二维联合分布函数构造方法及其对结构可靠度的影响分析

研究了2种构造联合分布函数的近似方法:基于Pearson相关系数的近似方法P和基于Spearman相关系数的近似方法S。推导了基于直接积分方法的构件失效概率计算公式。结果表明近似方法P与近似方法S构造的联合概率密度函数的唯一差别是相关标准正态空间中Pearson 相关系数的不同。2 种近似方法的构件失效概率的计算精度取决于失效概率大小、功能函数形式及变量间相关程度。总体来说2种近似方法的计算精度较高,近似方法的失效概率的误差随着失效概率的减小而增加。只有当失效概率小于10-3且失效区域刚好可以反映失效概率差异时,近似方法得到的失效概率才会有较大的误差。     

联合分布函数蒙特卡罗模拟及结构可靠度分析

针对复杂极限状态方程可靠度计算问题,提出了基于理论联合分布函数以及2 种近似联合分布函数的结构失效概率蒙特卡罗模拟方法,并给出了计算流程图.采用2 个算例证明了所提方法的有效性.结果表明:所提的失效概率模拟方法的计算精度很高,尤其适用于复杂极限状态方程的可靠度计算问题.2 种联合分布函数近似构造方法得到的失效概率精度相当,近似方法与精确方法结果的差异随失效概率的减小而增大,而且随着变量间相关性的增加而增加.当失效概率小于10-3时,近似方法的失效概率误差较大.     

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。     

联合分布函数构造的Copula函数方法及结构可靠度分析

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可靠度的影响还缺少系统地研究。为此,提出了基于Copula函数的变量联合概率分布函数构造方法,并分析了不同Copula函数类型对结构可靠度的影响规律。首先,简要介绍了基于Copula函数的变量联合分布函数构造方法。其次,提出了构件失效概率计算的直接积分方法。最后以构件可靠度问题为例研究了Copula函数的类型对结构可靠度的影响规律。结果表明:不完备概率信息条件下构件可靠度是不唯一的,表征变量间相关性的Copula函数类型对构件可靠度具有明显的影响,不同Copula函数计算的构件失效概率存在明显的差别,这种差别随构件可靠指标的增大(或失效概率的减小)而增大。Copula函数尾部相关性对结构可靠度具有重要的影响。当功能函数的失效区域位于Copula函数尾部时,计算的失效概率明显比没有尾部相关性的Copula函数的失效概率大。基于功能函数的均值和标准差计算的可靠指标不能反映Copula函数的类型对结构可靠度的影响,而基于功能函数实际分布求得的失效概率则可以有效反映不同Copula函数对结构可靠度的影响。     

考虑状态模糊性时广义失效概率计算的矩方法

针对失效状态和安全状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的矩方法。所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散化的积分区域中,极限状态函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为一般的随机可靠性问题,进而可以利用近似的矩方法求得广义失效概率。该文给出了所提方法的实现步骤和原理,算例结果表明所提方法对于中低维问题具有很高的精度和效率。     

基于加权线性响应面法的支持向量机可靠性分析方法

针对估算非线性隐式极限状态函数的失效概率问题,提出了一种基于加权线性响应面法的支持向量机可靠性分析方法。首先采用加权线性响应面确定设计点,在线性响应面迭代的同时获得一定数量的样本,然后在这些样本和设计点附近补充抽取样本的基础上,采用具有良好小样本学习能力的支持向量机方法来训练样本,保证了在设计点周围获得更好的非线性极限状态函数的替代。这种方法既保证了对设计点的精确近似,又保证了对设计点附近非线性极限状态函数的良好近似,大大提高了失效概率的计算精度,为非线性隐式极限状态的可靠性分析提供了一种合理可行的方法。     

基于蒙特卡罗模拟的高效边坡可靠度修正方法

传统的蒙特卡罗模拟方法在分析由于参数不确定性修正而引起的可靠度修正问题时效率较低。为此,提出了一种基于蒙特卡罗模拟的高效边坡可靠度修正方法,该方法主要包括2个关键步骤:1)根据参数初始分布利用蒙特卡罗模拟方法计算边坡的失效概率,并输出蒙特卡罗模拟的失效样本;2)利用参数统计特征值修正后的联合概率密度函数和蒙特卡罗模拟失效样本计算修正后边坡的失效概率。以两个边坡问题为例说明了所提方法的有效性。结果表明:所提出的方法在计算修正的失效概率过程中无需重新执行蒙特卡罗模拟,计算过程简单、计算效率高。此外,所提方法能够适用于隐式表达功能函数的边坡可靠度修正问题,并能够有效地解决单变量和多变量修正的边坡可靠度修正问题。     

风速风向联合分布对结构风致疲劳寿命可靠性的影响

在进行结构风振疲劳寿命可靠性分析时,需要先求得建筑结构所在位置处的风速风向联合分布函数。本文首先对建筑结构附近两个气象站的气象资料进行统计分析,得到建筑结构位置处两个不同的风速风向联合分布函数,然后分析了不同的风速风向联合分布函数对一实际结构系统风振疲劳主要失效模式以及结构系统风振疲劳失效概率的影响。本文分析表明：用不同的风速风向联合分布函数计算风振疲劳寿命时会得到不同数目的主要失效模式,并且对结构系统的风振疲劳失效概率影响较大。     

基于频响函数和遗传算法的结构损伤识别研究

提出一种基于频响函数和遗传算法的结构损伤识别方法.以单元刚度折减因子为遗传算法的优化变量,以测试频响函数和计算频响函数的形状相关系数来构造遗传算法的优化目标函数和适应度函数;为克服二进制编码的缺点,采用浮点数编码方案;最后通过一个桁架结构模型进行数值模拟,计算结果表明,即使在考虑一定测量噪声水平的情况下,仍然能够准确识别出结构的多处损伤,验证了该方法的有效性和可行性.     

基于非均匀方向向量近似积分法的结构系统可靠性评价

本文提出了一种新的基于非均匀方向向量求解结构系统失效概率的近似积分法,给出了结构系统失效概率的近似积分公式。通过求解具体问题,证明该方法相当有效,适合于多破损模式、非线性安全边界的结构体系可靠性问题。     

Evaluating small failure probabilities of multiple limit states by parallel subset simulation

A novel subset simulation algorithm, called the parallel subset simulation, is proposed to estimate small failure probabilities of multiple limit states with only a single subset simulation analysis. As well known, crude Monte Carlo simulation is inefficient in estimating small probabilities but is applicable to multiple limit states, while the ordinary subset simulation is efficient in estimating small probabilities but can only handle a single limit state. The proposed novel stochastic simulation approach combines the advantages of the two simulation methods: it is not only efficient in estimating small probabilities but also applicable to multiple limit states. The key idea is to introduce a “principal variable” which is correlated with all performance functions. The failure probabilities of all limit states therefore could be evaluated simultaneously when subset simulation algorithm generates the principal variable samples. The statistical properties of the failure probability estimators are also derived. Two examples are presented to demonstrate the effectiveness of the new approach and to compare with crude Monte Carlo and ordinary subset simulation methods.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

INTENT: a method for estimating human error probabilities for decisionbased errors

The development of a method, INTENT, for estimating probabilities associated with decisionbased errors is presented. These errors are not ordinarily incorporated into probabilistic risk assessments (PRAs) due to both the difficulty in postulating such errors and to the lack of a method for estimating their probabilities from existing data. By failing to include decisionbased errors in their analyses, most PRA practitioners seriously underestimate the true contribution of human actions to systems failure. This paper attempts to extend the identification of such errors and to quantify them. Two sources, Nuclear Computerized Library for Assessing Reactor Reliability (NUCLARR) and licensee event reports (LERs) were reviewed and two methods, HSYS and SNEAK, were used to identify a generic list of twenty potential errors which may be manifest as erroneous acts. Four categories of influence emerged from the data: consequence, attitudes, response set, and dependency. Corresponding human error probabilities (HEPs) for each error were generated by expert judgment methods. Lower and upper bounds for the HEPs for each error were determined by positing a situation reflecting optimized and degraded performance shaping factors, respectively. To allow analysts the opportunity to refine these extreme HEP values when evaluating a particular scenario of interest, normalization procedures were conducted and generic importance weights were computed for each of 11 performance shaping factors (PSFs) believed to affect the 20 decisionbased errors. It is believed by the authors that PSFs constitute a performance influence which, in some cases, such as in that for training, can serve to either augment or reduce the intellectual resources used by people to successfully accomplish tasks. These derived importance weights are used in conjunction with situation specific PSF ratings to compute a composite PSF score which, in turn, is mapped onto an HEP distribution. Distribution assumptions are presented and a function defining the relationship between composite PSF scores and HEPs is presented for use by the analyst.     

Analysis of complex system reliability with correlated random vectors

The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately.The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability.     

Non-invariant failure probabilities with invariant reliability index

This paper presents a critical examination of some basic limit state functions that led to development of the invariant code format for reliability analysis. Proper methods of evaluating failure probabilities from these limit state functions are used to check failure probabilities estimated by reliability index methods, and the results show that failure probability for a limit state function that may assume different but seemingly equivalent forms is not always invariant as the invariant format would indicate.