考虑模型不确定性的结构可靠度分析方法

Reliability analysis methods of structures considering modeling uncertainty

摘要:

为了更充分地研究模型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模型不确定性,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模型不确定性进行建模和分析;然后研究考虑模型不确定性的结构可靠度分析方法,给出考虑模型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,分析模型不确定性对结构可靠度的影响.

Abstract:

To fully investigate the influence of modeling uncertainty on reliability of structures,in this paper,the statistical reliability problem of structures considering two kinds of uncertainties,i.e.,physical uncertainty and modeling uncertainty is deeply studied on the basis of Bayesian statistics.First,the fundamental principles of Bayesian statistics are summarized.The modeling uncertainty in structural engineering is then modeled and analyzed by Bayesian updating approach,and the various measures for structural statistical reliability are introduced.To treat with the aleatory and epistemic uncertainties,two methods,i.e.,the integrated approach and the separate approach for statistical reliability analysis of structures considering both physical uncertainty and modeling uncertainty are proposed.Two examples are given,one of which is a numerical one;the other is a problem of soil liquefaction.The examples demonstrate the effects of modeling uncertainty on the reliability indices of structures.