基于径向基函数的机翼二维气动代理模型设计

采用多学科设计优化方法进行机翼气动/结构优化时,结构学科的优化需要气动学科提供机翼压力分布的代理模型。本文引入了等参单元形函数的几何变换思想,利用径向基函数,解决了复杂形状机翼的二维气动代理模型的构造问题,进行了某巡航导弹弹翼考虑结构变形的气动力代理模型的构建。算例结果表明,本文所用代理模型构造方法简单易行,预测结果的精度很好。     

基于代理模型和等效刚度模型的加筋柱壳混合优化设计

针对轴压作用下的加筋柱壳后屈曲性能优化计算较大的问题,本文提出了一种基于代理模型和等效刚度模型的混合优化策略,即运用基于等效刚度的平铺模型进行有限元后屈曲分析以代替试验设计中大量的精细加筋模型分析,并通过控制等效模型的单元尺寸来调整其分析精度,而等效刚度模型计算时长仅约为精细加筋模型的1/3。对构建的代理模型采用多岛遗传算法进行极限承载力等约束下的轻量化设计,调用精细模型有限元后屈曲分析对代理模型进行更新,从而保证代理模型的拟合精度并得到优化解。工程算例结果表明,本文提出的混合优化方法,使加筋柱壳结构在满足承载力情况下减重效果明显。     

基于凸模型的复杂多学科系统可靠性设计研究

复杂工程系统通常涉及到多个相互耦合的学科，而且其中往往存在不确定性因素。本文采用凸模型描述不确定性变量，将序列优化和可靠性评价方法应用于多学科可靠性优化之中，提出了一种新的多学科系统可靠性设计方法。在该方法中，可靠性分析采用功能度量法，多学科优化方法采用多学科可行方法或者二级系统一体化合成优化方法。数值算例和工程算例说明，该方法求解效率较常规嵌套求解方法效率高，为复杂工程系统的可靠性设计提供了一种新型求解算法。     

航天器天线桁架结构多目标优化设计

针对有附加结构的卫星天线桁架结构，提出了一种实现结构多目标优化的综合设计方法。首先，探讨了附加结构刚度对桁架结构动力学特性的影响，以便建立精确的有限元模型，为进行优化设计奠定基础。之后，交替采用代理模型方法和人机交互方式进行结构拓扑构型设计。其中代理模型是采用优化拉丁超立方法进行试验设计，结合径向基函数近似方法生成的。最后，应用NSGA-II全局优化方法实现以重量最小化和频率最大化的多目标优化设计，并根据分层图定量可视化地从Pareto前端和Pareto最优解集中筛选最优设计方案。优化结果表明，相对于初始方案可以在基频几乎不变的情况下，重量减小29.66%。该方法有利于提高设计效率，降低全局优化的复杂度，同时能够得到满足设计要求的设计方案，适用于多目标结构优化设计。     

一种基于两级集成系统合成法的多学科稳健优化方法

针对多学科设计优化中约束存在不确定性的问题,提出了一种稳健优化方法。在该方法中采用区间模型描述不确定性设计变量,约束变化区间的最大值采用遗传算法求得,然后通过选定的满意度水平确定相应的约束值。多学科优化过程依靠两级集成系统合成法实现。通过算例验证了该方法的有效性,对处理多学科不确定性优化设计问题有一定的指导意义。     

基于凸模型的复杂多学科系统可靠性设计研究

复杂工程系统通常涉及到多个相互耦合的学科,而且其中往往存在不确定性因素。本文采用凸模型描述不确定性变量,将序列优化和可靠性评价方法应用于多学科可靠性优化之中,提出了一种新的多学科系统可靠性设计方法。在该方法中,可靠性分析采用功能度量法,多学科优化方法采用多学科可行方法或者二级系统一体化合成优化方法。数值算例和工程算例说明,该方法求解效率较常规嵌套求解方法效率高,为复杂工程系统的可靠性设计提供了一种新型求解算法。     

基于可靠性的车辆防护组件优化

在传统的优化流程中，不考虑设计变量的不确定性将引起设计目标的性能波动，甚至设计失败。为提高军用车辆底部防护能力，针对一种车辆防护组件进行了可靠性优化。在爆炸防护优化中引入多目标可靠性优化，通过实验设计和灵敏度分析筛选设计变量，再构建并选择准确度最高的代理模型，运用多目标遗传算法完成防护组件的可靠性优化。实验和数值模拟结果表明，优化后的防护组件满足防护性和轻量化的要求，且设计的可靠性得到了提升，可为后续防护组件设计生产提供参考。     

高压捕获翼前缘型线优化和分析

为分析翼前缘形状变化对高压捕获翼构型气动性能的影响,基于一种锥体组合捕获翼概念构型,采用幂次函数和余弦函数组合形式对翼前缘型线进行了参数化设计,在比较了多项式和径向基函数两种代理模型的拟合精度基础上,以飞行马赫数7,飞行攻角0?为计算条件,结合使用均匀实验设计方法、计算流体力学、径向基函数代理模型方法和遗传算法,选择升阻比最大化为目标开展了数值优化,最后基于优化结果进行了单参数的灵敏度分析.优化结果表明,相对于基准外形而言,优化后构型升力系数增大了约8.1%,阻力系数减小了约12.2%,升阻比提高了约23.4%.此外,灵敏度分析结果表明升阻比与5个设计参数均呈非线性关系,其中展向角度对升阻比影响最大,其次为幂次曲线的比例参数,其余3个参数对升阻比的影响相对较弱.     

基于Kriging代理模型的连梁金属阻尼器性能研究与参数优化设计

连梁阻尼器是剪力墙连梁结构中主要的耗能部件,其构造形式直接影响剪力墙的性能。本文从连梁阻尼器的几何特征入手,在用料相同的前提下,对四种典型开孔形式金属平面内屈服连梁阻尼器进行耗能性能对比研究,引入Kriging代理模型,构造出不同开孔尺寸与滞回耗能的关系。然后,分别对四种开孔形式的连梁阻尼器几何参数进行进一步优化,以获得最优构型。为简化优化迭代过程中反复的多步加载非线性求解计算,在优化过程中以Kriging代理模型作为反演优化平台,代替原有的几何参数与滞回耗能关系,并采用最大期望提高加点方法,不断提高代理模型在最优解附近的精度,在提高代理模型的代理精度同时,也提高了优化设计效率。所提算法为寻求一种形式简单、性能优越的金属平面内屈服连梁阻尼器提供了新的解决框架。     

基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

多可信度代理模型已经成为提高基于代理模型的优化算法效率和可信度水平最有效的手段之一. 然而目前流行的co-Kriging和分层Kriging (HK)等多可信度代理模型泛化能力不足, 缺乏对高阶/高非线性建模问题的适应性, 难以广泛应用. 文章基于发展的自适应多可信度多项式混沌-Kriging (MF-PCK)代理模型, 在提高建模效率和对高阶/高非线性问题近似准确率的同时, 建立了基于该自适应MF-PCK模型的高效全局气动优化方法. 在发展的方法中, 提出了基于MF-PCK模型的新型变可信度期望改进加点方法, 使代理优化算法效率进一步提高. 为了验证发展方法的全面表现, 将其应用在经典的数值函数算例以及多个跨音速气动外形的确定性优化和稳健优化设计中, 并与基于Kriging和HK模型的代理优化算法进行了全面比较. 结果表明, 发展的新型多可信度全局气动优化方法其优化效率相对于基于Kriging和HK模型的优化效率显著提高, 结果更好也更加可靠, 并且稳健优化设计效率和结果也更符合工程应用需求, 证明了其相对于基于Kriging和HK模型的代理优化算法的显著优势.      

Global sensitivity analysis based on high-dimensional sparse surrogate construction

Surrogate models are usually used to perform global sensitivity analysis(GSA) by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos(PC) expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruction are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices(Sobol indices). These are orthogonal matching pursuit(OMP), spectral projected gradient for L_1 minimization(SPGL1), and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA.     

A thermo-mechanical continuum theory with internal length for cohesionless granular materials

A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory [1–3]; it is constructed by removing these inconsistencies through the introduction of an internal length ℓ. Four constitutive models are proposed and discussed in which ℓ is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.     

A General Algebraic Formulation for Multi-parameter Dynamic Subgrid-scale Modeling

This paper proposes a general algebraic formulation able lo unify all the previous developments in (he frame of subgrid-scale modeling using dynamic mixed models. This formulation can serve as a guide for the design of new multi-parameter SGS models. All usual cases of coupling between momentum and energy (or transport) equation are treated formally, and properties of the associated linear or non-linear system are discussed. It is shown thai all the existing models found in the literature can be grouped into a seven-parameter dynamic model, referred to as the Maximal Complexity Dynamic Model (MCDM) A priori lests on this MCDM are carried out for the subsonic plane channel flow problem, which aim at selecting the most important contributions in multi-parameter dynamic models.     

基于高斯过程分类的结构贝叶斯可靠性分析

贝叶斯可靠性方法是处理不完备信息条件下结构可靠性问题的有效途径之一。在实际应用中，由于可靠性分析的计算量较大，常须采用各种近似替代模型以提高计算效率。传统的替代模型方法是对结构的功能函数予以近似建模。这种方法不易定量考虑模型误差对可靠性分析的影响，且难以应用于诸如功能函数不连续和失效域不连通等情况。为此，本文提出一种基于高斯过程分类的替代模型，直接辨识结构的极限状态曲面，并将其应用于结构贝叶斯可靠性分析之中。分析了替代模型不确定性对可靠性预测结果的影响，给出了失效概率分布参数的方差算式，进而提出了改善模型精度的补充采样准则。通过算例验证了方法的适用性和有被性．     

基于k-fold交叉验证的代理模型序列采样方法

在代理模型序列采样框架下,针对现有研究中的不足之处,通过引入k-fold交叉验证计算样本的预测误差,并结合泰森多边形法和最大距离最小化准则,发展了一种适用于任意代理模型的k-fold CV-Voronoi自适应序列采样方法。相较于传统序列采样方法,本文方法具有计算简单和自适应性强等显著优势。通过数值算例和工程算例对比分析发现所提序列采样方法具有较高的近似精度和计算效率,此外,进一步讨论了k-fold交叉验证中k的不同取值对于代理模型精度的影响,总结出k的最优取值范围以供参考。     

MODELING TWO-PHASE FLOW IN PULSED FLUIDIZED BED

Mathematical models for pulsed fluidization are systematically discussed. Several undetermined constitutive relationships are included in the General Two-Fluid Model (GTFM), the adjustable parameters of which are always chosen at will to some extent. Although there are no adjustable parameters in the Basic Two-Fluid Model (BTFM), its eigenvalues are complex numbers and it is ill-posed for initial-value problems. The Local Equilibrium Model (LEM), a further simplification of BTFM, is discussed at length. Although the model is very simple, it is highly capable of simulating complex processes in pulsed fluidization over a broad range of operating parameters, and its numerical results well fit experimental results in both the variation of bed height and the distribution of particle concentration as fluidizina velocitv varies.     

A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models

Transport in Porous Media - In this paper, we develop a surrogate modelling approach for capturing the output field (e.g. the pressure head) from groundwater flow models involving a stochastic...     

Discussion of Finite Deformation Viscoelasticity Laws with Reference to Torsion Loading

In a previous paper two classes of finite deformation viscoelasticity laws, referred to as Model A and Model B, respectively, have been introduced. They were derived as finite deformation counterparts of two well-known spring-dashpot linear solids, the first one being a spring in parallel with a Maxwell element and the second model consisting of a spring in series with a Kelvin element. In particular, two special forms of the free energy function related to Model A (respectively to Model B) were considered, implying two different finite deformation viscoelasticity laws referred to as Model A1 and Model A2 (respectively Model B1 and Model B2). In the present paper we discuss predicted responses of these models with reference to simple torsion as well as torsion with free ends. Generally, the investigations of the paper have fundamental character in what concerns the basic concepts in formulating viscoelastic models of rate type. Received August 26, 1999     

基于Chebyshev展开的区间穿孔板超材料分析

目前对于声学超材料的传输特性分析和优化大多是基于确定的数值和确定的模型,然而在实际工程和结构设计中存在大量材料自身特性和几何物理参数的不确定性.如果忽略这些不确定变量对声学超材料传输特性分析和优化过程的影响,得到的结果可能不正确.针对这一现状,拟将切比雪夫区间模型引入多层穿孔板超材料,提出多层穿孔板超材料声学透射率的区间切比雪夫展开-蒙特卡洛模拟法(interval Chebyshev expansionMonte Carlo simulation method,ICE-MCSM).该方法采用截断切比雪夫多项式近似拟合多层穿孔板超材料的声学透射率响应曲线,构造声学透射率响应曲线的切比雪夫代理模型;然后采用蒙特卡洛模拟法(Monte Carlo simulation method,MCSM)随机生成一定数量的不确定区间变量的样本数据点,并将生成的不确定区间变量样本数据点代入切比雪夫代理模型,预测单个不确定区间变量和多个不确定区间变量条件下的多层穿孔板超材料声学透射率区间的上界和下界.数值分析结果表明,ICE-MCSM预测的声学透射率变化区间的上界和下界与直接蒙特卡洛法(direct Monte Carlo simulation method,DMCSM)预测的声学透射率上界和下界的结果非常接近.与DMCSM相比,ICE-MCSM具有更高的计算效率.因此,ICE-MCSM可有效且高效地分析不确定区间变量条件下多层穿孔板超材料声学透射率传输特性,具有良好的工程应用前景.     

STABILITY ANALYSIS FOR TWO KINDS OF EQUATIONS IN TWO-SPECIES POPULATION DYNAMICS

In this paper we study the stability for equilibrium points of equations in two-population dynamics.We discuss two predator-prey-patch models.Model1 is described by a differential equation.Model2 is described by an integral differential equation.We obtain the conditions for the stability of their equilibrium points.The results show that the overall population stability despite local extinction is realizable.