterway,LouisianaInvestigation of the effects of large woody debris structures on the fluvial processes in the Little Topashaw Creek,Mississippi ͑Wu et al.2005͒6/JOURNAL OF HYDRAULIC ENGINEERING ©ASCE /JANUARY 2008D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y Z h e j i a n g U n i v e r s i t y o n 01/26/13. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

We bring quality to light.RC 100 Reflex CheckerRapid and simple production control for reflex reflectorsThe RC 100 Reflex Checker serves for rapid testing of the retro-reflecting characteristics of retro-reflectors and retro-reflecting materials used mainly for vehicle purpos-es in accordance with ECE R3.Because of its compact design it can replace extensive and time consuming measurements in the photometric laboratory with goniometer.The RC 100 follows a relative measurement method with the aid of a reference retro-reflection standard measured under laboratory conditions.RC 100 total viewApplicationsComparative measurement in mcd/lx Production control of reflex reflectors Supervision of the performance of injection moulding machinesSpecial featuresCompact design: The RC 100 works with a measuring distance proportionally shortened to 1 meter at an observation angle of 20 angular minutes (0.333°). It is equipped with optics especially designed for simulat- ing the conditions in the light channel proportionally. There are no special requirements referring to the installation place so that the device can be installed right at the assembly / production line, e.g. close to the injection moulding machine. No dark room or photometrical lab necessary: The system works independently from secondary lightsources; the sample is being illuminated by an integrat- ed powerful Xenon flash light source with extremely long life time. The triggered amplifier as well as the housing screening of the light enable the system to be used under conditions with normal workplace illumination.Short measurement time: There are no time consuming adjusting procedures necessary. The measurement time is extremely short – less than 0.1 sec. The device consists of the optical housing with test distance of 1 m. At the upper part, the housing contains a photopic detector and the electroniccomponents. The optical housing is fixed to the test table. On the test table an optional adapter plate for interchangeable sample holders are located. The unit is equipped with a serial interface. Via a terminal program, values can be read out for further statistical analysis. Optionally there are available adapter plates and adapters individually designed for specific samples.2Test table topTechnical specificationTypical test samplesAdapter plateAdapter with calibration reflectorOrder Information3Instrument Systems GmbH Kaiserin-Augusta-Allee 16-24 10553 Berlin, Germany Tel.: +49 30 34 99 41-0Fax: +49 30 34 55 054*********************************/optronikInstrument Systems is continually working on the further development of its products.Technical changes, errors and misprints do not justify claims for damages.For all other purposes, our Terms and Conditions of Business shall be applicable.。

数据分析英语试题及答案一、选择题（每题2分，共10分）1. Which of the following is not a common data type in data analysis?A. NumericalB. CategoricalC. TextualD. Binary2. What is the process of transforming raw data into an understandable format called?A. Data cleaningB. Data transformationC. Data miningD. Data visualization3. In data analysis, what does the term "variance" refer to?A. The average of the data pointsB. The spread of the data points around the meanC. The sum of the data pointsD. The highest value in the data set4. Which statistical measure is used to determine the central tendency of a data set?A. ModeB. MedianC. MeanD. All of the above5. What is the purpose of using a correlation coefficient in data analysis?A. To measure the strength and direction of a linear relationship between two variablesB. To calculate the mean of the data pointsC. To identify outliers in the data setD. To predict future data points二、填空题（每题2分，共10分）6. The process of identifying and correcting (or removing) errors and inconsistencies in data is known as ________.7. A type of data that can be ordered or ranked is called________ data.8. The ________ is a statistical measure that shows the average of a data set.9. A ________ is a graphical representation of data that uses bars to show comparisons among categories.10. When two variables move in opposite directions, the correlation between them is ________.三、简答题（每题5分，共20分）11. Explain the difference between descriptive andinferential statistics.12. What is the significance of a p-value in hypothesis testing?13. Describe the concept of data normalization and its importance in data analysis.14. How can data visualization help in understanding complex data sets?四、计算题（每题10分，共20分）15. Given a data set with the following values: 10, 12, 15, 18, 20, calculate the mean and standard deviation.16. If a data analyst wants to compare the performance of two different marketing campaigns, what type of statistical test might they use and why?五、案例分析题（每题15分，共30分）17. A company wants to analyze the sales data of its products over the last year. What steps should the data analyst take to prepare the data for analysis?18. Discuss the ethical considerations a data analyst should keep in mind when handling sensitive customer data.答案：一、选择题1. D2. B3. B4. D5. A二、填空题6. Data cleaning7. Ordinal8. Mean9. Bar chart10. Negative三、简答题11. Descriptive statistics summarize and describe thefeatures of a data set, while inferential statistics make predictions or inferences about a population based on a sample.12. A p-value indicates the probability of observing the data, or something more extreme, if the null hypothesis is true. A small p-value suggests that the observed data is unlikely under the null hypothesis, leading to its rejection.13. Data normalization is the process of scaling data to a common scale. It is important because it allows formeaningful comparisons between variables and can improve the performance of certain algorithms.14. Data visualization can help in understanding complex data sets by providing a visual representation of the data, making it easier to identify patterns, trends, and outliers.四、计算题15. Mean = (10 + 12 + 15 + 18 + 20) / 5 = 14, Standard Deviation = √[(Σ(xi - mean)^2) / N] = √[(10 + 4 + 1 + 16 + 36) / 5] = √52 / 5 ≈ 3.816. A t-test or ANOVA might be used to compare the means ofthe two campaigns, as these tests can determine if there is a statistically significant difference between the groups.五、案例分析题17. The data analyst should first clean the data by removing any errors or inconsistencies. Then, they should transformthe data into a suitable format for analysis, such ascreating a time series for monthly sales. They might also normalize the data if necessary and perform exploratory data analysis to identify any patterns or trends.18. A data analyst should ensure the confidentiality andprivacy of customer data, comply with relevant data protection laws, and obtain consent where required. They should also be transparent about how the data will be used and take steps to prevent any potential misuse of the data.。

Transfer matrix method applied to the parallel assembly of sound absorbing materialsK e vin Verdie `re,a)Raymond Panneton,and Sa €ıd ElkounGAUS,Department of Mechanical Engineering,Universit ede Sherbrooke (Qc),J1K 2R1,Canada Thomas Dupont and Philippe LeclaireDRIVE,ISAT,Universit ede Bourgogne,49Rue Mademoiselle Bourgeois,58027Nevers Cedex,France (Received 24October 2012;revised 5February 2013;accepted 11February 2013)The transfer matrix method (TMM)is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer.In this work,a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks,acoustic mosaics,or a collection of acoustic elements in parallel.In this method,it is assumed that each parallel element can be modeled by a 2Â2transfer matrix,and no diffusion exists between elements.The resulting transfer matrix of the parallel assembly is also a 2Â2matrix that can be assembled in series with the classical TMM.The method is validated by comparison with finite element (FE)simulations and acoustical tube measurements on different parallel/series configurations at normal and oblique incidence.The comparisons are in terms of sound absorption coefficient and transmission loss on experimental and simulated data and published data,notably published data on a parallel array of resonators.From these comparisons,the limitations of the method are discussed.Finally,applications to three-dimensional geometries are studied,where the geometries are discretized as in a FE pared to FE simulations,the extended TMMyields similar results with a trivial computation time.VC 2013Acoustical Society of America .[/10.1121/1.4824839]PACS number(s):43.55.Ev,43.55.Rg,43.20.Bi [KVH]Pages:4648–4658I.INTRODUCTIONIn our modern society,noise pollution is a serious con-cern as it has a profound impact on the economy,health,and productivity.Thus,the need to reduce noise has led to the development of a wide range of sound barriers and/or absorbing materials.Among the most used sound-absorbing materials,porous materials exhibit,in general,fairly high sound absorption coefficients.However,their acoustic per-formances are highly dependent upon frequency and are still poor at low frequency.To overcome this problem,different porous materials canbe stacked to obtain porous multilay-ered materials.Knowing the properties of each layer,the acoustical behavior of multilayered materials can easily be predicted using the transfer matrix method (TMM)for mate-rials stacked in series.1In contrast,for parallel stacking of materials,the Finite Element Method (FEM)is the most gen-eral approach to derive acoustic properties.For instance,the acoustic properties of micro-perforated panels (MPPs)with different parallel cavity sizes,2parallel tubes in mufflers,3parallel periodic structures,4,5and parallel assembly of po-rous material 6can be obtained using FEM simulations or an-alytical models developed for specific cases and,therefore,limited to few applications and difficult to generalize.As far as we know,no study has been published yet using TMM for deriving the acoustic properties of multilayered materials made of parallel stacking of various materials and structures.In electrical engineering,transfer matrices are widely used to model portions of circuits that are connected together.Transfer matrices are not only used to describe series and parallel circuits but combinations of these matrices are fre-quently used to solve various problems.7The aim of this paper is to give an extension of the TMM to account for the assembly of materials (or acoustic elements)in parallel and series and not in series only.In this work,the parallel arrangement is also referred to as patch-work or acoustic mosaic and its development is based on a method reported in the literature to simulate dead-end pores in aluminum foams.8The proposed method is generalized and validated through examples and its limits are discussed and applied to complex three-dimensional (3D)geometries.II.THEORYThe TMM is regarded as a powerful method to predict sound absorption and sound transmission of multilayered mate-rials.1It is mainly used to obtain the sound absorption coeffi-cient and transmission loss of assemblies consisting of laterally infinite and homogeneous material layers stacked in series.In this work,a method for assembling transfer matrices of elements stacked in parallel is developed.This parallel arrangement of elements is also referred to as a patchwork construction or an acoustic mosaic.An example is shown in Fig.1.The construction is defined by a periodic elementary patchwork shown in bold in Fig.1.The key assumptions underlying the method are:(1)Only plane waves propagate upstream and downstream of the construction;(2)only normal incidence plane waves propagate in the construction;(3)noa)Author to whom correspondence should be addressed.Electronic mail:Kevin.Verdiere@USherbrooke.capressure diffusion exists between adjacent parallel elements,(4)the wavelength is much larger than the periodic elemen-tary patchwork,and (5)each element can be represented by a 2Â2transfer matrix.Following the latter assumption,ele-ments could be either perforated plates,fluids,porous materi-als modeled as equivalent fluids,9a serial assembly of the aforementioned elements,a measured 2Â2transfer matrix,10or whatever that can be expressed by a 2Â2transfer matrix.The two-dimensional (2D)schematic representation of the studied parallel construction is depicted in Fig.2.It con-sists of the stacking of N elements arranged in parallel sepa-rating two air domains.Following assumption (2),each element may be seen as being locally reacting and a wave-guide along the x axis.Each element can consist of a single material or a stack of materials in series.To link the acoustic pressures P and the x -component U of the acoustic velocities in the air on either side of element i ,the following 2Â2transfer matrix relation is used:P ðM i ÞU ðM i Þ¼T iP ðM 0i ÞU ðM 0i Þ ¼t i ;11t i ;12t i ;21t i ;22 P ðM 0i ÞU ðM 0i Þ;(1)where t i,mn are the coefficients of transfer matrix T i .Assuming element i is a rigid frame open cell porous ele-ment of thickness h ,the transfer matrix would be given by 1T i ¼cos ðk eq ;i h ÞjZ ceq ;i sin ðk eq ;i h Þj 1Z ceq ;i sin ðk eq ;i h Þcos ðk eq ;i h Þ2435;(2)where j 2¼À1,and Z ceq,i and k eq,i are the characteristic imped-ance and wave number of the equivalent fluid element—to be distinguished from the characteristic impedance Z c,i of the fluidphase.9The relation between both impedances is Z ceq,i ¼Z c,i //i ,where /i is the open porosity of the element.It is worth mentioning that Eq.(2)assumes propagation parallel to the element axis to conform to assumption (2).Since the elements are in parallel,it is more convenient to work with admittances.Consequently,Eq.(1)can be writ-ten in terms of an admittance matrix Y i as follows:U ðM i ÞU ðM 0i Þ ¼Y i P ðM i ÞP ðM 0i Þ;(3)withY i ¼y i ;11y i ;12y i ;21y i ;22¼1t i ;12t i ;22t i ;21t i ;12Àt i ;22t i ;111Àt i ;11:(4)If the reciprocity principle 11applies,the determinant of T i is equal to unity (i.e.,t i,11t i,22Àt i,12t i,21¼1),and y i,12¼Ày i,21.In this case,up to sign,Eq.(4)shows that the ad-mittance matrix is symmetric.This is expected since the x -component of the acoustic velocity was used instead of the normal acoustic velocity with normal vector inward to the construction domain as usually done following an admit-tance approach.Here,the x -component is preferred with a view to comply with the classical TMM description.1A.Case with all open elements upstream and downstreamConsider that initially all the elements of the construction are open to air on the upstream and downstream sides.Following assumptions (1)and (4),since only plane waves propagate in the surrounding air,the pressure is uniform over the upstream and downstream faces in the air.This imposes continuity of pressure at each air-element interface.Similarly,FIG.1.Example of a patchwork construction,or acoustic mosaic,made from a periodic assembly of parallel acoustical elements (e.g.,Helmholtz or quarter wavelength resonator)or materials (e.g.,porous or fibrous material).The periodic elementary patchwork is shown in bold.In this example,the el-ementary patchwork is composed of N ¼3elements.FIG.2.Plane wave impinging on the studied parallel construction made of N parallel elements.The arrows represent plane waves.continuity of flow rate is preserved at the interfaces.These continuity conditions can be written asP ðM i ÞP ðM 0i Þ¼P P 0(5)andU U 0¼X r iU ðM i ÞU ðM 0i Þ;(6)where P and U are the uniform acoustic fields in the incident air medium on the upstream surface of the construction,and P 0and U 0are the uniform acoustic fields in the transmitted air medium on its downstream surface.In Eq.(6),r i is the surface ratio of element i given byr i ¼S i =S total ;(7)where S i and S total are the cross-sectional surface areas of element i and the construction,ing the conti-nuity conditions,Eqs.(5)and (6),and the admittance matrix system,Eq.(3),it followsU U 0¼X r iy i ;11y i ;12y i ;21y i ;22PP 0: (8)This is the admittance system of the whole parallel construc-tion.This admittance system can be reformulated in terms ofa transfer matrix system asP U ¼T pPU 0;(9)withT p ¼À1R r i y i ;21ÂR r i y i ;22À1R r i y i ;22R r i y i ;11ÀR r i y i ;12R r i y i ;21ÀR r i y i ;11!;(10)where T p is the transfer matrix of the parallel construction when all the elements are open at their ends.This transfer matrix relates the acoustic fields in the air before the con-struction to the acoustic fields in the air behind the material.B.Case with closed elements downstreamConsider the particular case where some elements are closed on the downstream side—the rest being open to air.In this case,each element must be clearly identifiable.Accordingly,subscript j will stand for open-ended elements while subscript k will refer to close-ended elements.While the continuity conditions on the flow rate and the upstream pressure remain unchanged,the continuity of pressure on the downstream side is only ensured for the open-ended ele-ments.Consequently,Eq.(5)becomesP ðM i ÞP ðM 0j Þ ¼PP 0 :(11)For element k closed to end,the normal velocity vanishes at M 0k ,and the admittance system,Eq.(3),yields the following condition:P ðM 0k Þ¼Ày k ;21y k ;22P :(12)Finally,replacing Eq.(5)by Eqs.(11)and (12),and applying the same procedure,the transfer matrix of the parallel con-struction can be rewritten asT p ¼À1j j ;21R r j y j ;22À1R r j y j ;22R r i y i ;11ÀR r k y k ;12y k ;21y k ;22ÀR r j y j ;12R r j y j ;21R r ky k ;12y k ;21y k ;22ÀR r i y i ;11B B @1C C A:(13)This time,T p is the transfer matrix of the parallel construc-tion where some elements are open to air on the down-stream side,and some are closed.One can verify that if there is no close-ended elements (i.e.,subscript k vanishes and subscript j is identical to i ),then Eq.(13)is identical to Eq.(10).A similar development can be done for the case where some elements are closed on the upstream side,or on both sides.While Eq.(13)seems to be general,one needs to pay attention to the case where all elements are close-ended(i.e.,no j subscript).In this case,Eq.(13)does not hold due a division by 0in the term before the matrix.As a matter of fact,to use Eq.(13),at least one element must be open-ended.In the situation where all elements are closed to end (i.e.,the construction is backed by a rigid wall),one should use Eq.(10)to retrieve the acoustic properties.This is simi-lar to the classical TMM and described in Sec.II C .Also,it is worth noting that if all elements of the con-struction are reciprocal,then both systems [Eqs.(10)and (13)]are in line with the reciprocity principle which stipulatesthat det(T p )¼1.However,if all elements respect the mate-rial symmetry condition t 11¼t 22(i.e.,same acoustical sur-face properties on both sides),then only the transfer matrix of Eq.(10)shows the same symmetry condition.Finally,it is highlighted that each porous element is counter-balanced by its surface ratio,and matrix T p is the same whatever the element position.Moreover,the construc-tion of matrix T p does not require to take into account or to know the number of similar entities that composed the patch-work construction.Indeed and for instance,a patchwork made of four equal elements,where two elements are filled with material A and the other two with material B,can be regarded as composed of two elements of material A and two elements of material B or,because of assumption (4),one element of material A (r 1¼50%)and one element of material B (r 2¼50%).In fact,with assumption (4),the acoustic wavelength is supposed to be much larger than the periodic elementary patch (or mosaic characteristic size)and thus can be considered as homogeneous.The validation of this approach is discussed in the experimental part of the present study.C.Coupling parallel and serial constructionsThe developed transfer matrix for parallel constructions can be assembled in series with other homogeneous layers following the classical method.As an example,consider an air cavity of thickness L modeled by the following 2Â2transfer:T air ¼cos ðk 0L cos w Þj Z 0cos w sin ðk 0L cos w Þj cos w Z 0sin ðk x L Þcos ðk 0L cos w Þ26643775;(14)where Z 0and k 0are the characteristic impedance and wave number in air,and w is the angle of incidence of the plane wave in air.If the air cavity is backing the patch-work,the global transfer matrix of the parallel/serial con-struction isP U ¼T GP 0U 0with T G ¼T p T air ¼T 11T 12T 21T 22:(15)From this global transfer matrix,one can calculate the hard-backing normal incidence sound absorption coefficient and the anechoic-end normal incidence sound transmission loss by,respectively,a ¼1ÀT 11cos W ÀT 21Z 0T 11cos W ÀT 21Z 02(16)andNSTL ¼20log 1012T 11þT 22þcos w Z 0T 12þZ 0cos w T 21 !:(17)Note that if the absorption and transmission loss of a patch-work construction is studied only,the transfer matrix coeffi-cients to use in Eqs.(16)and (17)are those given by T p .III.MATERIALS AND METHODSTo obtain the transfer matrix of the patchwork construc-tion,the transfer matrix of each element must be known.Forthe validation results presented in Sec.IV ,only rigid or limp frame open-cell porous elements are considered.Consequently,transfer matrices of Eq.(2)are used.The equivalent fluid properties Z ceq and k eq populating Eq.(2)are computed by the use of the Johnson-Champoux-Allard model.1This model requires five parameters:Porosity,static airflow resistivity,tortuosity,viscous,and thermal character-istic lengths (or six parameters for limp frame 9with the addi-tional parameter being the bulk density of the porous aggregate).These properties are obtained as described by Doutres et al.12Table I depicts the selected porous materials and their main physical characteristics.Except for material D,all properties have been experimentally assessed follow-ing Ref.12.For material D,where diffusion phenomena have been evidenced,data published by Olny and Boutin have been used.13The predictions obtained with the TMM are systemati-cally compared to impedance/transmission tube measure-ments.The schematic of the tube is shown in Fig.3.It consists of a 44.5mm or a 100mm diameter tube supporting three microphones.The cut-off (maximum)frequencies of the tubes are 4100and 1800Hz,respectively.From pressure measurements at the three microphones,normal incidence (i.e.,w ¼0)sound absorption coefficient and sound transmis-sion loss are deduced according to the three microphone method 10and standard ASTM E2611-09.14All experimental data are compared to virtual measurements obtained with 3D acoustical FEM simulations using COMSOL software.The FEM model is a reproduction of the setup shown in Fig.3.InTABLE I.Physical properties of selected materials.Material/r (N s m -4)K (l m)K 0(l m)a 1q 1(kg/m 3)A Melamine foam 0.9999724110122 1.008.3B Glass wool 0.9991595797530 1.0040C Rock wool 0.960415549292 2.5990DRock wool (diffusion)(Ref.13)0.94013500049166 2.10—E Polyurethane foam0.95811188702091.9429FIG.3.Experimental and FEM model diagram of the three-microphone impedance/transmission tube.the FEM model on COMSOL,parabolic tetrahedral elements are used to mesh the different acoustic domains of the tube,and convergence of the results is verified in the frequency range of interest.Also,the porous elements of the construc-tion samples are modeled as equivalent fluids using complex sound speed (c eq ¼x /k eq ,where x is the angular frequency)and dynamic density (q eq ¼Z ceq k eq /x )given by the Johnson-Champoux-Allard model previously described.IV.RESULTS AND DISCUSSION A.Parallel construction 1.Normal incidenceThe first construction studied is a cylindrical assembly of N ¼4materials in parallel under a normal incidence plane wave (w ¼0).The materials are the melamine foam,glass wool,rock wool,and polyurethane foam corresponding to materials A,B,C,and E of Table I .Each material represents 25%of the total surface and the cylinder is longitudinally split into four pieces.The cylinder is 50mm thick and its di-ameter is 100mm.For the impedance tube test,with a view to respect assumption (3)of the TMM (no pressure diffusion between elements),each material is isolated by an ABS plas-tic cross grid inserted in the tube,see Fig.4.The same setupis used for the FEM simulation.Figure 4depicts the absorp-tion coefficient and the transmission loss of this parallel construction as a function of frequency.One can notice that both acoustic properties obtained by the TMM are consistent with data predicted by the FEM simulation and experiment.However a divergence between the TMM and FEM data can be observed at frequencies above 1600Hz.This is due to the fact that the grid creates a sound field disturbance that lowers the cutoff frequency of the tube from 1800to 1600Hz.A modal analysis with the FEM model has confirmed this.To improve the validity of the TMM,insets of acoustic proper-ties of each material which compose the parallel assembly are added in Fig.4.As you can see,these properties are clearly different from those of the construction.2.Oblique incidenceThe acoustic properties of the previous construction are now obtained under oblique incidence.Since no experimen-tal setup is available for the oblique incidence test,the TMM is compared to FEM simulation only.The FEM model for oblique incidence is shown in Fig.5.A sample is excited by an oblique plane wave.Since the sample reacts locally [assumption (2)],the wave is guided along the normal to its surface,comes out at the same incidence angle,andreflectsFIG.4.Normal incidence sound absorption coefficient and transmission loss of a parallel assembly of four materials:Melamine foam (A),glass wool (B),rock wool (D),and polyurethane foam (E).The four materials are inserted in an impervious cross parison between TMM,FEM,and experimental results.Acoustic parameters of each material composing the assembly areinset.FIG.5.Schematic view of the oblique incidence impedance tube setup for the FEM.on the rigid wall.To evaluate the absorption coefficient and transmission loss,the three microphone method described in Sec.III is used.This oblique incidence arrangement has al-ready been used experimentally by Mei et al.15to estimate absorption coefficient of a metamaterial under an oblique incidence plane wave;however,the transmission loss was not evaluated.With the aforementioned FEM model,results are obtained with and without the cross grid at an angle of inci-dence of 30 .The FEM results with and without the grid are compared to the TMM results in Fig.6.Apart from frequen-cies above 1600Hz (see discussion above),the TMM correlates with the cross grid FEM case.However,for the case without the grid,the discrepancy observed in the trans-mission loss can be explained by the fact that there is a weak diffusion between materials.For more about the diffusion phenomenon,the reader should refer to Sec.IV C .One can notice,even without the impervious walls between materials,the absorption coefficient is in line with the TMM results.This is probably due to the fact that the diffusion is low and the impedance mismatch between materials acts as a wall.Overall,from the previous results,one can reasonably con-clude that the proposed parallel TMM is valid for the parallel stacking of elements made of different porousmaterialsFIG.6.Oblique (30 )incidence sound absorption coefficient and transmission loss of the parallel assembly of four materials,with the cross grid (top),and without the cross grid (bottom).Comparison between TMM and FEMresults.FIG.7.Normal incidence sound absorption coefficient and transmission loss of a parallel/series patchwork of melamine foam and parison between TMM,FEM,and experimental yout 1and Layout 2are simulated with TMM.Acoustic parameters of a full double layer are inset.provided that each component is independent [assumption (3)]or diffusion between adjacent elements is weak (low perme-ability contrast between adjacent elements).Note that similar conclusions have been also obtained using different surface ratios.B.Parallel/series patchworkIn this section,TMM is used to describe sound absorp-tion coefficient and transmission loss for a two layered con-struction,where the first layer is a homogeneous melamine foam,and the second layer is a parallel stacking of melamine foam (r ¼50%)and air (r ¼50%).The construction is 100mm thick Â100mm in diameter.Figure 7shows a sche-matic view of the construction,and particularly the two selected layouts for modeling.For the experimental test and FEM simulation,no rigid wall between the air and the mela-mine in the second layer was used.A priori ,it seems con-trary to assumption (3).However,it will be discussed in Sec.IV C that assumption (3)can be violated under certain circumstances.The construction depicted in Fig.7can be modeled fol-lowing two layouts with the TMM.The first layout consists in modeling a homogeneous layer (layer 1)in series with a paral-lel construction (layer 2).In that case,the global transfer ma-trix T G of the multilayer (referred to as layout 1)is obtained by multiplying transfer matrix T 1[Eq.(2)]of layer 1and transfer matrix T p of heterogeneous layer 2.The second lay-out consists in modeling two elements in parallel.In that case,the global transfer matrix T G of the multilayer (referred to as layout 2)is obtained by the parallel assembly of transfer ma-trix T 1T air of element 1and transfer matrix T 2of element 2.Figure 7depicts the absorption coefficient and the trans-mission loss of the parallel/series configuration predicted by the TMM,the FEM,and the experiments.As one can note,the experimental results show frame resonance.Below the first frame resonance at 400Hz,the behavior is mainly stiffness-controlled,and above the first resonance it becomes partially mass controlled.Consequently to take into account for the mass effect of the frame above the resonance,a limp frame equivalent fluid model 9is used for the TMM.However,if one wants to better capture the low-frequency behavior,a rigid frame model could be used below the first resonance.Overall,the comparisons in Fig.7show that the TMM correlates well with both the FEM and the experiments.However,one can notice that the TMM predictions of the transmission loss of the two layouts are slightly different (61dB).It is thought that this difference is associated with the fact that assumption (2)is partly violated in layout 1in the vicinity of the interface between both layers.However,the predictions remain satisfactory with both layouts.To comfort it,in Fig.7,the insets of acoustic parameters of a full double layer are presented.By halving the second layer,sound absorption is similar to one obtained for a full double layer with a slight decrease at 1500Hz However,its impact on transmission is most important and well reproduced by the model developed TM.Halving the second layer reduces TL by approximately 3dB in this case.A similar configuration has also been studied by Lanoye et al.16Their work is an investigation of the acoustic per-formance of sound absorbing patches through a numerical wave based prediction method (WBM),where its main advantage is that the sound absorbing patches do not havetoFIG.8.Normal incidence sound absorption coefficient of the two parallel/s-eries patchworks of melamine foam and air (case 4),and melamine foam and rigid solid (case 5).Comparison between TMM and the results of Lanoye et al.forWBM.FIG.9.Acoustic pressure field at 2000Hz in the middle plane of an impedance tube (source is on the right)to highlight the diffusion phenomenon in a macro perforated rock wool sample backed by an air cavity.be locally reacting.This method has been validated experi-mentally for a normal incidence sound absorption case in a 0.6Â0.6m 2impedance tube.Figure 8shows the comparison between the TMM and the WBM for two configurations.The first configuration is 50mm thick layer of melamine foam stacked on a 50mm thick parallel assembly of 50%melamine foam and 50%air.This configuration refers to case 4in the paper by Lanoye et al.The second configura-tion is similar to the first one,where the air element is replaced by a perfectly rigid element.This second configura-tion refers to case 5in the paper by Lanoye et al.As can be seen in Fig.8,the TMM correlates with the WBM;however,the TMM is more computationally efficient.Note that the melamine foam is modeled as a poroelastic material in the work by Lanoye et al.;this explains oscillations in the WBM results due to frame vibrations.C.Double porosity media with diffusionDouble porosity medium can be seen as parallel con-structions.Olny et al.13have shown that for such media,interaction phenomena may occur depending upon perme-ability contrast.This latter is given by media size,surface ratio between media,contact shape,and distribution of the first medium with regard to the second one.Indeed,in the case of low permeability contrasts,no interaction exists.According to Olny and Boutin,the velocity field is slightly disturbed and thus the pressure field is almost uniform.Consequently,the TMM is expected to give good results.Moreover,for low permeability contrasts,no physical rigid walls are required to isolate media,which allows new decompositions as discussed in Sec.IV B .For high perme-ability contrasts,the pressure and velocity fields are both disturbed and the interaction appears as diffusion phenom-ena.The TMM is used to attempt modeling a diffusion case.Based on a previous work published by Sgard et al.,17a rock wool block sample having a perforated hole at the center is modeled by FEM.The block is 83mm high,83mm wide,and 115mm thick,and the perforation diame-ter is 32mm.Figure 9shows the acoustic pressure field at 2000Hz obtained by FEM simulation in the middle plane of the simulated impedance tube.As can be seen,this pres-sure is not uniform along the plane and seems to be diffused in rock wool.Figure 10depicts the absorption coefficient and the transmission loss of this sample obtained by TMM and FEM simulations.It is clear that data obtained by FEM and TMM are not in line.It is also interesting to note that the transmission loss obtained by TMM exhibits a drop at around 1500Hz corresponding to the perforation length.It can be explained by the fact that the perforated rockwool behaves as an expansion chamber because TMM creates a virtual impervious wall between air and rockwool andtheirFIG.10.Normal incidence sound absorption coefficient and transmission loss of a macro perforated rock wool of high static airflow parison between TMM and FEMresults.FIG.11.Normal incidence sound absorption coefficient of the MPP absorber array consisting of a MPP of 1%perforation ratio,0.5mm thick,and orifice di-ameter d .The MPP is backed by three parallel air gap of thickness 25,50,and 100mm,parison between TMM and Wang and Huang results for two orifice diameters:0.5mm (left)and 0.8mm (right).。

对比类比的英语作文模板Title: Comparison and Analogy English Composition Template。

Introduction:The purpose of this essay is to explore the concept of comparison and analogy in English composition. We will delve into the definitions of these two literary devices, examine their differences, and provide examples to illustrate their usage.Definition of Comparison:Comparison is a literary device used to describe the similarities between two or more things. It is often used to create vivid imagery and enhance the reader's understanding of a concept. Comparisons can be made using similes, metaphors, or analogies.Similes:Similes are comparisons that use the words "like" or "as" to show the similarities between two things. For example, "Her smile was as bright as the sun" is a simile that compares the brightness of a smile to the brightness of the sun.Metaphors:Metaphors are comparisons that do not use "like" or "as." Instead, they directly equate one thing to another. For example, "The world is a stage" is a metaphor that compares the world to a stage, suggesting that life is like a play with different acts and characters.Analogy:An analogy is a comparison between two things, typically for the purpose of explanation or clarification. It is used to show how two things are alike in some ways. For example, "Just as a caterpillar transforms into a butterfly, so too does a student transform into a scholar."Definition of Analogy:An analogy is a literary device used to explain or clarify a concept by comparing it to something that is familiar to the reader. It is often used to make abstract ideas more concrete and understandable. Analogies can be found in literature, speeches, and everyday conversations.Differences between Comparison and Analogy:While both comparison and analogy involve drawing similarities between two things, they differ in their purpose and usage. Comparisons are used to create vivid imagery and enhance the reader's understanding, while analogies are used to explain or clarify a concept by comparing it to something familiar. Comparisons can be made using similes, metaphors, or analogies, while analogies are specifically used for explanation and clarification.Examples of Comparison and Analogy:To further illustrate the differences between comparison and analogy, let's look at some examples:Comparison:1. The night sky was as dark as coal.2. Her laughter was like music to his ears.3. The old man's eyes were as sharp as an eagle's.Analogy:1. Just as a seed needs water and sunlight to grow, so too does a student need guidance and support to thrive.2. The relationship between a teacher and a student is like a gardener nurturing a plant, providing the necessary care and attention for growth.3. Learning a new language is similar to unlocking a door to a whole new world, with endless opportunities and experiences.Conclusion:In conclusion, comparison and analogy are powerful literary devices that enhance the reader's understanding and create vivid imagery. While both involve drawing similarities between two things, they differ in their purpose and usage. Comparisons are used to create vivid imagery, while analogies are used to explain or clarify a concept by comparing it to something familiar. By understanding the differences between these two devices, writers can effectively convey their ideas and engage their readers in a meaningful way.。

两个学科比较英语作文范文Title: A Comparative Analysis of Two Academic Disciplines: English and Mathematics。

Introduction:In the realm of academia, English and Mathematics stand as two pillars of knowledge, each possessing distinct characteristics and methodologies. While English explores the nuances of language and communication, Mathematics delves into the realm of numbers, patterns, and logic. This essay aims to compare and contrast these two disciplines in terms of their nature, methodologies, and practical applications.Nature of the Disciplines:English:English is a multifaceted discipline that encompasseslanguage, literature, and communication. It involves the study of grammar, vocabulary, writing styles, literary devices, and critical analysis of texts. Beyond linguistic aspects, English also delves into cultural contexts,societal issues, and historical perspectives through literature.Mathematics:Mathematics, on the other hand, is characterized by its focus on numbers, quantities, shapes, and patterns. It operates through logical reasoning and rigorous proofs, aiming to describe and understand the fundamentalstructures of the universe. Mathematics is often considered a universal language due to its precise and abstract nature, transcending cultural and linguistic barriers.Methodologies:English:The study of English involves a diverse range ofmethodologies, including close reading, textual analysis, comparative literature studies, and creative writing. It often relies on interpretation and subjective analysis, encouraging students to engage critically with texts and express their ideas through written communication.Mathematics:Mathematics, in contrast, relies heavily on deductive reasoning, logical proofs, and problem-solving techniques. It emphasizes precision, clarity, and rigor in its approach to understanding abstract concepts such as algebra, calculus, geometry, and statistics. Mathematics often involves a step-by-step process of problem-solving, where each solution builds upon established principles and theorems.Practical Applications:English:The skills acquired through the study of English havediverse practical applications in fields such as education, journalism, publishing, advertising, and creative industries. Proficiency in English enhances communication skills, critical thinking, and cultural awareness, makingit indispensable in a globalized world.Mathematics:Similarly, mathematics finds extensive applications across various domains, including science, engineering, finance, computer science, and data analysis. From designing bridges to modeling natural phenomena, mathematics serves as the foundation for technological advancements and scientific discoveries. Proficiency in mathematics equips individuals with analytical skills, problem-solving abilities, and logical reasoning, essential for success in many professions.Conclusion:In conclusion, while English and Mathematics may seem worlds apart in terms of their subject matter andmethodologies, both disciplines play crucial roles in shaping our understanding of the world and honing essential skills. Whether it's through the eloquence of language or the precision of numbers, the study of these disciplines enriches our lives and empowers us to navigate the complexities of the modern era. Ultimately, embracing the diversity of knowledge offered by English and Mathematics opens doors to endless opportunities for learning and growth.。

第24卷第12期2009年12月航空动力学报Journal of Aerospace Pow erVol.24No.12Dec.2009文章编号:100028055(2009)1222784205仿真结果距离检验方法和TIC 方法对比分析傅惠民,陈建伟(北京航空航天大学小样本技术研究中心,北京100191)摘 要:针对仿真结果动态一致性的检验,将距离检验方法和TIC (Theil πs inequality coefficient )方法进行了对比分析.距离检验方法可以在一定显著性水平下给出一致性检验的拒绝域,在时域内实现了定量检验.TIC 方法的检验指标是TIC 系数,经过研究发现,TIC 系数的计算结果可以通过坐标原点的选取而进行人为调整,大大增加了误判的可能性,所以TIC 方法既不能定量检验,也不能有效的定性检验.对比研究表明:距离检验方法不受量纲、坐标原点选取等因素影响,其检验结果具有更高的可信性.关　键　词:仿真结果;动态一致性;距离检验法;TIC (Theil πs inequality coefficient )方法中图分类号:TP39119 文献标识码:A收稿日期:2009209221;修订日期:2009210215基金项目:国家自然科学基金(10472006);北京市教育委员会共建项目(XK100060418)作者简介:傅惠民(1956-),男,浙江遂昌人,“长江学者”特聘教授,博士,主要从事小样本信息技术、软校准技术、数据融合方法及可靠性研究.Comparison bet w een distance test method and TIC methodfor simulation resultsFU Hui 2min ,C H EN Jian 2wei(Research Center of Small Sample Technology ,Beijing U niversity of Aeronautics and Astronautics ,Beijing 100191,China )Abstract :According to dynamic co nsistency test of simulation result s ,comparative a 2nalysis of distance test met hod and TIC (Theil ’s inequality coefficient )met hod was given.As t he rejection regions for dynamic simulation result test were obtained at a given level of significance by t he distance test met hod ,quantitative test of dynamic consistency was real 2ized.TIC coefficient was used to test t he simulation result consistency ,but t he coefficient could be affected by selection of coordinate origin ,causing possibly misjudgement.There 2fore ,t he met hod cannot realize quantitative test ,nor realize effectively qualitative test.The comparative analysis shows t hat t he distance test met hod will not be affected by dimension and selection of coordinate origin ,and reach a high credibility of test result s.K ey w ords :simulation result ;dynamic consistency ;distance test met hod ;TIC (Theil πs inequality coefficient )met hod 仿真技术在航空、航天、核工业、电力等领域都有着广泛的应用,但是仿真结果的正确性和可信性长期受到质疑,严重制约了仿真技术的发展.如果仿真不正确,极有可能产生严重的误导后果,从而导致重大的损失和浪费.工程中最直接、最基本的检验方法就是检验在相同输入条件下仿真试验输出结果和实际试验输出结果之间是否一致.根据输出结果的不同分为动态一致性检验和静态一致性检验,仿真结果动态一致性检验分析与处理的难度较大,工程中一直未能得到很好解决.距离检验方法和TIC (Theil πs inequality co 2efficient )方法都是时域内仿真结果动态一致性检　第12期傅惠民等:仿真结果距离检验方法和TIC方法对比分析验方法,其中TIC方法是目前工程中常用的仿真结果动态一致性的检验方法[124],但是,该方法所采用检验统计量的统计特性无法确定,工程中一般将其作为定性方法使用.对此,文献[5]建立了仿真结果动态一致性距离检验方法,能够在一定的显著性水平下给出检验拒绝域,实现了时域内仿真结果动态一致性的定量检验.文献[6]进一步提出了动态仿真结果相关性检验和分析方法,该方法能分析和判断样本序列在哪些时段已被正确仿真,在哪些时段尚未被正确模拟,从而指导仿真软件的编制和修改.本文针对TIC方法和距离检验方法,从理论层次上对其检验原理、特点进行对比分析,进一步指出TIC方法中存在的问题,并给出一个对比验证算例.1　距离检验方法和TIC方法的对比分析　111　距离检验方法仿真结果动态一致性距离检验方法是一种在相同的输入条件下,以实测试验结果与其仿真试验结果之间的平均马氏距离等为指标的一致性检验方法,其检验原理如下[5]:设X=x(1),x(2),…,x(n)T为样本序列{x(t)}前n项所组成的向量,Y=y(1),y(2),…,y(n)T为其对应仿真结果.Y i=y i(1),y i(2),…,y i(n)T为第i个仿真样本,i=1,2,…,m.Y—={y-(1),y-(2),…,y-(n)}T为m个仿真样本的均值向量,则实测样本向量X与其仿真样本均值向量Y—之间的平均马氏距离D M(X,Y—)可以由下式给出D M(X,Y—)=1n(X-Y—)T S-1(X-Y—)(1)式中Y—=1m∑mi=1Y i(2)S=1m-1∑mi=1(Y i-Y—)(Y i-Y—)T(3)当实测样本向量X与其仿真样本向量Y均服从多维正态分布时,根据文献[5]可知m(m-n)m2-1D M(X,Y—)2～F n,m-n(4)因此,在给定的显著水平α下,若实测样本与其仿真样本均值之间的平均马氏距离满足下式D M(X,Y—)≥m2-1m(m-n)Fα,n,m-n(5)则可以断定两个时间序列之间的差异是显著的,即实测时间序列X的仿真结果Y不正确,详细的检验步骤可以参见文献[5].若只关心时间序列的均值和方差,而不关心相关性是否被正确仿真,则可以采用文献[5]中平均标准化距离检验或平均欧氏距离检验.112　TIC方法TIC方法是在相同的输入条件下,根据实测样本和仿真样本所得的TIC系数为检验指标,依据该指标来衡量实测样本与其仿真结果的差异大小,以此判断仿真结果是否正确,具体原理如下:根据实测样本和仿真样本数据,可得实测样本X与仿真样本均值Y—之间的TIC系数ρ(x,y)为ρ(x,y)=1n∑nt=1[x(t)-y-(t)]21n∑nt=1[x(t)]2+1n∑nt=1[y-(t)]2(6)式中y-(t)由式(2)可得.可以证明,0≤ρ(x,y)≤1.判断方法是如果ρ(x,y)较小,接近于0则说明实测时间序列X与其仿真结果Y之间的差异小,如果ρ(x,y)较大,接近于1则说明实测时间序列X与其仿真结果Y 之间的差异大.由于ρ(x,y)统计分布未确定,一般工程上认为该方法只能作为定性方法使用,并且工程中通常以013作为判定实测时间序列与其仿真结果是否一致的阈值,即若ρ(x,y)≤013,则可以认为实测时间序列X与其仿真结果Y之间的差异不显著,否则认为两者之间存在显著差异,仿真结果不正确.113　对比分析由上述可知,TIC方法不能对仿真结果动态一致性进行定量检验,只能用来定性检验.然而,经过深入研究发现,TIC系数与坐标原点选取有关,无法形成统一的判定标准,所以该方法也不能有效地对仿真结果动态一致性进行定性检验,下面给出具体的对比分析.由于实测样本向量X与其仿真样本均值向量Y—可以由n维欧氏空间的两个点x0=(x(1), x(2),…,x(n))和y0=(y　-(1),y　-(2),…,y　-(n))表示,图1给出了TIC系数在欧氏空间中与坐标5872航　空　动　力　学　报第24卷原点选取有关的几何意义示意图(以三维欧氏空间为例).图1　TIC 系数与坐标原点选取有关的几何意义示意图Fig.1　G eometric meaning schematic diagram ofrelationship between TIC coefficient andselection of coordinate origin根据欧氏空间距离的定义可知,x 0和y 0之间的TIC 系数ρ(x ,y )可以表示为ρ(x ,y )=x 0y 0Ox 0+Oy 0(7)式中x 0y 0=∑nt =1[x (t )-y -(t )]2(8)Ox 0=∑nt =1[x (t )]2(9)Oy 0=∑nt =1[y -(t )]2(10)为考察选取不同坐标原点对TIC 系数的影响,如图1所示,将原坐标原点O 平移到O ′,根据欧氏距离的定义可知点x 0和点y 0之间的距离并不发生变化,所以根据式(7),此时x 0和y 0之间的TIC 系数ρ′(x ,y )可以表示为ρ′(x ,y )=x 0y 0O ′x 0+O ′y 0(11)式中O ′x 0=∑nt =1[x ′(t )]2(12)O ′y 0=∑nt =1[y -′(t )]2(13)比较式(7)和(11)可知,两式分子相等.通过选取不同的坐标原点,可以使得两式分母满足O ′x 0+O ′y 0>O x 0+Oy 0(如图1所示),则ρ′(x ,y )<ρ(x ,y ),即通过坐标原点的选取可以人为控制TIC 系数,使其低于工程中常用的阈值013,甚至无限接近于零,使其通过仿真结果动态一致性检验,也就是利用坐标原点的选取,任何仿真结果既可以让它通过检验,也可以不让它通过检验,这样就大大增加了误判的可能性,从而不能将TIC 系数作为定性检验仿真结果动态一致性的依据.与之相比,距离检验方法采用实测样本序列与其仿真样本均值序列之间的平均马氏距离作为检验指标,根据平均马氏距离的性质[7]可知,当选取不同的坐标原点时,实测样本序列X ′与仿真样本均值序列Y —′之间的平均马氏距离D M (X ′,Y —′)并不发生变化,并且该指标考虑了时间序列的相关性,具有线性变换不变性的特点,所以避免了量纲、坐标原点的选取对检验结果的影响,从根本上保证了检验结果的有效性.同时该平均马氏距离指标服从特定的统计分布,可以在一定的显著性水平下,给出检验的拒绝域,实现仿真结果一致性的定量检验.2　算例分析表1给出了一个实测时间序列数据x (t ),t =1,2,...,20.表2给出了50次仿真得到的时间序列数据y i (t ),t =1,2,...,20;i =1,2, (50)表1　实测样本数据T able 1　Data of measured samplet x (t )t x (t )1101011110115211126127133391001361194910914516859144155186691091651637817317515688168185164991041951701091052061366872　第12期傅惠民等:仿真结果距离检验方法和TIC方法对比分析表2　仿真样本数据T able2　Data of simulation samplesi t12 (1920)19.5511.63… 6.98 5.5628.9911.08…7.90 6.2139.9411.54… 6.59 6.9148.7612.50… 5.64 6.4359.589.59… 6.43 5.16610.309.92… 5.92 5.5279.6410.43… 6.21 4.9889.4110.27…8.72 6.09910.6312.06…7.12 5.10109.589.59… 6.43 5.16……………408.9911.08…7.90 6.21419.9811.43… 4.97 5.36429.4712.70… 4.82 5.90439.5511.63… 6.98 5.564410.9810.20…7.907.27458.6410.57…7.597.984610.779.55… 4.51 5.63477.9110.60… 6.84 5.704810.7311.10…7.29 6.734910.8111.70… 6.947.275010.3212.68… 5.86 5.09首先,采用距离检验方法对表1和表2给出的数据进行一致性检验.根据式(1)得到实测样本数据X与仿真样本数据Y—之间的平均马氏距离D M(X,Y—)的计算结果列于表3,在显著性水平α=0105下,查表[8]得Fα,n,m-n=F0105,20,30= 11932,根据式(5)可得距离检验的拒绝域为D M(X,Y—)≥m2-1m(m-n)Fα,n,m-n=11794(14)由表3结果可得,D M(X,Y—)=11855>11794,所以在显著性水平α=0105下,判定实测时间序列与其仿真序列之间的差异显著.图2给出了实测数据和仿真数据的对比图,从中可以看出,实测样本和仿真样本均值之间确实存在显著差异,这与检验结果一致.图2　实测样本和仿真样本均值对比Fig.2　Comparison between measured sample andsimulation sample mean然后,采用TIC方法,对表1和表2给出的数据进行一致性检验,根据式(6)计算TIC系数列于表3,由于ρ(x,y)<013,一般工程可以认为实测序列与其仿真结果之间的差异不显著,显然这与实际情况不符.为了进一步考察原点选取对检验指标的影响情况,令x′(t)=x(t)-c,y′i(t)=yi(t)-c,其中c=120∑20t=1x(t)=7187,分别采用距离检验方法和TIC方法对新序列x′(t)和y′i(t)之间的一致性进行检验,检验结果列于表3.由表3可见,选取不同的坐标原点,计算出的TIC系数也会不同,从而得到不同的甚至完全相反的检验结果.所以,TIC方法无法对仿真结果动态一致性进行定量检验,也不能进行有效的定性检验,而距离检验方法不受坐标原点选取的影响,检验结论与实际情况相吻合,能够很好的表征实测结果和仿真结果的一致性.7872航　空　动　力　学　报第24卷表3　动态一致性检验对比结果T able3　Comparison result of dynamic consistency tests检验方法检验统计量检验拒绝域检验结果坐标变换前坐标变换后距离检验方法DM (X,Y—)D M(X,Y—)≥1179411855,拒绝仿真结果11855,拒绝仿真结果TIC方法TIC系数越大越不一致,一般为ρ(x,y)>01301069,接受仿真结果01367,拒绝仿真结果3　结　论采用理论分析和模拟算例,对距离检验方法和TIC方法进行对比研究,得出如下结论:1)距离检验方法能够给出拒绝域,实现了实测样本序列和仿真样本序列一致性的定量检验;而TIC方法所采用检验统计量TIC系数的统计分布未知,不能用来定量检验.2)TIC系数与坐标原点选取有关,可以通过坐标原点的选取使TIC系数变大或变小,甚至无限接近于零,也就是利用坐标原点的选取,任何仿真结果既可以让它通过检验,也可以不让它通过检验,因此,TIC方法也不能对仿真结果动态一致性有效地进行定性检验.3)距离检验方法与坐标原点选取无关,不受量纲等因素的影响,这些特性从根本上保证了距离检验结果的有效性,提高了仿真结果动态一致性距离检验结果的可信程度.4)理论分析和大量工程应用表明,距离检验方法能够很好地对实测样本与仿真样本之间的一致程度进行定量检验.参考文献:[1]　刘藻珍,魏华梁.系统仿真[M].北京:北京理工大学出版社,2004.L IU Zaozhen,WEI Hualiang.System simulation[M].Beijing:Beijing Institute of Technology Press,2004.(inChinese)[2]　Kheir N A,Holmes W M.On validating simulation mod2els of missile systems[J].Simulation,1978,30(4):1172128.[3]　刘秀海,邓四二,滕弘飞.卫星动量轮轴承组件的仿真可信度评估[J].航空动力学报,2008,23(9):172421730.L IU Xiuhai,DEN G Sier,TEN G Hongfei.Simulationcredibility evaluation of t he momentum wheel bearing sub2assembly in t he satellite[J].Journal of Aerospace Power,2008,23(9):172421730.(in 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专利名称：Apparatus and method for measurementand temporal comparison of skin surfaceimages发明人：Ze'ev Leshem,Tuvia Kutscher申请号：US09137513申请日：19980820公开号：US06215893B1公开日：20010410专利内容由知识产权出版社提供专利附图：摘要：Apparatus and method for temporal comparison of skin surface images which is fully automatic and based on robust parameters, using a CCD camera provided withtelecentric optics to enabling the capture of images with constant magnification independent of the camera-object distance. The camera is linked to a PC with a frame grabber for storing the image and processing means for calibrating light and for calculating statistics of the image. The illumination source provides a homogeneous illumination of the skin, and the light is calibrated by transforming an acquired image into the model image which would have resulted if illumination of the object were solely by the reference (white) light. Three monochromatic images are produced, one for each of three color channels. The three images are grabbed and processed, and a combination of these three images gives the true color (red, green and blue or RGB) image. An algorithm uses the image and reference image to calculate the skin/lesion border which the eye would suggest if the lesion was illuminated by a standard white light. The image is processed to give the contour of the lesion, and statistics are extracted to score the necessary parameters (metrics). Therefore, the physician is provided with various metrics in a more reliable fashion than could be done manually and these are displayed together with the images obtained at various times. The images can be examined for visual changes over time and for quantitative change in the metrics over time, providing a comprehensive solution to the problems encountered in previous lesion tracking systems. The system assists the physician in the decision making process of malignancy determination. The features are extracted in a manner which is fairly immune to noise, i.e. robust, thus leading to a high repeatability and reliability of the system. The features extracted have a high correlation with the malignancy of the lesion enabling the physician to make a decision regarding the type of lesion with high specificity and sensitivity.申请人：ROMEDIX LTD.代理人：Edward Langer, Pat. Atty.更多信息请下载全文后查看。