考虑统计不确定性的结构可靠度分析方法

Reliability analysis methods of structures considering statistical uncertainty

摘要:

为了充分研究统计不确定性对结构可靠度的影响,本文将综合考虑物理不确定性和统计不确定性,以Bayes理论为数学工具,对结构的统计可靠度问题进行研究.首先对Bayes理论进行概括和总结,采用该理论对结构工程中的统计不确定性进行建模和分析.然后研究考虑统计不确定性的结构可靠度分析方法,给出考虑统计不确定性的各种结构可靠性测度,并研究综合考虑主观不确定性与客观不确定性的整体式与分离式可靠度计算方法.最后通过2个算例,分析了统计不确定性对结构可靠度的影响.

Abstract:

In order to fully investigate the influence of statistical uncertainty on reliability of structures,in this paper,the statistical reliability theory of structures considering two kinds of uncertainties,i.e.,physical un-certainty and statistical uncertainty,is deeply and thoroughly studied on the basis of Bayesian statistics.First,the fundamental principles of Bayesian statistics are summarized.The statistical uncertainty in structural engi-neering is then modeled and analyzed by Bayesian updating approach.The various measures for structural sta-tistical reliability are introduced.After that,two methods for statistical reliability analysis of structures consid-ering statistical uncertainty are proposed to treat with the aleatory and epistemic uncertainties:the integrated approach and the separate approach.Two examples are given,one of which is a numerical one;the other is a fracture reliability problem.The examples demonstrate the influence of statistical uncertainty on the reliability indices of structures.