Frequency reliability analysis of large-scale high-dimensional stochastic structures

Abstract

This article presents a numerical framework for frequency-based reliability analysis of series systems. Multiple failure modes are caused by different stochastic natural frequencies and excitation frequencies. The key of the proposed method relies on an efficient iterative solution algorithm for stochastic natural frequencies of structures, which provides stochastic frequency sample realizations cheaply and accurately. The failure probability of a series system can thus be calculated directly using these sample realizations. Furthermore, the Polynomial Chaos expansion is further used to represent the obtained sample realizations and generate a larger number of random samples to evaluate very small failure probabilities. More importantly, the proposed method only solves the original stochastic problem once and can be used to evaluate failure probabilities of different scenarios, which is different from existing methods that require recalculations for different limit state functions. Two engineering applications are given to show promising performance of the proposed method, even for very small failure probabilities of large-scale structures with high-dimensional random inputs