基于随机摄动法的可靠性灵敏度计算的修正公式

为了更好地解决工程实际中的非线性系统的可靠性求解问题,基于可靠性设计的随机摄动法,将可靠性设计理论和灵敏度分析方法相结合,对具有正态分布随机参数的可靠性灵敏度计算方法进行了修正,使其更加适用于工程实际中的非线性结构系统.编制了参数化的计算机程序,得到了结构可靠度随基本随机变量均值的变化曲线,并结合数值算例证明了针对强非线性的极限状态方程,运用修正后的方法使结构的可靠度对基本随机变量均值灵敏度的计算精度得到了明显的提高,为工程实际提供了更加精准的理论依据.

A Modified Formula of Reliability-Based Sensitivity Calculation on the Basis of Stochastic Perturbation Theory

To solve well the problem of reliability of a nonlinear system in engineering practice, the design of reliability is theoretically combined with sensitivity analysis on the basis of the stochastic perturbation theory of reliability design to modify the formula to compute the reliability-based sensitivity with normally distributed stochastic parameters, thus making the modified computing formula more adaptable to the nonlinear structural system in engineering practice. With the parameterized computation program provided, the relationship between structural reliability and the mean value of basic random variables is given. A numerical example verifies that the computational accuracy of the sensitivity based on structural reliability to the mean value of basic random variables is greatly improved by the modified formula referring to the highly nonlinear ultimate state equations, with a more exact reference provided theoretically for engineering practice.