Model-independent Constraints on Topcolor from $R_b$

进行mechanical分析的步骤：1)建立几何模型:在Pro/ENGINEER中创建几何模型。

2)识别模型类型:将几何模型由Pro/ENGINEER导入Pro/MECHANICA中，此步需要用户确定模型的类型，默认的模型类型是实体模型。

我们为了减小模型规模、提高计算速度，一般用面的形式建模。

3)定义模型的材料物性。

包括材料、质量密度、弹性模量、泊松比等4)定义模型的约束。

5)定义模型的载荷。

6)有限元网格的划分：由Pro/MECHANICA中的Auto GEM(自动网格划分器)工具完成有限元网格的自动划分。

7)定义分析任务，运行分析。

8)根据设计变量计算需要的项目。

9)图形显示计算结果。

下面将上述每一步进行详解：1、在Pro/ENGINEER模块中完成结构几何模型后，单击“应用程序”→“Mechanical”,弹出下图所示窗口，点击Continue继续。

弹出下图，启用Mechanical Structure。

一定要记住不要勾选有限元模式前面的复选框，最后确定。

2、添加材料属性单击“材料”，进入下图对话框，选取“More”进入材料库，选取材料Name---------为材料的名称；References-----参照Parrt（Component）-----零件/组件/元件V olumes-------------------体积/容积/容量；Properties-------属性Material-----材料；点选后面的More就可以选择材料的类型Material Orientation------材料方向，金属材料或许不具有方向性，但是某些复合材料是纤维就具有方向性，可以根据需要进行设置方向及其转角。

点选OK，材料分配结束。

3、定义约束1）：位移约束点击，出现下图所示对话框，Name 约束名称Number of Set 约束集名称，点击New可以新建约束集的名称。

Reference 施加约束时的参照，可以是surfaces（面）、edges/curves（边或曲面）、points（点）等Coordinate System 选择坐标系，默认为全局坐标系Translation 平动约束（Free为自由，fixed为固定，Prescribed为指定范围）Rotation 旋转约束单位为度Individual--------------单独的、孤立的Surf Options----------面选项Part Boundary---------零件的选择。

a r X i v :a s t r o -p h /0604217v 1 11 A p r 2006Mon.Not.R.Astron.Soc.000,000–000(2005)Printed 5February 2008(MN L A T E X style file v2.2)Redshift-Space Distortions with the Halo OccupationDistribution II:Analytic ModelJeremy L.Tinker 1⋆1KavliInsitute for Cosmological Physics,University of Chicago,933E.56th St.,Chicago,IL 60637ABSTRACTWe present an analytic model for the galaxy two-point correlation function in redshift space.The cosmological parameters of the model are the matter density Ωm ,power spectrum normalization σ8,and velocity bias of galaxies αv ,circumventing the linear theory distortion parameter βand eliminating nuisance parameters for non-linearities.The model is constructed within the framework of the Halo Occupation Distribution (HOD),which quantifies galaxy bias on linear and non-linear scales.We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo.Two-halo velocity statistics are a combination of virial motions and host halo motions.The velocity distribution function (DF)of halo pairs is a complex function with skewness and kurtosis that vary substantially with ing a series of col-lisionless N-body simulations,we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair,and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass.We calibrate a model for the conditional probability function of densities around halo pairs on these simulations.With this model,the full shape of the halo velocity DF can be accurately calculated as a function of halo mass,radial separation,angle,and cosmology.The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in pre-vious models of redshift-space clustering.The parameters of the occupation function are well constrained by real-space clustering alone,separating constraints on bias and cosmology.We demonstrate the ability of the model to separately constrain Ωm ,σ8,and αv in models that are constructed to have the same value of βat large scales as well as the same finger of god distortions at small scales.Key words:cosmology:theory —galaxies:clustering —large-scale structure of universe1INTRODUCTIONThe growth of structure through gravity creates peculiar velocities with respect to the smooth Hubble flow,mak-ing the line of sight a preferred direction when redshift is used as a measure of distance.The systematic differ-ences between the distribution of structure in real and red-shift space contain information about both the cosmology of the universe and the bias of galaxies observed (see,e.g.,Peebles 1976;Sargent &Turner 1977;Kaiser 1987).In Pa-⋆E-mail:tinker@per I (Tinker et al.2006a),we used numerical simulations to develop a blueprint for determining cosmological parameters from redshift-space distortions.In this paper,we use those simulations to calibrate an analytic model for redshift-space galaxy clustering that has the necessary accuracy to inter-pret high-precision measurements from large-scale galaxy redshift surveys,like the Two-Degree Field Galaxy Redshift Survey (2dFGRS;Colless et al.2001)and the Sloan Digital Sky Survey (SDSS;York et al.2000).The effect of redshift-space distortions is most apparent at small scales,where the internal motions of galaxies in groups and clusters spread out close pairs along the line ofc2005RAS2J.L.Tinkersight,creating the so-called“fingers-of-god”(FOGs).This picture of clustering in redshift space can be expressed as a convolution of the real-space two-point correlation function ξR(r)with the probability distribution function(PDF)of galaxy pairwise velocities P(v z),i.e.,1+ξ(rσ,rπ)= ∞−∞[1+ξR(r)]P(v z)dv z,(1)whereξR(r)is the real-space correlation function,rσis the projected separation,rπis the line-of-sight separation, r2=r2σ+z2,and v z=H(rπ−z),where H is the Hubble constant.Equation(1)is often referred to as the“stream-ing model”(Peebles1980).Although this approach has been used primarily to model observations of small-scale distor-tions(e.g.,Peebles1979;Davis&Peebles1983;Bean et al. 1983),equation(1)is valid in the linear regime as well (Fisher1995).Scoccimarro(2004)demonstrated that,pro-vided P(v z)is correct,the streaming“model”is a valid de-scription of the relation between the real-and redshift-space correlation functions on all scales.As presented,equation(1)contains no cosmology.The aforementioned investigations utilized the streaming model to estimate the velocity dispersion of galaxy pairs,which was used to estimate the matter density parameterΩm through a“cosmic virial theorem”.More recent studies of redshift-space distortions have utilized a modified linear the-ory model of anisotropies that,when applied to the real-space galaxy power spectrum P R(k),takes the formP Z(k,µ)=P R(k)(1+βµ2)2(1+k2σ2kµ2/2)−1,(2) whereβ=Ω0.6m/b g,b g is the linear bias parameter,andµis the cosine of the angle between the wavevector k and the line of sight.The term(1+βµ2)2,derived from linear the-ory by Kaiser(1987),models the coherentflow of matter out of underdense regions and into overdense regions.The last term on the right hand side represents an exponential dis-tribution of random,uncorrelated peculiar velocities,which dominates P Z on small scales and is meant to encapsulate the FOG effect described above.Equation(2),commonly re-ferred to as the“dispersion model”,has two free parameters,βand the galaxy velocity dispersionσk.Scoccimarro(2004) points out several deficiencies in this model,both in the inability of linear theory to properly describe anisotropies even in the large-scale limit,and in the oversimplification of using a single parameterσk,which has no clear physi-cal definition,to model small-scale velocities.Consequently, equation(2)introduces a10−15%systematic error in the determination ofβ(Hatton&Cole1999;Paper I),a level of error significant compared with the precision achievable with SDSS and the2dFGRS.The goal of this paper is to create an analytic model for the redshift-space correlation function by combining the streaming model of equation(1)with the Halo Oc-cupation Distribution(HOD;see, e.g.,Jing et al.1998; Ma&Fry2000;Peacock&Smith2000;Seljak2000;Benson 2001;Scoccimarro et al.2001;Berlind&Weinberg2002; Cooray&Sheth2002).The HOD quantifies bias on both linear and non-linear scales for a given galaxy sample by specifying the probability P(N|M)that a halo of mass M contains N galaxies of a given type,together with any spa-tial and velocity biases between galaxies and dark mat-ter within individual halos.The HOD has been utilized to model the real-space clustering of galaxies in the SDSS (Zehavi et al.2004,2005;Tinker et al.2005)and the2dF-GRS(Tinker et al.2006b;see also Yang et al.2003).In this paper we extend the HOD model from real space to redshift space by providing a model for P(v z)which is physically motivated and empirically calibrated on numerical simula-tions.Several recent papers have presented calculations of redshift-space distortions using halo models of dark matter and galaxy clustering(Seljak2001;White2001;Kang et al. 2002;Cooray2004;Skibba et al.2005;Slosar et al.2006), providing insight into the role of non-linear dynamics and non-linear bias in shaping clustering and anisotropy.How-ever,these studies rely on the same linear theory compo-nent of equation(2)for large-scale anisotropies.Kang et al. (2002)show that their model only reproduces the dark mat-ter P Z(k,µ)from N-body simulations after introducing a σk parameter for the halos,even after the virial motions of particles within halos were taken into account.Skibba et al. (2005)demonstrate the difficulty is modeling redshift-space galaxy clustering in the transition region between quasi-linear and fully non-linear regimes using a linear theory de-scription of halo velocities.Other recent papers have used the halo approach to model galaxy and dark matter ve-locity statistics(Sheth et al.2001a;Sheth&Diaferio2001; Sheth et al.2001b).While the model outlined in these pa-pers is derived fromfirst principles,in contrast to the cali-brated model presented here,it is still based on linear theory, which does not provide the required accuracy for a robust implementation of equation(1).The purpose of our model is less as afirst-principles derivation of P(v z)than as a tool to extract information from forthcoming observational data. In this context,the accuracy of the model is the paramount concern.In the course of developing the model,we will also gain new insight into the physics that determines P(v z),es-pecially the role of environment in producing a non-Gaussian velocity distribution.An accurate model forξ(rσ,rπ)with the HOD must properly incorporate halo motions.A proper model for halo pairwise velocities P h(v)must correctly describe the distri-bution function for an arbitrary pair of halo masses,at any angle with respect to the line of sight,and as a function of separation.In the large-scale limit,linear theory is ade-quate for describing the mean infall velocities of halos(see, e.g.,Juszkiewicz et al.1999;Sheth et al.2001a).However, the applicability of linear theory is problematic at scales where the observational data are robust.At all scales,linear theory does not accurately predict the pairwise dispersion (Scoccimarro2004).Higher order moments also play an im-portant role in P h(v).N-body results have shown that the radial velocity PDF of dark matter halos exhibits significant skewness and kurtosis(Zurek et al.1994;Juszkiewicz et al. 1998).1The skewness arises from the infall of matter into overdense regions(Juszkiewicz et al.1998).The kurtosis, 1In this paper we use the convention of radial being the directionc 2005RAS,MNRAS000,000–000Redshift-Space Distortions with the HOD3manifesting as exponential wings in both the radial and tan-gential velocities,is due to local non-linear effects for each halo in the pair.Scoccimarro(2004)concludes that a Gaus-sian is never a good description of velocities,even at the largest scales.Scoccimarro(2004)focuses on velocity statis-tics of dark matter,but local non-linear effects apply to halos as well(Kang et al.2002),and P h(v)from simulations are non-Gaussian at all scales.It is not sufficient for P h(v)to describe thefirst two moments of the velocity distribution. To accurately modelξ(rσ,rπ),P h(v)must reasonably de-scribe higher order moments of the distribution as well(see, e.g.,Fisher et al.1994).As stated in Paper I,our method for analyzing redshift-space distortions is tofirst use measurements of the pro-jected correlation function w p(r p)to determine the param-eters of the HOD for a given cosmology.If HOD parameters cannot be found that allow the cosmological model to re-produce the observed w p(r p)then that model is ruled out. Once the HOD has been determined,the redshift-space clus-tering is investigated by the analytic model presented here or the N-body approach of Paper I.The cosmological param-eters that most directly influence redshift-space clustering are the matter density parameterΩm,the amplitude of the linear matter power spectrum,defined here byσ8,the rms linear-theory massfluctuation in8h−1Mpc spheres(where h≡H0/100km s−1Mpc−1),and the velocity bias of the galaxy sample,which we parameterize byαv,the ratio be-tween the satellite galaxy velocity dispersion and the virial velocity dispersion of the dark matter halo.One can con-sider models in which the velocities of central galaxies are biased with respect to mean motion of the host halo.In Pa-per I we considered the shape of the linear matter power spectrum P lin(k)to be determined by measurements of the cosmic microwave background(CMB)anisotropies and the large-scale galaxy power spectrum(e.g.,Percival et al.2002; Spergel et al.2003;Tegmark et al.2004a).An advantage of the analytic model forξ(rσ,rπ)is that it allows for marginal-ization over P lin(k)without the cumbersome process of run-ning multiple N-body simulations.The redshift-space ob-servables explored here and in Paper I are largely indepen-dent of P lin(k),thus the constraints on HOD parameters come primarily from w p(r p)and to a small degree the as-sumed P lin(k),and the constraints on our cosmological pa-rameter space ofΩm,σ8,andαv come from the redshift-space data.Any degeneracies between cosmology and HOD parameters can be identified and marginalized over as well.In§2we outline the analytic model,presenting analytic expressions forξ(rσ,rπ)by combining the HOD model for real-space clustering with the streaming model of equation (1).In§3we detail the model for halo pairwise velocities, the key ingredient in the two-halo term,and calibrate it on the N-body simulations.§4tests the model against the mock galaxy samples of Paper I,demonstrating that the model can recover the correct cosmological parameters from a wide va-connecting the halo pair,tangential being in a direction orthog-onal to the radial,and line-of-sight to be the direction from the observer.Velocities in these directions will be referred to as v r, v t,and v z,respectively.Figure1.A slice through one simulation showing the locations of halos of different rge open circles are halos of mass M>3×1013.Smallfilled circles are halos of mass∼2×1012 h−1M⊙.The inset box plots the probability distribution function (PDF)of radial velocities for the lower-mass halo pairs in the slice.The shaded regions of the histogram highlights the skewness toward high-velocity pairs.All halo pairs within the shaded region of the histogram are connected in the slice plot.riety of cosmologies which produce significant degeneracies in redshift-space clustering.In§5we summarize and discuss prospects for applying the model to current data sets.2MODELING THE CORRELATIONFUNCTION IN REAL AND REDSHIFTSPACEThe real-space galaxy correlation functionξR(r)can be cal-culated analytically with the HOD for a given galaxy sample and cosmology.In the HOD framework,galaxy clustering is separated into two distinct parts;pairs of galaxies within a single halo and those from two separate halos.The total correlation function is the sum of these two contributions (see,e.g.,Berlind&Weinberg2002;Cooray&Sheth2002; Zheng2004;and Tinker et al.2005for details on calculating the real-space correlation function).The real-space one-halo term is written as1+ξ1h(r)=1dMN(N−1) M2R vir(M)F′ r4J.L.TinkerIn practice,F′(x)is different for galaxy pairs which involve the central galaxy and those between two satellite galaxies, and the calculation is separated into these two terms.In real space,one-halo pairs dominateξR(r)at small scales.In redshift space,these pairs have large relative mo-tions due to the virial dispersion of the halos they oc-cupy,spreading these pairs out along the line of sight. We model the velocity distribution within each halo as an isotropic,isothermal Gaussian distribution,an approx-imation supported by numerical hydrodynamic simulations (Faltenbacher et al.2004)and observational analysis of rich SDSS clusters(McKay et al.,in preparation).The satellite galaxy velocity dispersion in a halo of mass M is propor-tional to the virial dispersion,σ2sat=α2vσ2vir=α2vG M h2σsat.For central galaxies,a natural as-sumption is that these galaxies are at rest with respect to the center of mass of the halo,orαvc=0.In Paper I we tested this assumption,demonstrating thatαvc=0.2has a negligible effect on redshift-space observables.We define σcen=αvcσvir,so the dispersion of central-satellite pairs is σcs=(α2v+α2vc)1/2σvir.Deviations from isotropy have lit-tle effect onξ(rσ,rπ)for any physically reasonable value of the anisotropy,while non-isothermality resulting from spa-tial bias or unrelaxed systems can be modeled as an“effec-tive”velocity bias parameter(Paper I).In equation(3),the total number of one-halo pairs in-volves an integral over the halo mass function.At a given separation,the velocity PDF for one-halo pairs is a super-position of Gaussians weighted by the relative number of galaxy pairs from each halo of mass M.This superposi-tion of Gaussians of varying dispersion makes the overall pairwise galaxy velocity dispersion approximately exponen-tial(Sheth1996),in accord with observational inferences (Davis&Peebles1983;Hawkins et al.2003).The combination of equations(1)and(3)for central-satellite pairs isξ(cs) 1h (rσ,rπ)=1dMN sat M N cen Mr2σ+z2√2σ2cs dz2π¯n2g ∞0dM dn4R vir∞−∞F′ss √2R vir 1π2σsat×exp −(rπ−z)2(r2σ+z2),(6)where N sat(N sat−1) is the second moment of the satelliteoccupation function,and F′ss(x)is the fraction of satellite-satellite pairs(see Sheth et al.2001a for a derivation ofF cs(x)and F ss(x)for the NFW profile).The full one-halocorrelation function isξ1h(rσ,rπ)=ξ(cs)1h+ξ(ss)1h.The two halo term is most straightforward to calculatethrough a direct implementation of the equation(1),1+ξ2h(rσ,rπ)= ∞−∞[1+ξR2h(r)]P2h(v z|r,φ)dv z.(7)whereξR2h(r)is the two-halo contribution to the real-spacecorrelation function,P2h(v z|r,φ)is the line-of-sight velocityPDF of galaxy pairs from two distinct halos,and cosφ=rσ/r.This PDF is a convolution of the line of sight PDFof halo pairwise velocities with the Gaussian distributionfor galaxy velocities within each halo.P2h(v z|r,φ)is a pair-weighted average integrated over all possible combinationsof halos;P2h(v z|r,φ)=2(¯n′g)−2 M lim,10dM1dndM2 N M2P g+h(v z|r,φ,M1,M2),(8)where P g+h is the velocity PDF for galaxy pairs from ha-los of masses M1and M2.P g+h includes both the internalmotions of the galaxies within each halo and the relativemotions of the halo centers of mass.The limits on each inte-gral in equation(8)are determined by halo exclusion;halopairs cannot be closer than the sum of their virial radii(i.e.,R vir,1+R vir,2 r).At large separation,this effect is neg-ligible because the largest collapsed objects have radii∼2h−1Mpc,and the limits of equation(8)approach infinitywhen r is large.At small scales,halo exclusion strongly in-fluences the number of pairs.In equation(8),M lim,1is themaximum halo mass such that R vir(M lim,1)=r−R vir(M min)and M lim,2is related to M1by R vir(M lim,2)=r−R vir(M1),where M min is the minimum mass halo that can host agalaxy.The restricted number density,¯n′g,is the total num-ber of two-halo galaxy pairs at separation r,also calculatedusing halo exclusion by¯n′g2= M lim,10dM1dn dM2 N M2.(9)We denote the velocity PDF of halo pairs asP h(v z|r,φ,M1,M2).This represents the center-of-massmotions only.Once the relative motions of the dark matterhalos are determined,P g+h is calculated by convolving P hc 2005RAS,MNRAS000,000–000Redshift-Space Distortions with the HOD5Figure 2.Velocity PDFs for halo pairs at different local densities.The top four panels plot PDFs as a function of local environment for low-mass halos (solid histograms)and high-mass halos (filled circles connected with dotted lines).The local density is calculated by a top-hat smoothing kernel centered on the midpoint between the halo pair,with radius equal to the halo separation.The bottom panel shows the unconditional velocity PDF for the same halos.with the Gaussian describing the internal motions of the galaxies within the halos.The model for P h (v z |r,φ,M 1,M 2)is important both for capturing the behavior of the redshift-space correlation function in the transition region between the one-and two-halo terms and for correctly modeling dis-tortions between quasi-linear to linear scales.We describe it in detail in the next section.3THE HALO VELOCITY MODEL 3.1Conditional matter PDFIn §1we listed the requirements an accurate model of P h (v )must satisfy.To meet these requirements,we use the N-body simulations from Paper I to explore halo velocity statistics.Our simulation set consists of five realizations of an inflationary ΛCDM cosmology with Ωm =0.1andσ8=0.95at z =0,using the public N-body code GAD-GET (Springel,Yoshida,&White 2001).We utilize outputs at higher redshifts to represent models at different values of σ8and Ωm .Each simulation is 3603particles in a cubic volume 253h −1Mpc on a side,yielding a mass resolution of 9.6410×Ωm h −1M ⊙.The simulations have a power spec-trum shape parameter Γ=0.2in the parameterization of Efstathiou et al.(1992),and a spectral index n s =1.See Paper I for further details regarding the simulations.Our fiducial cosmology is Ωm =0.3,σ8=0.8,corresponding to z =0.55.Unless otherwise stated,N-body results will be using this output.Figure 1elucidates the complexity of P h (v |r,φ,M 1,M 2).The inset box shows the PDF of radial velocities of halo pairs of mass M 1=M 2≈2×1012h −1M ⊙at a separation of r ∼10h −1Mpc.Negative radial velocities are defined as the halos going toward one another.The PDF is not well described by either a Gaussian or anc2005RAS,MNRAS 000,000–0006J.L.TinkerFigure parison between the conditional matter PDFs measured from the simulations (solid histograms )and the model of Equation (11)(dotted lines ).Top row:P m (δ|r,M 1,M 2)for fixed mass (1012h −1M ⊙)and σ8=0.8,but changing radius.Middle row:P m (δ|r,M 1,M 2)for fixed radius (10h −1Mpc)and σ8=0.8,but increasing halo mass.Bottom row:P m (δ|r,M 1,M 2)for fixed mass (1012.3h −1M ⊙)and radius (10h −1Mpc),but changing σ8.exponential.The shaded regions of the PDF highlights the skewed tail of halo pairs rapidly approaching each other.The outer panel plots the positions of these halos in a 40h −1Mpc slice through one realization.Small,filled circles indicate the 2×1012h −1M ⊙halos of the inset histogram.The open circles in the plot represent high mass halos,M >3×1013h −1M ⊙.All pairs inside the shaded region of the histogram have been connected with a line.These high-velocity pairs are almost exclusively in regions that include a high mass halo.Because high mass halos prefer-entially occupy dense regions,we recover the well-known result that the non-linear halo velocity field is coupled to the non-linear density field.However,Figure 1leads us to investigate the velocity PDF as a function of environment.In Figure 2,the lower panel plots the same PDF from Figure 1for 1012h −1M ⊙halos at r ∼10h −1Mpc.This panel also plots the PDF for 3×1013h −1M ⊙at the same separation.The width of these mass bins is a factor oftwo.The PDF for high-mass halos is noisier due to lower statistics,but it is apparent that the PDF for high-mass halos peaks at v ∼−150km s −1,while the mode of the low-mass PDF is at zero.It is unlikely to find high-mass halos moving away from one another at this scale,while that probability is nearly 40%for low-mass halos.The upper panels of Figure 2show the PDFs for the same halos,now binned by local overdensity,δ≡ρ/¯ρ−1.We calculate δinside spheres of radius equal to the separation of the halo pairs,centered on the midpoint between the two halos.Setting the radius of the smoothing kernel equal to the halo separation allows for cleaner determination of the pair’s environment.The four top panels span a range in mean local density of δ ∼0to 3.From these data the origin of the high-velocity tail is clear;the negative skewness arises from halo pairs which lie in dense environments.At δ=0,the velocity distribution is narrow and peaked at v ≈0km s −1.As δincreases,both the mean velocity and the dispersionc2005RAS,MNRAS 000,000–000Redshift-Space Distortions with the HOD7Figure 4.The scale and mass dependence of parameters of the two-halo velocity model.Each line represents of halo pair with mass ratio M 2/M 1=4i ,with i =0−3and M 1=1012h −1M ⊙.Panel (a):cutoffdensity scale for the 2-halo conditional mat-ter PDF (Eq.[13]).Panel (b):Power-law index for the density-dependence of the pairwise velocity dispersion (Eq.[19]).There is only one line in this panel because there is no dependence on mass.Panel (c):Normalization of the density dependence of the pairwise radial velocity dispersion (Eq.[21]).Panel (d):Normal-ization of the density dependence of the pairwise tangential ve-locity dispersion (Eq.[22]).increase as well.At fixed δ,the PDFs no longer show strong skewness or kurtosis;a Gaussian is a good approximation.Therefore the total distribution in the bottom panel can be modeled as a superposition of Gaussians weighted by the probability of finding a halo pair at a given δ.At a given density,Figure 2also demonstrates that the PDFs for high-and low-mass halos are very similar.It is the different distributions of local environments which leads to the differences in the total PDFs in the lower panel.We therefore propose the ansatz P h (v [r,t ]|r,M 1,M 2)=P G (v [r,t ]|r,δ,M 1,M 2)P m (δ|r,M 1,M 2)dδ,(10)to model the radial and tangential pairwise motions of ha-los.In equation (10)P G is a Gaussian,and P m (δ|r,M 1,M 2)is the conditional matter density PDF in spheres of radius r centered on a halo pair of masses M 1and M 2.An ansatz of this type has been used to model one-point velocity statistics of halos and galaxies (Sheth &Diaferio 2001;Hamana et al.2003).Although the PDFs in the upper panels of Figure 2appear independent of halo mass,P G varies moderately with mass at small scales because at small r the halos themselves contribute a large fraction of the total local mass.At scalessignificantly larger than the halo radii,P G becomes inde-pendent of mass.The PDF for the unconditional matter distribution P m (δ|r )is well fit by a lognormal distribution function with dispersion that varies with smoothing scale (e.g.,Coles &Jones 1991;Kofman et al.1994).The relationship between the halo mass function and the large-scale den-sity field can also be quantified (e.g.,Bond et al.1991;Sheth &Tormen 2002;Pavlidou &Fields 2005).The con-ditional mass function can be roughly approximated as n (M |δ)≈[1+b (M )δ]n (M )(Mo &White 1996),where b (M )is the large-scale bias factor for halos of mass M (here we use the halo bias formula in Appendix A of Tinker et al.2005).The distribution of densities at which a halo of a given mass can be found is roughly P m (δ|r,M )≈[1+b (M )δ]P m (δ|r )(Hamana et al.2003).The term [1+b (M )δ]effectively shifts the matter PDF to higher densities by an amount which depends on the bias of the halo.The density distribution around pairs of halos,de-noted as P m (δ|r,M 1,M 2),is a murky theoretical prob-lem with no obvious straightforward approach.To model P m (δ|r,M 1,M 2)we truncate the unconditional matter dis-tribution with an exponential cutoffat low densities,i.e.,P m (δ|r,M 1,M 2)=A exp−˜ρ0(r,M 1,M 2)2πσ21exp−[ln(1+δ)+σ21/2]21+δ,(12)where σ21(r )=ln[1+σ2m (r )]and σm (r )is the mass vari-ance in top-hat spheres of radius r (e.g.,Coles &Jones 1991;Kofman et al.1994).To calculate σm (r ),we use the non-linear matter power spectrum of Smith et al.(2003).The cutoffdensity scale ˜ρ0is˜ρ0=˜ρ1[b (M 1)+b (M 2)]+r8J.L.TinkerFigure parison between the velocity statistics of N-body halos and the velocity model integrated over all halo masses.In all panels the solid line plots the N-body results and the open circles connected by dotted lines plots the model.The top four panels present the first four moments of the radial velocity PDFs as a function of scale:mean µ,dispersion σr ,skewness µ3/σ3,and kurtosis κ.The bottom two panels show the dispersion σt and kurtosis κof the tangential PDFs.For proper comparison,the integrals over velocity for the moments are binned in the same manner as the N-body results and are truncated at the high and low velocities of the N-body statistics.of Tinker et al.(2005).Equation (11)accurately tracks thechange in P m (δ|r,M 1,M 2)with smoothing scale.The middle row of panels in Figure 3compares the model to the N-body results for different halo masses at the same smoothing scale of 10h −1Mpc.N-body halo pairs of mass ∼2×1012h −1M ⊙,which have large-scale bias of ∼0.8in our fiducial cosmology,reside on average in overdense re-gions,with δ =0.80.As the mass increases by factors of 4and 16(with b ∼1.1and 1.5,respectively), δ increases to 1.00and 1.36.The mean density calculated from equa-tion (11)for each halo mass is 0.82,1.02,and 1.32,in good agreement with the numerical results.The bottom panel in Figure 3isolates the effect of changing σ8on P m (δ|r,M 1,M 2).The three panels present numerical results for M ∼5×1012h −1M ⊙halos at r ∼10h −1Mpc for σ8=0.6,0.8,and 0.95.In equation (12),the dependence of the matter distribution on the power spec-trum is through the parameter σm (r ),which is proportional to σ8.As σ8increases,the dispersion in the unconditional P m (δ|r )from equation (12)increases.The same is true for P m (δ|r,M 1,M 2);the N-body results broaden substantially from σ8=0.6to 0.95.The results from equation (11),plot-ted once again with the dotted lines,model the changes of P m (δ|r,M 1,M 2)with σ8accurately.With three adjustable parameters,the quantities ˜ρ1,α0and r 0of equation (13),our model for the conditional matter PDF P m (δ|r,M 1,M 2)reproduces the distinct effects of varying halo mass,smooth-ing scale,and power spectrum normalization.3.2Parameters of the GaussianFor a halo pair at separation r and density δ,we approximate the radial velocity PDF as a distribution of the form P (v r |δ,r,M 1,M 2)=12πσrexp−(v −µr )23.(15)At small scales,µr is approximated by the non-linear spher-ical collapse model (see,e.g.,Peacock 1999).In this model,the dependence of the velocity perturbation on density is expressed parametrically as δ=9(γ−sin γ)2(1−cos γ)2−1.(17)The mean radial velocity isµsc (δ,r )=H r Ω0.6m u (δ)exp[−(4.5/r ˜ρ)2],(18)where the exponential term is added to better match the N-body results at the smallest scales but has little influ-ence on the overall behavior of µsc .Investigation of our N-body results shows that the spherical collapse model best describes the N-body simulations at r 4h −1Mpc,while linear theory is an excellent description of the results for r 20h −1Mpc.In the transition region,we express µr as a weighted mean of equations (15)and (18),which smoothly transitions between the two regimes.The weighting fac-tor,w µincreases linearly from 0to 1in ln(r )in the range 4 r 20h −1Mpc,with µr =wµsc +(1−w )µlin .Recalling Figure 2,the skewness of the radial veloc-ity PDF arises from the combination of halo pairs in high-density regions,which have a large streaming velocity and high dispersion,with halo pairs in mean-to low-density re-gions,which have low mean streaming velocity (relative to Hubble flow)and small dispersion.In our N-body simula-tions,the skewness of the radial velocity distribution does not monotonically increase as halo separation decreases.As halo pairs become close,of order twice the sum of their virial radii,the skewness decreases and the PDF becomes more symmetric.Because µsc diverges rapidly as δbecomes large,the skewness of the model will always increase with decreasing r .To compensate for this effect,we enforce the condition that at r =4R vir ,1,µr is held constant for all δat the value of the most probable δfor that separation,remov-ing the skewness entirely.In the full halo+galaxy PDF,this change from skewed to symmetric distribution functions isc2005RAS,MNRAS 000,000–000。

即以此功德，庄严佛净土。

上报四重恩，下救三道苦。

惟愿见闻者，悉发菩提心。

在世富贵全，往生极乐国。

（一）优化模型的组成优化模型包括以下3部分：l Objective Function：目标函数是一个能准确表达所要优化问题的公式。

l Variables：Decision variables（决策变量），在模型中所使用的变量。

l Constraints：约束条件。

（二）Lingo软件使用的注意事项（1）LINGO中不区分大小写字母，变量（和行名）可以使用不超过32个字符表示，且必须以字母开头。

（2）在命令方式下（Command Window中），必须先输入MODEL：表示开始输入模型。

LINGO中模型以“MODEL:”开始，以“END”结束。

对简单的模型，这两个语句也可以省略。

（3）LINGO中的语句的顺序是不重要的，因为LINGO总是根据“MAX=”或“MIN=”语句寻找目标函数，而其它语句都是约束条件（当然注释语句和TITLE除外）。

（4）LINGO模型是由一系列语句组成，每个语句以分号“;”结束。

（5）LINGO中以感叹号“!”开始的是说明语句（说明语句也需要以分号“;”结束）。

（6）LINGO中解优化模型时假定所有变量非负（除非用限定变量取值范围的函数@free或@sub或slb另行说明）。

（7）当您要判断表达式输入是否有错误时，也可以使用菜单“Lingo“的”Picture“选项。

(8) 用命令"@BND(下界, 变量名, 上界)"设置变量的上界和下界(9) 用命令"@free(x1)"取消变量x1的非负限制，x1可以取正实数和负实数(10)一般整数变量可以用"@GIN(变量名)"来标识，0-1型变量可以用"@BIN(变量名)"来标识（三）Solution Report各项的含义例1 将以下模型粘贴到Lingo中求解，其中第一行MODEL和最后一行END在Lingo Model 窗口下可以不要。

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3DSHU SUHVHQWHG DW WKH 0RGHOLFD :RUNVKRS 2FW /XQG 6ZHGHQ $OO SDSHUV RI WKLV ZRUNVKRS FDQ EH GRZQORDGHG IURP KWWS ZZZ 0RGHOLFD RUJ PRGHOLFD SURFHHGLQJV KWPO:RUNVKRS 3URJUDP &RPPLWWHH3HWHU )ULW]VRQ 3(/$% 'HSDUWPHQW RI &RPSXWHU DQG ,QIRUPDWLRQ 6FLHQFH /LQN|SLQJ 8QLYHUVLW\ 6ZHGHQ FKDLUPDQ RI WKH SURJUDP FRPPLWWHH0DUWLQ 2WWHU *HUPDQ $HURVSDFH &HQWHU ,QVWLWXWH RI 5RERWLFV DQG 0HFKDWURQLFV 2EHUSIDIIHQKRIHQ *HUPDQ\+LOGLQJ (OPTYLVW '\QDVLP $% /XQG 6ZHGHQ+XEHUWXV 7XPPHVFKHLW 'HSDUWPHQW RI $XWRPDWLF &RQWURO /XQG 8QLYHUVLW\ 6ZHGHQ :RUNVKRS 2UJDQL]LQJ &RPPLWWHH+XEHUWXV 7XPPHVFKHLW 'HSDUWPHQW RI $XWRPDWLF &RQWURO /XQG 8QLYHUVLW\ 6ZHGHQ 9DGLP (QJHOVRQ 'HSDUWPHQW RI &RPSXWHU DQG ,QIRUPDWLRQ 6FLHQFH /LQN|SLQJ8QLYHUVLW\ 6ZHGHQ. /XQGH2EMHFW 2ULHQWHG 0RGHOLQJ LQ 0RGHO %DVHG 'LDJQRVLV0RGHOLFD :RUNVKRS 3URFHHGLQJV SSObject-Oriented Modeling in Model-BasedDiagnosisKarin Lundermatik GmbH,Schloßstr.34,D-89518HeidenheimOctober13,20001IntroductionIn the life cycle of a product,engineers have toperform many analysis tasks,from design lay-out,over system simulation and risk analysis,todiagnosis during product operation.Most anal-ysis tools are specialized for just a few of theseanalysis tasks.This forces the engineer to workwith a whole tool suite using various model for-mats(often even different models)for the sameproduct.But modeling a technical system is akind of art—it requires both expert domainknowledge and the ability to structure a problemand tofind out the appropriate level of abstrac-tion for it.It is a creative,time-consuming andexpensive task.To increase efficiency in prod-uct development,it would be desirable to haveanalysis tools which reduce the modeling effortas far as possible,by providing means to reuseexisting models,and by offering multiple ana-lyzes of a product on the base of a single prod-uct model.For programming languages like Java orSmalltalk,the advantages of object-orientedconcepts are well-known.They can be em-ployed to support hierarchical structuring ofproblems,to allow wide reuse of code,andmaintenance of large and evolving software sys-tems.The same applies to object-oriented mod-eling languages.They are especially well-suitedto model complex and multi-domain systems.Avery promising attempt to introduce a coherentobject-oriented modeling language based on theexperience of previous languages is Modelica[Mod99].Figure2:An automatically generated decision tree for model-supported diagnostics by the service.methods with AI technology(see[Sei97]).It provides the following analyzes using the same knowledge base:requirements analysis(design layout)design verificationrisk analysis–fault tree analysis–failure mode and effect analysis–sneak circuit analysis–tolerance analysisprocess monitoringmodel-supported diagnosis–decision trees–diagnostic rulesmodel-based diagnosis(on or off board) 2.1Declarative modelingTo build the necessary knowledge base,a tech-nical system is mapped to a hierarchical model consisting of a number of functional units which are connected with each other.The behavior of each functional unit(component)is described in terms of physical laws,in the form of con-straints.A constraint defines a relation between model variables.Thus,the component behavior is formulated declaratively,in contrast to many conventional simulation tools like Simulink or Matrix X,where all system equations are es-sentially assignments,and all component ports have to be either inputs or outputs.The declar-ative(or non-causal)modeling concept allows to model component behavior independently of the context where the component shall be used.This leads to more simple andflexible model libraries,which are reusable in many contexts. At the same time,it remains possible to formu-late certain constraints as assignments if neces-sary,for instance in subsystems where a behav-ior description by signalflow is an appropriate abstraction.A declarative modeling approach reflects also the fact that in physical systems,a steady state is an equilibrium determined by the interaction between all components.For instance,model-ing a complex electrical circuit by signalflow is nearly impossible.Moreover,if the behav-ior of one component in the circuit changes (e.g.in case of a defect),the model had to be re-designed because of the different signalflow. This shows that for model-based diagnosis,a declarative formulation of model behavior is es-sential.Risk analyzes as well as diagnostics bene-fit from the definition of additional behavioral modes modeling the component behavior in typical failure states.How behavior modes can be used in model-based diagnosis will be de-scribed in Section2.3.2.2Simulation in RODONIn real technical systems,some model parame-ters may be subject to manufacturing tolerances, others may be inaccurate because of measure-ment errors.For diagnostic purposes,it is es-pecially important that the simulation results of a model match the behavior of the real system, because discrepancies are interpreted as defec-tive behavior.Hence,it is dangerous to define those uncertain parameters by sharp real num-Figure3:A diagnosis:in case that gr-node-2is disconnect,a leakage current causes the high beam lamps to shine dimmed,although they are switched off.bers,more or less arbitrarily,as is usually done with conventional simulation tools.To reflect these uncertainties,in RODON the basic value type is not the real number but the interval.More precisely,since interval opera-tions may result in multiple intervals,the values of RODON variables are represented by interval sets,and all operations are carried out by inter-val arithmetics(see[HHKR95],[AH74]). Since product specifications often contain tol-erances or ranges,this value representation also suggests the use of RODON as a tool in require-ments analysis or design verification.The simulation algorithm of RODON seeks to constrict the values of all model variables as far as possible,without losing any solution.It bases on a local constraint propagation tech-nique which was adapted for interval constraint propagation by E.Hyv¨o nen(see[Hyv91]).The iterative algorithm starts by assigning undeter-mined values to all variables except for those whose values are given by the user(or in case of diagnosis:where input from the real system is available).An agenda mechanism is initialized with a list of all constraints.Now,the problem solver takes the constraints from the agenda one by one and evaluates them.If the value of some variable changes after evaluation,the problem solver collects all constraints which depend on this variable and puts them on the agenda again. They have to be evaluated anew,to propagate the new value through the system.This itera-tive process does not stop while the agenda con-tains constraints,that means,while some values keep changing(with respect to some accuracy, which is adjustable by the user).This algorithm is called local constraint propagation because changes are propagated through the system by passing them to the immediate neighbors in the constraint net.Local constraint propagation has a number of advantages.For instance,it allows to solve con-straint systems which are under-or overdeter-mined.This is especially important in model-based diagnosis,where a system has to be overdetermined in order to allow conclusions about defective components.2.3Model-based diagnosis Suppose one is given a description of a system, together with an observation of the system’s be-havior which conflicts with the way the sys-tem is meant to behave.The diagnostic prob-lem is to determine those components of the system which,when assumed to behave abnor-mally,will explain the discrepancy between the observed and correct system behavior[Rei87]. The observed system behavior is given by pro-cess data,i.e.by a set of values measured by the real system in operation.A diagnosis starts with a simulation of the nominal system behav-ior together with the given process data.The resulting equation system has to be overdeter-mined.If it has no solution,a conflict occurs during local propagation,which means that one or more components must be defect(i.e.behave abnormally).In case of a conflict,RODON analyzes the conflict and generates hypotheses(candidates) which may explain the abnormal system be-havior.A candidate is a minimal set of vi-olated assumptions,where an assumption can have a form like”the component XY behaves normally”.For the efficient generation of hypotheses it is not sufficient to know that a simulation ended with a conflict.Without additional information about where the conflict occured candidate gen-eration would be a search in a gigantic search space.Simulation by local constraint propaga-tion provides us with this information.With each value set,RODON manages the assump-tions the value set depends on.This is done by means of a truth-maintenance system(TMS).If a conflict occurs,RODON is able to backtrack the assumptions corresponding to the conflict-ing values.They can be used to narrow the search space to candidates containing these as-sumptions.This diagnostic approach is based on the GDE (general diagnostic engine)introduced by de Kleer([dKW87],[dKW89]).It is characterized byan incremental diagnostic procedureuse of behavioral modes for candidate ver-ificationa truth-maintenance system(TMS)toreuse knowledge in multiple contextsa scalable candidate generatorthe ability to diagnose multiple faults aswell as unspecified faults 3Object-Oriented Modeling in RODONThe tool goes back to ideas of W.Seibold [Sei92]in the early80’s,and has developed over the past10years.From the very begin-ning,an object-oriented modeling approach was used to define hierarchies of model component classes.It agrees with the Modelica philosophy [Mod99]in central points,namelyhierarchical modelingcomponent-oriented modelingdeclarative modelingquantitative modelingmulti-domain modelingsupport by object-oriented model libraries This remarkable similarity suggests the idea to support Modelica as a modeling language in RODON.To gain experience for the integra-tion of Modelica into RODON,we implemented a prototype of a model representation module, and combined it with a new version of the RODON diagnostic engine.While structure and topology representation of Modelica models could be adopted without any changes,the behavior representation had to be slightly modified.In the following subsections,we will explain the alterations made for our application.All exam-ples are written in the Modelica dialect we cur-rently use with our prototype implementation. Its behavior section isfitted to our special needs. Note that the language specification is notfixed entirely.3.1Modeling behavior modesLet us start with a simple example model-ing an electrical wire class with two behav-ioral modes:the nominal behavior,and the most common failure modes disconnect,and shortT oGround.An appropriate class hierar-chy could be the following.package Rose.Electricalconnector Porttype Current=Interval(unit="A",quantity="current");type Resistance=Interval(unit="Ohm",quantity="resistance"); type Voltage=Interval(unit="V",quantity="voltage");type FM=Discrete(min=0,quantity="failure mode");Figure4:Type definitions in RODON.Voltage u;flow Current i;end Port;partial model TwoPortPort p,n;FM fm(max=1);behaviorif(fm==0|fm==1)Kirchhoff(p.i,n.i);if(fm==1)p.i=0;end TwoPort;model IdealWire2extends TwoPort(fm(max=2)); protected Interval iGnd;behaviorif(fm==0|fm==2)p.u=n.u;if(fm==2)p.i+n.i+iGnd=0; if(fm==2)p.u=0;end Wire2;end Rose.Electrical;The model TwoPort is a general electri-cal component providing basic physical laws for the current in case of nominal behavior (fm==0)and the failure mode disconnect (fm==1).The alternative behavior for dif-ferent behavioral modes is defined using con-ditional constraints,where the discrete failure mode variable fm serves as a kind of switch. The model IdealWire2extends this base class by adding a constraint for the voltage(it is an ideal wire without resistance)as well as constraints defining the behavioral mode short-T oGround(fm==2).Recall that all variables in a RODON model are represented by sets of values.This is reflected by the type definitions in Fig.4.The basic type Interval has all attributes of the Modelica type Real,but its value attribute is a set of in-tervals.Accordingly,the value attribute of the basic type Discrete is a set of integer values. An important semantic difference to the equa-tion section in Modelica is that in our be-havior section,any variable can participate in any number of constraints.Our iterative simu-lation algorithm does not rely on the fact that the equation system contains exactly the same number of state variables and equations.It can handle over-or underdetermined equation sys-tems easily.3.2Modeling alternatives3.2.1if-clauses in RODONThe example above illustrated one way to model alternative behavior by means of a syntacti-cal element known from Modelica—the if-clause.However,there are some semantic dif-ferences between if-clauses in RODON and Modelica.In RODON,the clauseif(<condition>)<relation> means that when the problem solver takes this constraint from the agenda,it checksfirst the condition.Only if the condition is decidable and true,the relation is evaluated,and the con-sequent value changes are propagated as usual. This approach allows the use of many if-clauses in a model without slowing down the simulation process significantly.For set-valued variables,logical expressions have not merely two possible values,but three: true,false,or undecidable.A condition is de-cidable if it is either true or false for all combi-nations of values out of the variable’s value sets. For instance,consider the constraintif(2<x&x<5)<relation>If x has the value set[04],there are some elements of the set for which the condition is true,but there are other elements in the value set of x for which it is false.During the itera-tive propagation process,the value set of x may be further constricted so that at some moment in the propagation process,the condition will have a unique logical value.But at the present moment,the problem solver cannot know whichlogical value that will be.Note that for set-valued variables,there are some subtleties when defining correct seman-tics for conditions.Conditions have to be evalu-able monotonly,i.e.if a condition has been de-cided to be true or false once,it must not change this logical value during propagation.This is due to the fact that if a condition has once been true,the corresponding relation has been evalu-ated,and the resulting value changes have been propagated further.If later on the condition be-comes false,we would have to withdraw all val-ues which depend on the earlier evaluation of that relation.To keep track of all these depen-dencies requires a huge effort.Therefore,only monotonously evaluable condi-tions are allowed.That means that a condition like(x subset y),where x and y are in-terval variables,is not permissible,because it is true for x=[010]and y=[-1020],but during the iterative propagation process y may be constricted to y=[-102],which renders the condition undecidable.An overview of all permissible logical relations for set-valued vari-ables is shown in Fig.5.Interval x,y;Real a;constant Interval s;x==ax!=a x!=yx<=a x<=yx<a x<yx>=a x>=yx>a x>yFigure5:Permissible logical relations for value sets.Another topic is the negation of logical expres-sions,which have a slightly different mean-ing for sets than for real values.For instance, the negation of the condition(x==a)is not (x!=a)but(a x).In general,the relation x!=y has to be interpreted as x y==/0.3.2.2The or-clauseThere are situations where it is desirable to have another kind of alternative behavior.Consider the following definition of a piecewise linearx yf xconstraint MyQuadraticSplineInterval x,y;extends Spline(final degree=2,periodic=true,final values=0.5,1,1,1.5, 1.5,3); end MyQuadraticSpline;model UseSplineInterval a,b;behaviorMyQuadraticSpline(a,b)(periodic=false,boundary= 1.3); end UseSpline;Figure7:An example of a simple constraint class.value based on a continuous variable.Consider the following model of an electrical light bulb.model Bulb extends TwoPort;Discrete light(max=2); parameter Current pNom=20; parameter Voltage uNom=12.0; protectedResistance r;Power pc;constant Power pLow=[-0.10.1];constant Power pMedium=[-0.3-0.1][0.10.3];constant Power pHigh=[-2-0.3][0.32];behaviorr=uNom*uNom/pNom;pc=p.i*(p.u-n.u)/pNom;if(fm==0)Ohm(p.u,n.u,p.i,r); if(fm==1)light=0;if(fm==0)or p.i=0;light=0;pc=pLow;light=0;pc=pMedium;light=1;pc=pHigh;light=2;end Bulb;The variable light is an indicator for the mechanic whether the bulb is off(light=0), is dimmed(light=1)or bright(light=2). If by some reason the constraint net is un-derdetermined so that the consumed power of the bulb pc=[0.21],the mechanic gets the information light=0,1,i.e.the bulb is off or dimmed,which may be an impor-tant indication.An analogous definition by means of conditional constraints would result in light=0,1,2,i.e.the whole range of this variable.3.3Defining constraint classes Very much like function classes in Modelica, RODON allows the user to define constraint classes.This may be useful for constraints which are used very often,like Ohm’s law or Kirchhoff’s law in the electrical domain.But it is also convenient for constraints which are laborious to define,e.g.characteristic curves of engines which are given in table form rather than in closed form.As for the function classes in Modelica,constraint classes define an argu-ment list and provide type checking when the constraint class is used.In the example shown in Fig.7,the constraint class Spline is a basic constraint class pro-vided by the RODON modeling language.It has pre-defined attributes degree,peri-odic,boundary and values.There are some other basic constraint classes.Constraint classes may be parameterized by means of the usual modification mechanism.4ConclusionThe striking correspondence of the modeling philosophies in Modelica and RODON as well as the neat class model of Modelica are strong arguments in favour of Modelica as the future modeling language of RODON.But there are some additional requirements caused by our dif-ferent simulation algorithm and the diagnostic approach,namelybasic data type:interval setmultiple behavioral modesalternative behavior:disjunctionsalternative behavior:conditional con-straints,semantics of conditions for set-valued variablesconstraint classescoping with over-or underdetermined con-straint netssimulation by local constraint propagation A few of them can possibly be met by provid-ing special libraries.However,our experience shows that there are features which require an extension of the Modelica language,or the defi-nition of a separate dialect for behavior descrip-tion.References[AH74]G.Alefeld and J.Herzberger.Einf¨u hrung in die Intervallarith-metik.Bibliographisches InstitutAG,Z¨u rich,1974.[dKW87]J.de Kleer and B.Williams.Di-agnosing multiple faults.ArtificialIntelligence,32:1297–1307,1987. [dKW89]J.de Kleer and B.Williams.Di-agnosis with behavioral modes.InProceedings of the IJCAI’89,pages1324–1330,1989.[HHKR95]R.Hammer,M.Hocks,U.Kulisch,and D.Ratz.C++Toolbox for Ver-ified Computing.Springer,1995. [Hyv91] E.Hyv¨o nen.Constraint Reasoningwith Incomplete Knowledge.PhDthesis,Helsinki University,1991. [Mod99]Modelica Association.Modelica-Language Specification,December1999.[Rei87]R.Reiter.A theory of diagnosisfromfirst principles.Artificial In-telligence,32:57–95,1987. [Sei92]W.Seibold.Grundlage der Diag-nose technischer Systeme—sechsThesen.ist–Intelligente Software-Technologien,2(3),1992.[Sei97]W.Seibold.First time right fromlayout to repair.In Proceedingsof the30th ISATA Symposium,Flo-rence(Italy),pages483–492,June1997.。

缩写中文解释3C3个关键零件（缸体、缸盖、曲轴）4 VDP四阶段的汽车发展过程A/D/V分析/发展/验证AA审批体系ABS防抱死制动系统ACD实际完成日期AI人工智能AIAG汽车工业产业群ALBS装配线平衡系统AP提前采购API先进的产品信息APM汽车加工模型APQP先进的产品质量计划AR拨款申请ARP拨款申请过程ARR建筑必要性检查ASA船运最初协议ASB船运第二个协议ASI建筑研究启动ASP船运标准协议ASR建筑选择审查B&U土建公用BCC品牌特征中心BEC基础设计内容BI开始冒气泡B-I-S最佳分节段BIW白车身BOD设计清单BOM原料清单BOP过程清单CAD计算机辅助设计CAE计算机辅助工程(软件)CAFÉ公司的平均燃油经济CAM计算机辅助制造CAMIP持续汽车市场信息项目CARE用户接受度审查和评估CAS概念可改变的选择CDD成分数据图CGS公司图形系统CI提出概念CIT隔间融合为组CKD完全拆缷CMM坐标测量仪CMOP结构管理工作计划CPP关键途径CPP关键途径CR&W 控制/机器人技术和焊接CRIT中心新产品展示执行组CS合同签订CTS零件技术规格D/EC设计工程学会DAP设计分析过程DCAR设计中心工作申请DDP决策讨论步骤DES设计中心DFA装配设计DFM装配设计DLT设计领导技术DMA经销商市场协会DMG模具管理小组DOE试验设计DOL冲模业务排行DQV设计质量验证DRE设计发布工程师DSC决策支持中心DVM三维变化管理DVT动态汽车实验E/M进化的EAR工程行为要求ECD计划完成日期EGM工程组经理ELPO电极底漆ENG工程技术、工程学EOA停止加速EPC&L工程生产控制和后勤EPL工程零件清单ETSD对外的技术说明图EWO工程工作次序FA最终认可FE功能评估FEDR功能评估部署报告FFF自由形态制造FIN金融的FMEA失效形式及结果分析FTP文件传送协议GA总装GD&T几何尺寸及精度GM通用汽车GME通用汽车欧洲GMIO通用汽车国际运作GMIQ通用汽车初始质量GMPTG通用汽车动力组GP通用程序GSB全球战略部HVAC加热、通风及空调I/P仪表板IC初始租约ICD界面控制文件IE工业工程IEMA国际出口市场分析ILRS间接劳动报告系统IO国际业务IPC国际产品中心IPTV每千辆车的故障率IQS初始质量调查IR事故报告ISP综合计划ITP综合培训方法ITSD内部技术规范图IUVA国际统一车辆审核KCC关键控制特性KCDS关键特性标识系统KO Meeting启动会议KPC关键产品特性LLPRLOI意向书M&E机器设备MDD成熟的数据图MFD金属预制件区MFG制造过程MIC市场信息中心MIE制造综合工程师MKT营销MLBS物化劳动平衡系统MMSTS制造重要子系统技术说明书MNG制造工程MPG试验场MPI主程序索引MPL主零件列表MPS原料计划系统MRD物料需求日期MRD物料需求时间MSDSMSE制造系统工程MSS市场分割规范MTBF平均故障时间MTS生产技术规范MVSS汽车发动机安全标准NAMA北美市场分析NAO北美业务NAOC NAO货柜运输NC用数字控制NGMBP新一代基于数学的方法NOA授权书NSB北美业务部OED组织和员工发展P.O采购订单PA生产结果PAA产品行动授权PAC绩效评估委员会PACE项目评估和控制条件PAD产品装配文件PARTS零件准备跟踪系统PC问题信息PCL生产控制和支持PDC证券发展中心PDM产品资料管理PDS产品说明系统PDT产品发展小组PED产品工程部PEP产品评估程序PER人员PET项目执行小组PGM项目管理PIMREP事故方案跟踪和解决过程PLP生产启动程序PMI加工建模一体化PMM项目制造经理PMR产品制造能要求PMT产品车管理小组POMS产品指令管理小组POP采购点PPAP生产零部件批准程序PPAP生产件批准程序PPH百分之PPM百万分之PR绩效评估PR采购需求PR/R问题报告和解决PSA潜在供应商评估PSC部长职务策略委员会PTO第一次试验PUR采购PVM可设计的汽车模型PVT生产汽车发展QAP质量评估过程QBC质量体系构建关系QC质量特性QFD质量功能配置QRD质量、可靠性和耐久力QS质量体系QUA质量RC评估特许RCD必须完成日期RFQ报价请求RFQ报价要求书RONA净资产评估RPO正式产品选项RQA程序安排质量评定RT&TM严格跟踪和全程管理SDC战略决策中心SF造型冻结SIU电子求和结束SL系统规划SMBP理论同步过程SMT系统管理小组SOP生产启动，正式生产SOR要求陈述SOR要求说明书SOW工作说明SPE表面及原型工程SPO配件组织SPT专一任务小组SQC供方质量控制SQIP供应商质量改进程序SSF开始系统供应SSLT子系统领导组SSTS技术参数子系统STO二级试验SUW标准工作单位TA 技术评估TAG定时分析组TBD下决定TCS牵引控制系统TDMF文本数据管理设备TIMS试验事件管理系统TIR试验事件报告TLA 技术转让协议TMIE总的制造综合工程TOE总的物主体验TSM贸易研究方法TVDE整车外型尺寸工程师TVIE整车综合工程师TWS轮胎和车轮系统UAW班组UCL统一的标准表UDR未经核对的资料发布UPC统一零件分级VAPIR汽车发展综合评审小组VASTD汽车数据标准时间数据VCD汽车首席设计师VCE汽车总工程师VCRI确认交叉引用索引VDP汽车发展过程VDPP汽车发展生产过程VDR核实数据发布VDS汽车描述概要VDT汽车发展组VDTO汽车发展技术工作VEC汽车工程中心VIE汽车综合工程师VIS汽车信息系统VLE总装线主管，平台工程师VLM汽车创办经理VMRR汽车制造必要条件评审VOC顾客的意见VOD设计意见VSAS汽车综合、分析和仿真VSE汽车系统工程师VTS汽车技术说明书WBBA全球基准和商业分析WOT压制广泛开放WWP全球采购PC项目启动CA方案批准PA项目批准ER工程发布PPV产品和工艺验证PP预试生产P试生产EP工程样车Descriptions3 Critical Parts(Cylinder-block, Cylinder-head, Crankshaft) Four Phase Vehicle Development ProcessAnalysis/Development/ValidationApprove ArchitectureAnti-lock Braking SystemActual Completion DateArtificial IntelligenceAutomotive Industry Action GroupAssembly Line Balance SystemAdvanced PurchasingAdvanced Product InformationAutomotive Process ModelAdvanced Product Quality PlanningAppropriation RequestAppropriation Request ProcessArchitectural Requirements ReviewAgreement to Ship AlphaAgreement to Ship BetaArchitecture Studies InitiationAgreement to Ship 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MillionPerformance ReviewPurchase RequirementProblem Reporting and ResolutionPotential Supplier AssessmentPortfolio Strategy CouncilPrimary TryoutPurchasingProgrammable Vehicle ModelProduction Vehicle DevelopmentQuality Assessment ProcessQuality Build ConcernQuality CharacteristicQuality Function DeploymentQuality, Reliability,andDurabilityQuality SystemQualityReview CharterRequired Completion DateRequest For QuotationRequirement for QuotationReturn on Net AssetsRegular Production OptionRouting Quality AssessmentRigorous Tracking and Throughout Managment Strategic Decision CenterStyling FreezeSumming It All UpSystem LayoutsSynchronous Math-Based ProcessSystems Management TeamStart of ProductionStatement of RequirementsStatement of RequirementsStatement of WorkSurface and Prototype EngineeringService Parts OperationsSingle Point TeamStatistical Quality ControlSupplier Quality Improvement ProcessStart of System FillSubsystem Leadership TeamSubsystem Technical Specification Secondary TryoutStandard Unit of WorkTechnology AssessmentTiming Analysis GroupTo Be DeterminedTraction Control SystemText Data Management FacilityTest Incident Management SystemTest Incident ReportTechnology License AgreementTotal Manufacturing Integration Engineer Total Ownership ExperienceTrade Study MethodologyTotal Vehicle Dimensional EngineerTotal Vehicle Integration EngineerTire and Wheel SystemUnited Auto WorkersUniform Criteria ListUnverified Data ReleaseUniform Parts ClassificationVehicle & Progress Integration Review TeamVehicle Assembly Standard Time DataVehicle Chief DesignerVehicle Chief EngineerValidation Cross-Reference IndexVehicle Development ProcessVehicle Development Production Process Verified Data ReleaseVehicle Description SummaryVehicle Development TeamVehicle Development Technical Operations Vehicle Engineering CenterVehicle Integration EngineerVehicle Information SystemVehicle Line ExecutiveVehicle Launch ManagerVehicle and Manufacturing Requirements Review Voice of CustomerVoice of DesignVehicle Synthesis,Analysis,and Simulation Vehicle System EngineerVehicle Technical SpecificationWorldwide Benchmarking and Business Analysis Wide Open ThrottleWorldwide PurchasingProgram CommencementConcept ApprovalPrograme ApprovalEngineering ReleaseProduct & Process ValidationPre-PilotPilot。