Application of cross-entropy method in multi limit-state reliability analysis

This paper is focused upon the development of an efficient multi limit-state reliability analysis method based on extended cross-entropy. In order to achieve a reliable state in the modern critical structural designs، it is necessary to utilize an efficient reliability analysis method to estimate the probability of failure. Reliability analysis of such designs is faced with several challenges، such as rarity of the probability of failure and multiplicity of limit-state functions. To address these issues، in this research an importance sampling (IS) -based method is developed which uses cross-entropy (CE) method to reduce sampling variance، and leads to a fast and accurate reliability analysis method. The main advantage of this method is the ability to perform reliability estimation (especially for rare events) without the most probable failure point (MPP) calculation. The proposed method is demonstrated on several test problems and the results are compared together. Results obtained show that method introduced in this paper provides an effective way of improving reliability analysis of multi limit-state functions. In addition، using the proposed method، prevents the mistake of over-designing while retains usability of the method.