基于Bayes方法的多元正态应力强度可靠度分析

摘要

实际工程中,应力和强度是多维相关的,且相关信息很难获得,使用传统的单维应力-强度干涉模型很难进行可靠度分析,需要研究多元应力-强度干涉模型的可靠度计算问题.描述了两种多元应力-强度干涉模型,针对应力、强度服从正态分布的情形,使用Bayes方法,充分利用验前信息,由多元应力-强度干涉模型获得分布参数验后分布,并基于多元统计学知识,采用仿真抽样方法,进行可靠度验后预报.巡航弹可用过载的仿真算例验证Bayes方法在应力、强度试验信息较少的情况下,可高精度地预测可靠度的验后分布.%In engineering, the reliability analysis is difficult by using general univariate stress-strength interference model under multivariate stresses and strengths, and the correlations between which is difficult to confirm, thus it is necessary to study the reliability analysis with multivariate stress-strength interference model. In this paper, two types of multivariate stress-strength interference model are described. The Bayesian method with prior information is adapted to solve the problem of posterior distributions of distribution parameters, and simulation sampling is used to gain the posterior distributions of reliability based on multivariate statistics. The simulation of over loading of cruise missile show that the Bayesian method is effective and precise to analyze the posterior distributions of reliability.