系统可靠性灵敏度分析方法及其应用研究

基于已有的单个失效模式可靠性灵敏度分析,建立多模式串、并联系统失效概率对基本变量分布参数的灵敏度分析方法,着重研究多模式并联系统可靠性灵敏度分析的近似方法.该方法以数字模拟为基础,根据样本点对系统失效概率的贡献,对计算失效概率的所有样本点进行筛选,并由筛选出的样本点线性回归模拟并联系统失效域,得到等价的单个线性极限状态方程,从而将多模式并联系统的可靠性灵敏度分析等价转换为单个模式的灵敏度分析.对于多模式串联系统的可靠性灵敏度分析,文中采用的方法是将串联系统的失效概率精确转换成单个模式失效概率与多个模式并联系统失效概率的代数和,然后逐项进行灵敏度分析,进而得到串联系统的可靠性灵敏度.对于结构系统的极限状态方程含有复杂综合随机变量的灵敏度分析问题,提出一种基于二次回归分析的近似处理方法,通过推导的综合随机变量分布参数对基本变量分布参数的偏导数公式和复合函数求导法则,最终得到复杂多模式系统失效概率对基本变量分布参数的灵敏度.文中用理论数值算例验证所提算法的精度与可行性,并将所提方法推广应用到工程算例中,验证其工程应用价值.

RELIABILITY SENSITIVITY ANALYSIS METHOD FOR STRUCTURAL SYSTEM AND ITS APPLICATION

Based on reliability sensitivity analysis method of single failure mode, the sensitivity method of system failure probability with respect to distribution parameters of basic variables is constructed for the structural system with multiple failure modes in series or in parallel. The reliability sensitivity method is first presented for the structural system with multiple failure modes in parallel, which is founded on the numerical simulation algorithm. By taking the contribution of the samplings to the system failure probability into consideration, the appropriate samplings are selected to fit the failure region of the structural system with multiple modes in parallel by regression. After the equivalent failure region described by single limit state equation is obtained to represent the failure region of the structural system described by multiple limit state equations, the reliability sensitivity analysis of the structural system in parallel is equivalently transformed to that of the single failure mode. For the structural system with multiple failure modes in series, since the system failure probability can be expressed by the algebra sum of the failure probabilities of each failure mode and those of multiple failure modes in parallel precisely, the reliability sensitivity analysis of the system in series might be completed by use of the reliability sensitivity methods for the single failure mode and for the system in parallel. When the complex random variable, the function of the basic random variable, is included in the structural system, a quadratic polynomial is proposed to fit the relationship of the complex random variable and the basic random variable. Combining the derived gradient function of the distribution parameters of the complex variables to those of the basic variables, the chain derivative law is proposed to get the reliability sensitivity for the structural system with complex variables. After the precision and the feasibility of the presented method are illustrated by the numerical examples, it is applied to the engineering example.