A novel reliability sensitivity analysis method based on directional sampling and Monte Carlo simulation

Abstract

Local reliability sensitivity and global reliability sensitivity are required in reliability-based design optimization, since they can provide rich information including variable importance ranking and gradient information. However, traditional Monte Carlo simulation is inefficient for engineering application. A novel numerical simulation method based on Monte Carlo simulation and directional sampling is proposed to simultaneously estimate local reliability sensitivity and global reliability sensitivity. By suitable transformation, local reliability sensitivity and global reliability sensitivity can be estimated simultaneously as by-products of reliability analysis for Monte Carlo simulation method. The key is how to efficiently classify Monte Carlo simulation samples into two categories: failure samples and safety samples. Directional sampling method, a classical reliability analysis method, is more efficient than Monte Carlo simulation for reliability analysis. A novel strategy based on nearest Euclidean distance is proposed to approximately screen out failure samples from Monte Carlo simulation samples using directional sampling samples. In the proposed method, local reliability sensitivity and global reliability sensitivity are by-products of reliability analysis using the directional sampling method. Different from existing methods, the proposed method does not introduce hypotheses and does not require additional gradient information. The advantages of the Monte Carlo simulation and directional sampling are well integrated in the proposed method. The accuracy and the efficiency of the proposed method for local reliability sensitivity and global reliability sensitivity are demonstrated by four numerical examples and two engineering examples including the headless rivet and the wing box structure.