Bayesian updating based method with dimension reduction integral technique for efficiently estimating multi-mode system failure probability function

Accurate estimation of multi-mode system failure probability necessitates rigorous evaluation of the system failure probability. However, system failure probability function estimation presents significant computational challenge due to the traditional double-loop analysis framework and the repeated explorations of the complex failure domain. To address these challenges, a Bayesian updating with dimension reduction integral technique is proposed. In the proposed method, a Bayesian updating based method is firstly established to estimate the system failure probability function, where the distribution parameter realizations are approximated as the newly available observations. Then the system failure probability function can be obtained through once exploration of the failure domain in the random input space augmented by the distribution parameter vector, thereby decoupling the double-loop analysis framework. Moreover, a variance reduction strategy, which is based on a universal dimension reduction integral technique, is designed to further enhance the efficiency for exploring the augmented failure domain. Finally, to address the issue of solving the inversion of the system performance function with respect to the reduced variable during the dimension reduction integral process, an economical Kriging model is adaptively incorporated. Numerical and engineering examples fully demonstrate the superiority of the proposed method in terms of both accuracy and efficiency.