基于随机无网格伽辽金法和蚂蚁算法的结构可靠性分析

 用摄动随机无网格伽辽金法(PSEFGM)求解随机结构的响应,然后采用蚂蚁算法对结构可靠性进行了分析。摄动随机无网格伽辽金法具有不需要划分单元和精度高等特点。蚂蚁算法是一种智能型随机搜素优化算法,对目标函数没有任何可微甚至连续的要求,可有效克服经典算法易于陷入局部最优解的常见弊病。数值实例表明,在随机结构可靠性分析方面,随机无网格迦辽金法与蚂蚁算法比经典算法具有明显的优势。     

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.     

A concurrent model reduction approach on spatial and random domains for the solution of stochastic PDEs

A methodology is introduced for rapid reduced‐order solution of stochastic partial differential equations. On the random domain, a generalized polynomial chaos expansion (GPCE) is used to generate a reduced subspace. GPCE involves expansion of the random variable as a linear combination of basis functions defined using orthogonal polynomials from the Askey series. A proper orthogonal decomposition (POD) approach coupled with the method of snapshots is used to generate a reduced solution space from the space spanned by the finite element basis functions on the spatial domain. POD methods have been extremely popular in fluid mechanics applications and have subsequently been applied to other interesting areas. They have been shown to be capable of representing complicated phenomena with a handful of degrees of freedom. This concurrent model reduction on the random and spatial domains is applied to stochastic partial differential equations (PDEs) in natural convection processes involving randomness in the porosity of the medium and the Rayleigh number. The results indicate that owing to the multiplicative nature of the concurrent model reduction, extremely large computational gains are realized without significant loss of accuracy. Copyright © 2005 John Wiley & Sons, Ltd.     

Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review

Monte Carlo methods have attracted constant and even increasing attention in structural reliability analysis with a wide variety of developments seamlessly presented over decades. Along the way, a number of specialized reviews and benchmark studies have been provided from time to time, aiming at summarizing and comparing selected few approaches in detail, mainly from an implementation point of view. In contrast, the aim of the present survey is to play a comprehensive role as a methodological guidebook on Monte Carlo simulation and its related, especially variance reduction, techniques through a covering of 444 references in the relevant literature. To achieve this goal, we present an extensive review of formulations and techniques along with insightful summaries of developments of existing numerical methods, ranging from the general formulation, sub-categories and variants, to their combined uses with other simulation techniques and surrogate models, as well as the key advantages and assumptions.     

基于随机过程跨越理论的钢轨动力可靠性分析与比较

采用模态分析方法建立车辆-轨道垂向耦合动力计算模型,使用Wilson-θ数值积分方法,得到钢轨在列车荷载作用下的随机振动响应。基于随机过程跨越理论,得到在不同的跨越假设以及极值分布条件下钢轨的动力响应可靠度,并与数值模拟法计算的结果进行比较。结果表明：对于低跨越界限,极值I型分布方法的计算结果与精确值最为接近;而对于高界限,高斯分布法效果最好。     

An efficient hybrid reliability analysis method with random and interval variables

Random and interval variables often coexist. Interval variables make reliability analysis much more computationally intensive. This work develops a new hybrid reliability analysis method so that the probability analysis (PA) loop and interval analysis (IA) loop are decomposed into two separate loops. An efficient PA algorithm is employed, and a new efficient IA method is developed. The new IA method consists of two stages. The first stage is for monotonic limit-state functions. If the limit-state function is not monotonic, the second stage is triggered. In the second stage, the limit-state function is sequentially approximated with a second order form, and the gradient projection method is applied to solve the extreme responses of the limit-state function with respect to the interval variables. The efficiency and accuracy of the proposed method are demonstrated by three examples.     

基于AR算法的小波技术在随机场模拟中的应用

采用线性滤波器法中的AR法模拟生成了地震动场和风场的时程信号。由于AR算法具有很高的计算效率,但模拟精度却不理想,故引入小波分析中的小波分解方法和小波包分解方法对AR算法模拟的信号进行调整,并对这两种方法改进的效果进行对比。算例分析表明由改进的AR法得到的样本信号频谱与目标谱吻合良好,且发现小波包分解方法调整信号具有比小波分解方法更好的精度。     

A new reliability analysis method for uncertain structures with random and interval variables

In this paper, a new reliability analysis method is developed for uncertain structures with mixed uncertainty. In our problem, the uncertain parameters with sufficient information are treated by random distributions, while some ones with limited information can only be given variation intervals. A complex nesting optimization will be involved when using the existing methods to compute such a hybrid reliability, which will lead to extremely low efficiency or instable convergence performance. In this paper, an equivalent model is firstly created for the hybrid reliability, which is a conventional reliability analysis problem with only random variables. Thus only through computing the reliability of the equivalent model the original hybrid reliability can be easily evaluated. Based on the above equivalent model, an algorithm with high efficiency and robust convergence performance is then constructed for computation of the above hybrid reliability with both random and interval variables. Two numerical examples are provided to demonstrate the effectiveness of the present method.     

Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

A method of human reliability analysis and quantification for space missions based on a Bayesian network and the cognitive reliability and error analysis method

Analyses of human reliability during manned spaceflight are crucial because human error can easily arise in the extreme environment of space and may pose a great potential risk to the mission. Although various approaches exist for human reliability analysis (HRA), all these approaches are based on human behavior on the ground. Thus, to appropriately analyze human reliability during spaceflight, this paper proposes a space‐based HRA method of quantifying the human error probability (HEP) for space missions. Instead of ground‐based performance shaping factors (PSFs), this study addresses PSFs specific to the space environment, and a corresponding evaluation system is integrated into the proposed approach to fully consider space mission characteristics. A Bayesian network is constructed based on the cognitive reliability and error analysis method (CREAM) to model these space‐based PSFs and their dependencies. By incorporating the Bayesian network, the proposed approach transforms the HEP estimation procedure into a probabilistic calculation, thereby overcoming the shortcomings of traditional HRA methods in addressing the uncertainty of the complex space environment. More importantly, by acquiring more information, the HEP estimates can be dynamically updated by means of this probabilistic calculation. By studying 2 examples and evaluating the HEPs for an International Space Station ingress procedure, the feasibility and superiority of the developed approach are validated both mathematically and in a practical scenario.     

Response and reliability analysis of a high-dimensional stochastic system

The efficiency of the probability density evolution method (PDEM) is improved in this paper by embedding the Kullback–Leibler (K–L) relative sensitivity in the response analysis of a stochastic dynamic system. The response reliability obtained and the probability density function of the response peaks are used for ranking to get a reduced set of random variables for the PDEM analysis. The need of complicated point selection technique with the high-dimensional uncertain variables is therefore alleviated. The proposed method is illustrated with the response analysis of a random crowd-structure system where the load randomness is considered. The acceleration response induced by the presence of the crowd is evaluated with the proposed method. Results obtained highlight the significant improvements in the computation efficiency of the probabilistic response analysis of a high-dimensional dynamic system.     

Dynamic response and reliability analysis of non-linear stochastic structures

A new probability density evolution method is proposed for dynamic response analysis and reliability assessment of non-linear stochastic structures. In the method, a completely uncoupled one-dimensional governing partial differential equation is derived first with regard to evolutionary probability density function (PDF) of the stochastic structural responses. This equation holds for any response or index of the structure. The solution will put out the instantaneous PDF. From the standpoint of the probability transition process, the reliability of the structure is evaluated in a straightforward way by imposing an absorbing boundary condition on the governing PDF equation. However, this does not induce additional computational efforts compared with the dynamic response analysis. The computational algorithm to solve the PDF equation is studied. A deterministic dynamic response analysis procedure is embedded to compute coefficient of the evolutionary PDF equation, which is then numerically solved by the finite difference method with total variation diminishing scheme. It is found that the proposed hybrid algorithm may deal with non-linear stochastic response analysis problem with high accuracy. Numerical examples are investigated. Parts of the results are illustrated. Some features of the probabilistic information of the response and the reliability are observed and discussed. The comparisons with the Monte Carlo simulations demonstrate the accuracy and efficiency of the proposed method.     

Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size

The main objective of this paper is to present a generic meso-scale probability model for a large class of random anisotropic elastic microstructures in order to perform a parametric analysis of the Representative Volume Element (RVE) size. This new approach can be useful for a direct experimental identification of random anisotropic elastic microstructures when the standard method cannot easily be applied to anisotropic elastic microstructures. Such a RVE is used to construct the macroscopic properties in the context of stochastic homogenization. The probability analysis is not performed as usual for a given particular random microstructure defined in terms of its constituents. Instead, it is performed for a large class of random anisotropic elastic microstructures. For this class, the probability distribution of the random effective stiffness tensor is explicitly constructed. This allows a full probability analysis of the RVE size to be carried out and its convergence to be studied. The procedure of homogenization is based on a homogeneous Dirichlet condition on the boundary of the RVE. The probability model used for the stiffness tensor-valued random field of the random anisotropic elastic microstructure is an extension of the model recently introduced by the author for elliptic stochastic partial differential operators. The stochastic boundary value problem is numerically solved by using the stochastic finite element method. The probability analysis of the RVE size is performed by studying the probability distribution of the random operator norm of the random effective stiffness tensor with respect to the spatial correlation length of the random microstructure.     

基于区间分析的舰船装备可靠性模糊分配方法

针对舰船装备可靠性分配工作中具有多种影响因素且部分影响因素较难定量分析的问题,提出了一种基于AHP、模糊综合评判和区间分析的可靠性模糊综合分配方法.采用模糊综合评判构建了系统的可靠性分配模型,并设计出分配的技术路线;综合分析了8种影响可靠性分配的因素及其量化方法,并采用AHP构造了系统的可靠性分配递阶层次模型;采用区间数代替单一数值来表达模糊信息,并将定量分析与定性分析相结合,合理利用专家经验和相似系统的可靠性数据来确定判断矩阵和各影响因素的权重,从而有效解决了舰船装备可靠性模糊综合分配过程中的不确定性问题.最后,以某型舰电力系统可靠性分配为例,研究表明:该方法可操作性强、分配合理有效,具有较好的工程实践指导意义.     

On the possibility and reliability of predictions based on stochastic citation processes

A statistical model for citation processes, a particular version of a non-homogeneous birth process, is analysed in the context of predictions of future citation rates. Important properties of the process were already studied by the author in earlier papers. Although the applicability of the model was demonstrated by several examples, practical aspects of predictions and questions of statistical reliability were not tackled so far. The present study is focused on the demonstration of the possibility of true predictions and on the analysis of the statistical reliability of predictions based on the mean value functionE(X(t)−X(s)/X(s)=i) of citation processes. The citation rates for papers published in 1980 and 1991 were recorded in the period 1980 through 1995, and 1991 through 1995, respectively, in all science areas. It is shown that parameters of mean value functions estimated for earlier time periods can be applied to more recent years, too. As a by-product, the model may serve as a validation tool for the particular choice of citation windows in evaluation studies.     

基于概率密度演化理论的结构抗震可靠性分析

运用随机过程的正交展开方法,将地震动加速度过程表示为由10个左右的独立随机变量所调制的确定性函数的线性组合形式。结合概率密度演化方法和等价极值事件的基本思想,研究了非线性结构的抗震可靠度分析问题。以具有滞回特性的非线性结构为例,对某一多自由度的剪切型框架结构进行了抗震可靠性分析。结果表明：按照复杂失效准则计算的结构抗震可靠度较之结构各层抗震可靠度均低。这一研究为基于概率密度函数的、精细化的抗震可靠度计算提供了新的途径。     

A CDM analysis of stochastic ductile damage growth and reliability

The accumulation of damage within a structure due to service loading or environmental conditions is a random phenomenon. Continuum damage mechanics (CDM) enables macroscopic manifestations of damage to be related to microscopic defects and discontinuities present within a material. This permits margins of safety to be assessed prior to the time at which damage becomes visible or detectable. Under fairly general thermodynamic conditions, equations of damage growth can be formulated in terms of the Helmholtz free energy. Spatial and temporal fluctuations in the state variables, caused first by the intrinsic variations in the material microstructure and second to environmental and loading conditions, are modeled by treating the Helmholtz free energy as a random process. This leads to a stochastic differential equation (SDE) of random damage growth, the solution of which describes the evolution of time-dependent random ductile damage and residual strength. Available experimental results are used to validate the CDM formulation.