可靠度对随机变量及失效模式相关系数敏感度分析及其工程应用

客观存在的诸多不确定性因素使得工程不可避免地存在着风险.随着重大工程的不断涌现,人们越来越关心如何提高工程系统的安全度,降低工程结构的风险.遗憾的是如何降低工程系统的风险直至目前还没有固定的科学方法,大多是基于工程师的经验.以可靠度理论为基础,从可靠度对工程结构的某些参数的敏感性及可靠度对失效模式的相关系数入手,探讨如何从加强或削弱结构参数及失效模式间的相关性的角度出发,来进行降低结构风险的研究.给出了两个算例来说明方法在工程中的应用.     

响应面法在结构体系可靠度分析中的应用

一个失效模式由许多的失效单元构成,它是一个并联系统;而所有的失效模式构成一个串联系统。整个结构体系可看成是许多并联系统(失效模式)组成的一个串联系统。首先,利用基于响应面的随机有限元法来获得失效模式中各个单元的极限状态方程,这些方程都是二次多项式;第二步,利用结构可靠度分析中的几何法得到这些方程的等效线性化方程从而可逐步得到该失效模式的等效线性化方程;第三步,计算各失效模式间的相关系数;最后,由Ditlevsen界限法来计算结构的体系可靠度。算例表明,利用该方法来获得大型、复杂结构的体系可靠度具有高效、实用的特点。     

灾害荷载下结构体系失效模式的相关性及可靠度计算

本文通过引入荷载粗糙度指标,根据有关统计参数讨论了灾害荷载的特性,研究了灾害荷载下结构体系失效模式的相关性及可靠度的近似计算方法,得到了以下结论：灾害荷载下结构体系的失效模式近似完全相关,结构体系可靠度由结构的最弱失效模式决定。     

三维结构可靠度对随机变量的敏感性研究

本文基于三维随机有限元提出了结构点可靠度、失效模式的可靠度及整个结构体系的可靠度分别对随机变量的＂分布参数＂和＂极限状态方程参数＂的敏感性计算方法，并以一典型重力坝为例进行了计算，得出了若干有益的结论。     

转子系统的频率可靠性分析

根据具有随机结构参数的转子系统的固有频率与激振频率差的绝对值不超过规定值的关系准则,定义了转子系统共振问题的可靠性模式和系统的可靠度,提出了避免转子系统发生共振的频率可靠性分析方法,根据失效准则,定义转子系统共振为串联系统问题,应用随机摄动技术、概率统计方法和可靠性理论,对具有随机结构参数的转子系统共振问题的准失效分析方法进行了探索和研究.     

土质边坡的单元失效概率与失效模式研究

土质边坡系统失效概率与土体抗剪强度参数以及地下水位息息相关，在传统边坡可靠度分析中一般只考虑了土体抗剪强度参数的变异性，忽略了地下水位随机性带来的影响。该文将有限元离散技术、上限法理论、相关非高斯随机场模拟方法以及随机规划理论结合起来研究随机地下水位作用下考虑参数空间变异性的边坡系统失效概率。采用有限单元离散边坡土体，将边坡地下水位作为随机变量并考虑土体抗剪参数的空间变异性，基于塑性极限分析上限法构建边坡可靠度分析的随机规划模型；采用基于蒙特卡洛的迭代方法进行求解，得到边坡稳定性系数和速度场；根据边坡中单元的失效信息首次采用AP聚类分析方法来估算边坡的系统失效概率，发展了边坡系统可靠度分析理论。对一个经典的边坡算例进行了系统分析并与极限平衡分析方法、有限元方法结果进行对比，结果表明：随机地下水位作用下考虑参数空间变异性时，边坡存在多种失效模式，AP聚类分析方法可以根据失效单元的位置信息识别出边坡所有失效模式以及对应的失效概率；基于Matlab编制了高效的上限法并行程序，大大提高了计算效率。     

基于最终层失效的复合材料舱体稳健性协调优化

传统可靠性设计难以符合现代设计要求,对舱体进行稳健性优化设计,可提高其综合可靠性。基于基体破坏和纤维断裂两种失效模式,采用验算点法求解复合材料单层可靠度。基于最终层失效假设,提出把结构看作由串联子系统组成的并联系统的思想,结合材料刚度比率退化准则和单层可靠度理论,采用概率逐步失效分析方法,计算出主要失效链,从而得出结构的失效概率。复合材料舱体设计变量复杂,提出二级优化方法思想：一级为系统级布局优化,对加强筋截面形状、位置确定等参数进行优化;二级为子系统级尺寸优化,对筋截面尺寸、复合材料各铺层厚度等参数进行优化。采用自适应随机搜索遗传算法,以复合材料舱体质量最小为目标函数,以可靠度要求为约束条件,采用稳健性协调优化方法,对存在初始缺陷的复合材料舱体进行稳健性优化,为复合材料结构优化设计提供参考。     

工程结构体系可靠度分析的最新研究进展

主要失效模式的识别是结构体系可靠度分析的难点和关键。该文首先综述了主要失效模式识别的国内外研究现状及存在的缺陷;然后针对传统失效模式识别方法主要依靠工程经验确定约界阈值、难以兼顾计算效率和计算精度的问题,介绍了一种结构体系可靠度分析的自适应动态约界法;同时,针对传统失效模式识别方法的路径依赖性所带来的计算量大、识别效率不高等缺陷,介绍了一种结构体系可靠度分析的无路径依赖性方法;最后通过算例分析,验证了这两种方法的有效性和适用性。     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

基于贝叶斯理论的结构动力可靠度更新方法与分析

通过一种基于结构动力测试数据和贝叶斯理论的方法来更新结构可靠度。该方法考虑了结构可能受到的激励和结构模型及其参数的不确定性,利用结构在服役期间的动力测试数据,通过贝叶斯概率方法对结构参数进行了识别。利用拉普拉斯渐近估计解法,对仅根据设计条件得到的结构可靠度进行了更新。对受随机动荷载作用的某桁架结构在三种情况下的可靠度进行了计算:一为仅考虑荷载的随机性,二为考虑荷载的随机性和结构模型参数的先验分布,三为考虑荷载的随机性和结构模型参数的更新分布。比较了实际结构和有限元模型更新后的自振频率和振型,并对更新的可靠度计算结果进行了分析。结果表明,与确定性名义模型的失效概率相比,测点处自由度的更新失效概率与真实值较为接近;未测试自由度的更新失效概率可能与真实值差别较大;增加测点数不一定改善失效概率的更新效果。     

含模糊-区间变量的结构非概率可靠性优化设计

工程结构中存在着诸多不确定性因素,可靠性方法是处理不确定因素的有效途径之一。针对大量工程结构中存在混合不确定信息的问题,提出了一种适用于工程的混合不确定性可靠度计算方法。将模糊变量转化为区间变量,基于体积比的区间可靠性模型,建立了含模糊-区间混合变量的结构非概率可靠性模型。由于该可靠性模型意义明确,对模糊信息的处理也比较合理,可作为混合可靠性计算方法的一种补充。应用此可靠性模型对某飞机机翼结构进行了优化设计,实例计算说明了该文的方法是有效和可行的。     

简化三阶矩拟正态变换及其在结构可靠度分析中的应用

针对三阶矩拟正态变换理论公式系数形式复杂及现有相关系数的转换公式适用范围未明确的问题,通过对公式系数进行简化和对相关系数的讨论,提出了独立随机变量和相关随机变量的简化三阶矩拟正态变换模型,并给出了相关系数转换公式的简明适用范围。通过将提出的简化三阶矩拟正态变换模型与一阶可靠度分析方法(FORM)结合,发展了随机变量分布未知条件下的可靠度分析方法,并采用数值算例验证了该方法的准确性和适用性。研究结果表明,所提出的简化三阶矩拟正态变换模型具有较高的准确性和适用性,能够与FORM分析方法结合,实现随机变量分布未知条件下的结构可靠度分析。     

An effective sensitivity analysis methodology for the reliability‐based structural optimization design to high temperature components

Most of physical parameters of high temperature components are usually correlated with the temperature parameter, which makes the reliability‐based structural optimization design more complicated. So far, few efficient sensitivity analysis methods adapted to highly nonlinear performance function with correlated non‐normal variables have been invented. An effective simulation approach is presented to perform reliability sensitivity analysis with the aid of Cholesky factorization and curve fitting. Moreover, in order to improve the programming and computational efficiency, the mixed programming technique of Visual Basic and MATLAB was employed to develop a reliability sensitivity analysis program. The numerical case shows that the results are consistent with those from other traditional methods, and the engineering cases indicate that the proposed method can be effectively used in highly nonlinear function with correlated non‐normal parameters. Meanwhile, the results also demonstrate that the correlation coefficient parameter of high temperature components is very important in the reliability‐based structural optimization design; hence, this parameter should be fully taken into consideration to ensure that the analysis results are accurate and reasonable. Copyright © 2011 John Wiley & Sons, Ltd.     

多变量函数统计矩点估计法的性能比较

多变量函数的统计矩估计是随机系统分析和可靠度分析中较为普遍的问题,点估计法则是解决这类问题的最为简单、高效的途径。为便于点估计法在实际工程中的合理应用,该文试图通过详细、系统的算例分析,对几类典型点估计法的计算性能展开讨论。通过二次函数和混合函数在多种变量工况下的低阶矩估计的精度比较研究,可以发现:1)点估计方法对高阶矩估计的精度较低阶矩低;2)函数非线性程度、变量类型和变异系数等对点估计法精度均有较为明显的影响,变量数目和相关系数的影响因方法而异;3)相对而言,Zhao&Ono方法精度最优,但用于强非线性、大变异性情形时,精度亦不甚理想,此时应慎用或者增加计算点的数量;4)Harr方法的计算精度在相关系数等于0处存在突变。     

The set-theory method for systems reliability of structures with degrading components

The times and frequencies of inspection, maintenance and replacement in structural systems are complicated by uncertain degradation rates of structural characteristics. Although degradation work at the component, or single failure mode level, is ongoing, this paper presents a method for assessing systems reliability where failure events may be described by time-variant parallel and/or series systems. Herein the models for the degradation rates contain random variables and time. For multiple failure modes and a sequence of discrete times, set theory establishes the true incremental failure region that emerges from a safe region. Probabilities via Monte-Carlo simulation require only time-invariant calculations. The cumulative failure distribution is the summation of the incremental failure probabilities. A practical implementation of the theory requires only two contiguous times. Error analysis suggests ways to predict and minimize errors so the method appears sufficiently accurate for engineering applications. Two structures with elastic-brittle material and time-invariant loads show the details of the method and the potential of the approach. It is shown that the proposed method provides a more realistic and efficient way to predict systems reliability than path-tracing methods that are available in the open literature.     

基于条件期望的改进线抽样方法及其应用

为减小线抽样可靠性及灵敏度分析计算结果的方差,该文在可靠性与可靠性灵敏度线抽样计算公式中巧妙地运用全方差原理,引入了条件期望,对传统计算方法进行了改进,同时为避免直接计算条件期望将导致计算量增加的问题,该文将计算公式进一步转化成与基本变量维数无关的形式,并采用核密度估计的方法进行求解。该文最后运用MATLAB软件将该文方法应用于工程实例分析,结果均表明:通过对传统线抽样方法的改进,有效地提高了线抽样方法求解失效概率和灵敏度的收敛性和稳定性。     

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.     

New reliability modeling methods for structural systems with hybrid uncertainty

The present study investigates the hybrid reliability modeling of structures in which the inputs contain both random variables and interval variables. Hybrid uncertainty is divided into three categories, including random variables mixed with random variables, interval variables mixed with interval variable, and random variables mixed with interval variables. In order to perform the reliability analysis of structural systems, first, the Bayes method is proposed in the present study to obtain distribution parameters of random variables. Moreover, the self-sample method is introduced to obtain the interval boundaries based on the least available measuring data. Then, the reliability models are established for three situations and the reliability indices are defined and derived accordingly. The abovementioned three types of reliability indices outline the general situation of structural systems. Finally, the specific calculation process is described in details through different examples. Furthermore, the accuracy and efficiency of the proposed method is discussed by comparing the results obtained from the Monte Carlo simulation and those of other methods. The obtained results indicate that the performance of the proposed model in solving reliability modeling problems is better.     

Closed form solutions of R-stress and stress singularity coefficient in rigid line problems

In this work, a new and efficient definition for a reliability index is explored for real structural engineering problems. The main innovative aspect is that it is based on a possibilistic criteria instead of a probabilistic one. Its definition deals with engineering cases where uncertain parameters of basic structural reliability problems can be operatively treated as fuzzy variables. A fuzzy-based version of classic Cornell proposed reliability index is discussed. Consequently, differences and advantages with respect to other non-probabilistic reliability measures reported in literature are critically analyzed with reference to well-specified criterions. Finally, two numerical examples are illustrated. The first, in the framework of the materials strength problem, is a simple comparison between these fuzzy reliability indicators, and is developed to clarify the applicability of our proposal. Subsequently, another more realistic numerical example is proposed; it is developed to appreciate its effectiveness in reliability assessment of complex structural systems.     

失效相关的齿轮一次四阶矩可靠性分析

齿轮是机械传动的关键零件之一,为了分析其可靠性,在改进的验算点一次二阶矩可靠性方法基础上,应用Taylor级数展开和Hermite多项式近似等方法,推导了齿轮功能函数的验算点前四阶矩,分析了具有齿根断裂和齿面点蚀两种主要相关失效模式的齿轮传动可靠性,给出了其相关系数和齿轮的可靠度。另一方面,因影响齿轮失效的因素繁杂众多,计算齿轮的可靠度时,不管是用一次二阶矩可靠性方法还是四阶矩可靠性方法,其计算量均偏大,且容易出错。针对该问题,提出了一种分类变差系数验算点一次四阶矩可靠性分析方法,该方法对齿轮功能函数的不同基本随机变量进行分类综合,减少了设计变量,使计算量明显减小,解决了用矩方法分析结构可靠性时计算量偏大且易出错的难题。最后应用所提分类变差系数验算点一次四阶矩可靠性分析法估计了某车床主轴箱一对传动齿轮的可靠性,计算结果显示该对齿轮齿根弯曲疲劳强度和齿面接触疲劳强度有一定的相关性,所用一次四阶矩方法因包含偏度、峰度等更高阶的统计信息可进一步提高估计精度。