状态模糊下主客观不确定性同时存在的重要性测度分析

为了分析状态模糊下主观不确定性对失效概率的影响,定义了两种重要性测度指标:相关系数和相关比。针对传统的Monte Carlo方法计算量大的缺点,利用近似方法引入一个比例系数C将三层Monte Carlo循环简化成双层循环。为了进一步减小计算量,本文建立了一种状态模糊下主客观不确定性同时存在时重要性测度指标求解的移动最小二乘MLS(Move Least Square)法。该方法通过移动最小二乘策略拟合主观变量与响应量输出之间的映射关系,并根据此关系可以很方便地得到模型的条件响应输出,进而得到主客观不确定性同时存在情况下的重要性测度。本文算例验证了所提方法的效率和精度。     

响应面法在结构参数灵敏度及可靠性分析中的应用

采用Box-Behnken 矩阵设计方法进行试验设计,并根据设计点的响应,利用最小二乘回归法建立响应面函数. 将响应面函数中参数的梯度信息与其分散程度结合,得到各参数的灵敏度系数,再归一化灵敏度系数得到概率灵敏度;将响应面模型与一次二阶矩法相结合计算结构的可靠度. 针对一个具体算例,分别采用基于响应面法与基于ANSYS 的Monte Carlo 法计算了结构的灵敏度及可靠度值,结果的一致性验证了该方法的有效性.     

模糊分布参数条件下结构系统的近似效应分析

针对结构系统中随机变量的分布参数具有不确定性的问题, 采用模糊数来描述分布参数的主观不确定性, 并且利用隶属度来衡量主观不确定性的大小. 在不同隶属度水平下, 分别建立了输出响应和失效概率的主效应和总效应模型, 研究了两种模型和隶属度水平之间的关系, 并且给出分布参数不确定性的平均效应指标. 针对所提指标计算量大的问题, 通过对输出响应的各阶矩进行一阶泰勒展开, 建立了两种指标的计算方法. 算例结果验证了所提指标的合理性和所提方法的高效性.     

不确定结构动力区间分析方法研究

将结构中的不确定性参数用区间数来表示,建立了系统的区间动力特征方程和动力控制方程.通过将Monte Carlo方法引入到区间分析中来,并改进了一般Monte Carlo方法在区间模拟中存在的缺陷,对区间动力特征方程和动力控制方程进行了求解,得到了结构的固有频率、位移响应和应力响应的区间计算结果.算例表明改进的Monte Carlo方法求解简单,具有普适性,能够给出较高精度的响应区间.     

CFRP加固RC梁的模糊随机可靠度数值模拟

CFRP加固RC结构可靠度的不确定性,不仅要考虑随机性,也要考虑模糊性.本文根据模糊数学与可靠性理论,研编了引入模糊示性函数的Monte Carlo计算程序,通过试验讨论模糊示性函数的确定方法.利用Matlab软件,直接产生随机变量数组,解决Monte Carlo 抽样困难.CFRP加固梁破坏试验获得全部随机变量的统计参量.编制基于Matlab的Monte Carlo计算程序,完成了对CFRP加固RC梁抗弯模糊随机可靠度数值模拟,模拟计算结果得到传统FOSM法验证.     

一种改进的全局重要性测度

基本输入变量对其响应量影响的重要度的量化问题是概率风险评估以及灵敏度分析重要组成部分.针对矩独立重要性测度和基于方差的重要性测度的不足,在Borgonovo重要性测度的基础之上,提出了一种新的全局重要性测度指标.该指标将矩独立方法与基于方差方法思想相结合,既考虑基本输入变量对输出响应量整个分布的平均影响,又考虑了这种影响的分散程度,并且还避免采用单一的矩作为其输出响应量不确定性的评价标准.这在一定程度上增加了决策时的信息,避免决策错误.通过Ishigami检验函数模型算例以及Iman模型算例说明该指标的正确性,同时,通过九盒段机翼结构以及悬臂梁结构两个力学模型来说明该指标的合理性.     

正态相关变量主客观不确定性分离和参数影响分析

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.      

AN SEPARATION OF THE ALEATORY AND EPISTEMIC UNCERTAINTIES WITH CORRELATED NORMAL VARIABLES AND ANALYSIS OF THE INFLUENCE OF PARAMETERS

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.     

轴弯曲与不平衡柔性转子共振稳态响应随机分析

系统参数随机性是影响准确预测转子动力学行为的重要因素。为此,研究了具有初始轴弯曲的不平衡柔性转子在故障参数随机情况下的不确定性分析问题。首先,基于转子动力学梁元有限元理论,推导了不平衡和轴弯曲故障共同作用下的系统稳态动力学方程,并以轴心轨迹长半轴作为关键响应量建立了柔性转子共振稳态响应与输入参数间的模型函数;其次,联合广义多项式混沌展开、留一法交叉验证以及最小角回归技术实现了柔性转子共振稳态响应的非嵌入式自适应稀疏多项式混沌展开,并与基于普通最小二乘法的多项式混沌展开和基于Monte Carlo仿真的结果作了对比分析,验证了自适应稀疏展开方案的有效性、精度和效率;最后,以构建的自适应稀疏多项式混沌展开式作为近似模型,重点分析了转子圆盘处一阶共振稳态响应的随机特性,并基于Sobol指标获得了响应对各故障参数的全局灵敏度指标。     

改进的移动最小二乘法

近年来发展的无网格方法大多采用移动员小二乘法来构造试函数，而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的，从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进，避免出现病态方程组，且在计算过程中不需要进行短阵求逆运算，提高了计算速度。之后，借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。     

Efficient design sensitivities of structures subjected to dynamic loading

Calculation of design sensitivities often involves much computational effort, particularly in large structural systems with many design variables. Approximation concepts, which are often used to reduce the computational cost involved in repeated analysis, are usually not sufficiently accurate for sensitivity analysis. In this study, approximate reanalysis is used to improve the efficiency of dynamic sensitivity analysis. Using modal analysis, the response derivatives with respect to design variables are presented as a combination of sensitivities of the eigenvectors and the generalized displacements. A procedure intended to reduce the number of differential equations that must be solved during the solution process is proposed. Efficient evaluation of the derivatives, using finite difference and the recently developed combined approximations approach, is presented. Numerical examples show that high accuracy of design sensitivities can be achieved efficiently.     

Optimal control problems with incomplete and different integral time domains in the objective and constraints

Optimal control problem with incomplete and different integral time domains is a class of very common practical engineering problems. In traditional way, the integral items are transformed to the transient items and treated as artificial states to reduce the complexity of programming. However, its main disadvantage is time wasting for the considered problems. In this paper, an efficient computational method is therefore proposed for this type of problem, where the integral time domains can be either fixed or variable. By employing the control vector parameterization and a timescaling transformation, the original problem is converted to an approximate optimal parameter selection problem. Moreover, new gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be easily applied to solve the generated approximate problem. For illustration, three classical numerical examples are tested. The research results, which save 10–22 % of time, show the effectivity of the proposed approach.     

动力可靠度计算的概率简单叠加法则法

首先给出了基于计算单元失效域的重要抽样法和区域分解法的计算步骤,随后利用基于计算单元失效域的重要抽样法的思想,引入构成总失效域的由持时内的时间点划分出的单元失效域;利用区域分解法的思想,引入构成总失效域的互斥的单元失效域,最后根据两种单元失效域的关系和概率简单叠加法则计算总失效概率.其中关键问题是计算结构反应时单位脉冲...     

工程结构优化的进化策略-高斯过程协同优化方法

针对采用仿生全局优化方法进行复杂工程结构优化时数值计算量浩大导致的计算代价过高的公开问题,将自适应协方差矩阵进化策略(CMAES)全局优化算法、高斯过程(GP)机器学习技术与有限元方法相结合,提出了基于自适应协方差矩阵进化策略-高斯过程协同优化算法(CMAES-GP)的结构优化方法。该方法利用全局寻优性好且寻优效率高的CMAES算法进行全局最优搜索,当搜索进入局部寻优阶段时,采用回归性能优秀的GP模型对适应度函数进行动态拟合,进而利用GP模型替代有限元分析进行个体适应度评价,以减小局部寻优阶段的有限元重分析次数,从而实现有效降低工程结构优化计算代价的目的。算例研究表明,与传统结构优化方法相比较,本文方法具有全局性好、计算效率高的优点。     

结构随机分析的概率与复合重要度及其求解

针对基于方差方法的重要度信息量不足而矩独立重要度计算量大、求解难的缺点,将响应量的偏度和蜂度信息引入灵敏度分析中,定义了概率重要度和复合重要度,用于衡量基本变量对响应量分布形状的主要影响趋势及在该影响趋势下的影响程度.同时针对传统方法求解矩的困难,将控制理论中的状态依存参数模型运用于本文所提重要度的求解,极大程度地化筒了计算.最后,通过算例中与基于方差方法的重要度与矩独立重要度的比较,可知本文所提重要度涵盖了基于方差方法重要度和矩独立重要度的主要信息,说明本文重要度的合理性和正确性,算例与Monte Carlo数值模拟方法的比较,表明状态依存参数模型求解方法具有较好的计算精度和效率.     

A Quasilinear Based Procedure for Saturated/Unsaturated Water Movement in Soils

The quasilinear form of Richards equation for one-dimensional unsaturated flow in soils can be readily solved for a wide variety of conditions. However, it cannot explain saturated/unsaturated flow and the constant diffusivity assumption, used to linearise the transient quasilinear equation, can introduce significant error. This paper presents a quasi-analytical solution to transient saturated/unsaturated flow based on the quasilinear equation, with saturated flow explained by a transformed Darcy's equation. The procedure presented is based on the modified finite analytic method. With this approach, the problem domain is divided into elements, with the element equations being solutions to a constant coefficient form of the governing partial differential equation. While the element equations are based on a constant diffusivity assumption, transient diffusivity behaviour is incorporated by time stepping. Profile heterogeneity can be incorporated into the procedure by allowing flow properties to vary from element to element. Two procedures are presented for the temporal solution; a Laplace transform procedure and a finite difference scheme. An advantage of the Laplace transform procedure is the ability to incorporate transient boundary condition behaviour directly into the analytical solutions. The scheme is shown to work well for two different flow problems, for three soil types. The technique presented can yield results of high accuracy if the spatial discretisation is sufficient, or alternatively can produce approximate solutions with low computational overheads by using large sized elements. Error was shown to be stable, linearly related to element size.     

基于更新径向基函数网络模型的广义Pareto分布函数拟合

广义Pareto分布函数GPD(Generalized Pareto Distribution)是一种针对随机参数尾部进行渐进插值的方法,能够对高可靠性问题进行评估。但这种方法要求样本空间较大,计算成本较高,尽管可以通过径向基函数网络RBFNN(Radial Basis Function Neural Network)辅助抽样的方法削减计算成本,但对于非线性程度较高的问题,RBFNN精度问题使得辅助抽样方法失效。针对这类问题,根据GPD的特点,提出了高效的更新RBFNN训练样本的方法,改善了RBFNN在功能函数分布尾部的精度,将RBFNN辅助抽样方法推广应用到非线性程度较高的问题,准确地得到了所有需要的尾部样本,基于该尾部样本集的GPD拟合结果与基于直接计算所有样本的GPD拟合结果完全一致。     

An Anisotropic Sparse Grid Numerical Integration-Based Statistic Moment Estimation Method

Statistic moment estimation is a paramount task in design optimization under uncertainty. In the existing isotropic sparse grid-based statistic moment estimation method, each dimension is considered to be of equal importance and collocated with the same number of integration points. Therefore, “curse of dimensionality” is still very serious. To address this issue, a new statistic moment estimation approach is developed by employing the anisotropic sparse grid technique from the numerical integration point of view in this paper. A new rule allowing different accuracy levels to each dimension according to their varying importance is proposed to determine the eligible multi-index combinations. Integration points can be collocated more reasonably, and more points can be removed from unimportant dimensions to the important ones. The effectiveness of the proposed approach is demonstrated through comparative studies on several mathematical examples and a practical engineering example. It is observed that compared with the existing method, the proposed approach can further mitigate “curse of dimensionality” and significantly improve the accuracy of statistic moment estimation with even less computational cost.