A New Technique in Analytical Reliability Estimation Involving Multi-modal Distributions: An Extended Laplace Approximation Approach

摘要

The paper presents an analytical method for reliability estimation problems involving multi-modal distributions. The analytical computation procedure consists of the extended Laplace approximation method, the first-order reliability method, and the inverse reliability method. The extended Laplace approximation method is developed to obtain the analytical expression of a given unnormalized multi-modal distribution. The idea is to approximate each of the modes locally using a multivariate normal distribution. The resulting approximation of the multi-modal distribution is expressed as a combination of multivariate normal distributions. The first-order reliability method is employed to calculate the reliability using the extended Laplace approximation result, and the inverse reliability method is used to compute system response predictions given reliability indexes. A realistic engineering example is used to demonstrate the overall method. Results are compared with traditional simulation-based methods to investigate the accuracy and efficiency of the proposed method.