Gaussian Process Machine-Learning Method for Structural Reliability Analysis

Abstract

To deal extensively with issues on implicit performance function and huge computational cost in reliability analysis, a new method for structural reliability analysis was proposed by combining the GP and importance sampling method (ISM). Firstly, a small amount of training dataset is generated by the structural analysis to train the GP. Then, the implicit performance and its derivatives are approximated by the trained GP using explicit formulations. Secondly, an iterative algorithm called as the GP-based first-order reliability method is implemented to obtain the design point. During iterations, the precision of the GP approximation in the important region, which contributes significantly to the failure probability, is improved continuously by adding the new iterative design point into the training set. Finally, an importance sampling around the design point is applied to obtain the failure probability. To assess the validity of the proposed method, five numerical examples were presented and discussed, which validated that accurate and computationally efficient results for structural reliability analysis can be obtained using the proposed method.