Dimensions Reduction Method By Conditional Probability For The Approximation To The Failure Probability Of Structural Systems

This paper mainly introduces a new method to approximating the failure probability of structural systems and the method is defined as dimensions reduction method by conditional probability. The paper is consisted of four chapters. Chapter 1 briefly reviews the necessity and character of structural systems reliability analysis as well as the existing approaches of estimating the failure probability of structural systems. Chapter 2 describes how to obtain the reliability index of a failure mode and the correlation coefficient between two failure modes. Chapter 3 details the derivation of the introduced approach. As shown in this chapter, the calculation of the failure probability of a structural system is firstly transformed to the evaluation of a multi-normal distribution that can be then approximated by a product of one-dimensional normal integrals by substituting the conditional probability by a standard normal distribution and using the idea of iteration. The examples of the calculations of the failure probability of a gravity dam and a frame structure that are outlined in chapter 4 show the simple operation and the accuracy and the engineering practicality of the proposed approximation.