基于等概率近似变换的 向量型层递响应面法分析结构可靠度

基于正交变换和等概率近似变换,研究建立了随机变量为非高斯互相关的工程结构可靠度分析的向量型层递响应面法。首先利用正交变换将非高斯互相关随机变量变换为互不相关的非高斯标准随机变量,建立结构总体刚度矩阵和荷载列阵,据此定义预处理器并形成预处理随机Krylov子空间,进而利用该空间的层递基向量将结构总体节点位移向量近似展开,建立关于互不相关非高斯标准随机变量的层递响应面;然后根据等概率近似变换,将独立标准正态空间的样本点转换为层递响应面在非高斯空间中的概率配点;最后通过回归分析确定层递响应面待定系数,并利用层递响应面建立极限状态方程求解结构可靠度。分析表明:该文提出的等概率近似变换方法不仅成功地将层递响应面法拓展到非高斯互相关随机变量下的结构可靠度分析,而且方法简便、适用范围广、计算精度和效率较高,具有良好的全域性。     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.     

Reliability analysis of excavator boom considering mixed uncertain variables

There are differences among sampling data and representation types of uncertain interval, fuzzy and random variables, which increases the complexity of structure reliability analysis. A α, β-Cut-FORM is proposed to analyze structure reliability considering the mixed uncertain variables. Fuzzy variables are optimized on the interval under two cut sets (α, β) based on the theory of cut set optimization. Interval variables are modeled with probability using a uniformity method. The proposed method involves the nested probabilistic analysis and interval analysis. The first-order reliability method (FORM) is used for probabilistic analysis and nonlinear optimization is used for interval analysis. The excavator boom performance function is established for reliability analysis considering the mixed uncertain input variables, which verifies the effectiveness and advantages of the proposed method. And it has great application for safe and reliable design of excavator boom.     

Reliability analysis of TLP tethers under impulsive loading

In the present study, reliability assessment of Tension Leg Platform (TLP) tethers against maximum tension (i.e. tension exceeding yield) has been carried out under combined action of extreme wave and impulsive forces. For this purpose, a nonlinear dynamic analysis of TLP has been carried out in time domain. A limit state function for maximum tension (i.e. tension exceeding yield) has been derived employing Von-Mises theory of failure. Using this derived limit state function and responses obtained after dynamic analysis under sinusoidal, half-triangular and triangular impulsive forces, reliability assessment of the TLP tethers has been carried out. Design point, important for probabilistic design of tethers, has been located on the failure surface after solving a constrained optimization problem. To study the influence of various random variables on tether reliability, sensitivity analysis has been carried out. Effects of angle of impact; effect of variable submergence; and effect of material yield strength on tether reliability have also been studied on parametric basis. Effect of uncertainty on overall tether reliability has also been discussed to show the importance of quality control in the various design parameters.     

Reliability-based evaluation of automotive wind noise quality

This paper proposes an efficient method for the reliability analysis of a vehicle body–door subsystem with respect to an important quality issue—wind noise. A nonlinear seal model is constructed for the automotive wind noise problem and the limit state function is evaluated using finite element analysis. A multi-modal adaptive importance sampling (AIS) method is developed for reliability analysis at system level, to improve the efficiency of the Monte Carlo simulation. The method can easily handle implicit and time-dependent limit-state functions, with variables of any statistical distributions. Existing analytical as well as simulation-based methods are also investigated to solve the car door wind noise problem. It is demonstrated through this industrial application problem that the multi-modal AIS method is superior to existing methods in terms of efficiency and accuracy. A generalized framework for reliability estimation is then established for series system reliability problems with large numbers of random variables and complicated, implicit limit states.     

A Copula Approach in the Point Estimate Method for Reliability Engineering

In order to arrive at realistic results in statistical analysis, it is often advisable to consider involved uncertainties as random variables. An important aspect in this context is the evaluation of the importance of parameter uncertainty. Because of the complexity of computational models, the point estimate method is usually adopted as an easy‐run approach for approximating the statistical moments of a system/model in a reliability analysis. The efficiency of this method highly depends on the correlation coefficient. However, the complex nature of parameters in computational problems often exhibits a nonlinear relationship. This paper aims to develop an original and efficient point estimate method based on the copula approach for reliability engineering problems. The paper discusses the use of the copula theory in the point estimate method for computing the statistical moments of a function involving random variables. The study performs two engineering applications to demonstrate the benefits of this approach. The performance of this proposed method can significantly improve the quality of the results in using the point estimate method when a nonlinear relationship exists between the parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability analysis of projectile penetration into geological targets

The present study is dedicated to the reliability analysis of projectile penetration into a buried concrete target. The expressions for depths of penetration in the buried target have been derived for crater and tunnel regions separately using the methodology proposed by earlier investigators. These penetration depths have then been employed for subsequent reliability analysis using first-order reliability method. Design points, important for probabilistic design, have been located on the failure surface. Sensitivity analysis has been carried out to study the influence of various random variables on projectile reliability. Some parametric studies have also been included to obtain some results of field interest.     

复合材料层合板非线性系统随机振动的样条有限元分析

工程结构中的复合材料的几何参数往往具有随机性质,如何研究随机参数非线性系统的随机响应及统计特性,对结构的可靠性设计和优化设计有着非常重要的意义。应用摄动法、随机中心差分法和线化和校正法,建立了复合材料非线性系统的振动方程和计算模型,采用样条有限元法研究了复合材料层合板具有随机参数的非线性系统在确定性荷载下的随机响应,数值算例说明了本算法的正确性。     

Reliability analysis of a mechanical contact between deformable solids

The contact problems in mechanics are very complex. The behavior of a structure, where a contact occurs, depends on some assumptions on the design parameters and is in general highly nonlinear. Several deterministic numerical methods have been developed on finite element codes and give accurate solutions of contact problems. However some design variables could be random and the deterministic results could be unacceptable. Thus a new reliability analysis of a mechanical contact is presented. A reliability–mechanical combination based on an augmented Lagrangian method and a response surface method is proposed to compute the failure probability of this nonlinear problem. Then the advantages of this probabilistic approach are exposed and commentated on an Hertz numerical application.     

Reliability analysis of metal‐composite adhesive joints under debonding modes I,II, and I/II using the results of experimental and FEM analyses

In the present study, the experimental and finite element (FE) analyses are first carried out to investigate the deboning behavior of metal‐composite adhesive joints under modes of I and mode II loading. To conduct an FE on the debonding propagation, cohesive zone method (CZM), as well as maximum nominal stress and energy criteria, is applied. In the reliability analysis, to achieve the probability of debonding growth (PODG), limit state functions are formulated based on the energy release rate. To that end, the first‐order reliability method (FORM), the second‐order reliability method (SORM), and the Monte Carlo simulation (MCS) are used to calculate the PODG. The effect of initial debonding length on the PODG in all mentioned modes is investigated. Results obtained from reliability analysis reveal that the random variables including the initial debonding length, width, and thickness are the most sensitive variables to ascertain the PODG.     

Reliability analysis of structures using neural network method

In order to predict the failure probability of a complicated structure, the structural responses usually need to be estimated by a numerical procedure, such as finite element method. To reduce the computational effort required for reliability analysis, response surface method could be used. However the conventional response surface method is still time consuming especially when the number of random variables is large. In this paper, an artificial neural network (ANN)-based response surface method is proposed. In this method, the relation between the random variables (input) and structural responses is established using ANN models. ANN model is then connected to a reliability method, such as first order and second moment (FORM), or Monte Carlo simulation method (MCS), to predict the failure probability. The proposed method is applied to four examples to validate its accuracy and efficiency. The obtained results show that the ANN-based response surface method is more efficient and accurate than the conventional response surface method.     

Time-varying reliability method based on linearized Nataf transform

In actual engineering, material properties, load effects, and other factors of mechanical structures change due to long-term use. In order to understand the operation of a mechanical structure in real time, it is crucial to obtain the dynamic trajectory of its reliability. Considering the time variability of a mechanical structure over time, uncertain random variables are introduced to express the uncertainty of various parameters of structures, and the Wiener process is used to describe the strength degradation process of structures so as to solve the calculation problem of time-varying reliability of mechanical structures. Based on the advanced first-order and second moment method (AFOSM), the proposed linearized Nataf change is used to complete the transformation from related nonnormal variables to independent standard normal variables in order to simplify the calculation process of reliability solution and solve the reliability calculation problem of random parameters subjected to arbitrary distribution. The deduced random variable sensitivity factor indicates the degree of influence of different random variables on the reliability of the mechanical structure, providing a theoretical basis for the optimal design and maintenance of a mechanical structure. The proposed method is analyzed using the cantilever beam and compared with the nonlinear Nataf transform and verified by the Monte Carlo simulation results. The results show that the proposed method can effectively solve the reliability sensitivity problem of structural system strength degradation.     

Prediction of reliability analysis of composite tubular structure under hygro-thermo-mechanical loading

The present paper focuses on reliability prediction of composite structure under hygro-thermo-mechanical loading, conditioned by Tsai-Wu failure criterion, where the Monte–Carlo method is used to estimate the failure probability(Pf). This model was developed in two steps: first, the development of a deterministic model, based on an analytical and numerical approach, and then, a probabilistic computation. Using the hoop stress for each ply, a sensitivity analysis was performed for random design variables, such as materials properties, geometry, manufacturing, and loading, on composite cylindrical structure reliability. The probabilistic results show the very high increase of failure probability when all parameters are considered.     

Reliability sensitivity analysis with random and interval variables

In reliability analysis and reliability‐based design, sensitivity analysis identifies the relationship between the change in reliability and the change in the characteristics of uncertain variables. Sensitivity analysis is also used to identify the most significant uncertain variables that have the highest contributions to reliability. Most of the current sensitivity analysis methods are applicable for only random variables. In many engineering applications, however, some of uncertain variables are intervals. In this work, a sensitivity analysis method is proposed for the mixture of random and interval variables. Six sensitivity indices are defined for the sensitivity of the average reliability and reliability bounds with respect to the averages and widths of intervals, as well as with respect to the distribution parameters of random variables. The equations of these sensitivity indices are derived based on the first‐order reliability method (FORM). The proposed reliability sensitivity analysis is a byproduct of FORM without any extra function calls after reliability is found. Once FORM is performed, the sensitivity information is obtained automatically. Two examples are used for demonstration. Copyright © 2009 John Wiley & Sons, Ltd.     

Sensitivity based reduced approaches for structural reliability analysis

In the reliability analysis of a complex engineering structures a very large number of system parameters can be considered to be random variables. The difficulty in computing the failure probability increases rapidly with the number of variables. In this paper, a few methods are proposed whereby the number of variables can be reduced without compromising the accuracy of the reliability calculation. Based on the sensitivity of the failure surface, three new reduction methods, namely (a) gradient iteration method, (b) dominant gradient method, and (c) relative importance variable method, have been proposed. Numerical examples are provided to illustrate the proposed methods.     

Reliability analysis of a buried concrete target under missile impact

This paper presents the methodology for reliability analysis of a buried concrete target against normal missile impact. The expressions for the depths of penetration in buried target have been derived using the methodology proposed in the literature. These equations have then been employed for reliability estimation. Design points, important for the probabilistic design, have been located on the failure surface. Sensitivity analysis has been carried out to study the influence of various random variables on target safety. Some parametric studies have also been included to obtain the results of field interest.     

一座现有拱桥面内失稳的可靠度随机有限元分析

用基于一次可靠度方法的可靠度随机有限元对一座现有的钢筋混凝土拱桥面内稳定性进行剩余可靠度计算,并对影响稳定性可靠度的主要参数进行了灵敏度分析。以随机变量和随机场表示现状荷载(汽车荷载、人群荷载、桥面二期恒载和结构自重)及结构参数(主拱圈弹性模量)。用作者提出的基于线性回归的随机场离散方法离散上述随机场,以有限元稳定分析的解作为复杂结构的隐式功能函数。上述功能以及失稳特征值对基本变量的梯度计算均已包含在作者开发的可靠度随机有限元程序RESFEP中。分析给出此桥稳定性可靠度值。灵敏度分析表明:在各随机变量中,拱肋弹性模量随机场离散变量对拱桥可靠度指标影响最大,汽车荷载随机场离散变量次之;在各随机变量的均值和标准差中,拱肋弹性模量随机场离散变量均值和标准差对拱桥可靠度影响最大,汽车荷载随机场离散变量的均值和标准差次之。     

Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation

Probabilistic uncertainty analysis quantifies the effect of input random variables on model outputs. It is an integral part of reliability-based design, robust design, and design for Six Sigma. The efficiency and accuracy of probabilistic uncertainty analysis is a trade-off issue in engineering applications. In this paper, an efficient and accurate mean-value first order Saddlepoint Approximation (MVFOSA) method is proposed. Similar to the mean-value first order Second Moment (MVFOSM) approach, a performance function is approximated with the first order Taylor expansion at the mean values of random input variables. Instead of simply using the first two moments of the random variables as in MVFOSM, MVFOSA estimates the probability density function and cumulative distribution function of the response by the accurate Saddlepoint Approximation. Because of the use of complete distribution information, MVFOSA is generally more accurate than MVFOSM with the same computational effort. Without the nonlinear transformation from non-normal variables to normal variables as required by the first order reliability method (FORM), MVFOSA is also more accurate than FORM in certain circumstances, especially when the transformation significantly increases the nonlinearity of a performance function. It is also more efficient than FORM because an iterative search process for the so-called Most Probable Point is not required. The features of the proposed method are demonstrated with four numerical examples.     

工程结构可靠度指标计算的混沌搜索方法

基于可靠度指标b的几何涵义提出了一种用混沌搜索工程结构可靠度指标和设计验算点的新方法该方法利用混沌内在的随机性与遍历性进行求解最终获得全局最优算例结果表明该方法简单实用性能良好能够处理基本随机变量的非正态分布和变量之间的相关性是解决非线性功能函数可靠度问题的有效途径     

Adaptive surrogate model coupled with stochastic configuration network strategies for time-dependent reliability assessment

Time-dependent reliability assessment is crucial in enhancing product development economics and product performance sustainability throughout the lifecycle. It is still a challenge to accurately and efficiently evaluate the time-dependent reliability of engineering systems. This paper proposes a novel adaptive surrogate model method combining stochastic configuration network (SCN) and Kriging strategies to evaluate time-dependent reliability. SCN has accurate approximation ability and learning efficiency for strongly nonlinear systems that can overcome the conventional time-dependent reliability calculation, which is time-consuming and characterized by low accuracy. The proposed method first applies SCN to establish the response model of the performance function with respect to time and obtain the extreme value of the performance function. Then, Kriging is used to establish the extreme value model of the performance function with respect to the random variables based on the extreme value of performance function. The adaptive process considering the characteristics of random variables samples is adopted to update the extreme value model until the model meets the confidence target. Lastly, Monte Carlo simulation is employed for time-dependent reliability assessment based on the established extreme value model. Three example studies are used to demonstrate the effectiveness of the proposed approach for time-dependent reliability assessment.