Sequential active learning for estimating small failure probabilities in high-dimensional problems: Application to nonlinear vessel responses

A new method for high-dimensional structural reliability analysis is proposed, with particular attention to estimating small failure probabilities. The proposed method is built upon an active learning framework, in which an active subspace for supervised dimensionality reduction and a surrogate model for bypassing the performance function are simultaneously updated. Heteroscedastic Gaussian process (hGP) modeling is employed for this purpose. To effectively address rare event problems, the method further incorporates a sequential sampling strategy based on the subset simulation. The resulting Sequential Active Learning with Active Subspace (SALAS) method is first demonstrated using the Sobol function to illustrate its accuracy and computational efficiency. Following this, its application is extended to specific high-dimensional engineering problems involving nonlinear vessel responses in waves. Two subject vessel responses are studied: vertical bending moment and roll motion of a vessel. A nonlinear strip theory and a two-degree-of-freedom roll motion model are used to analyze these responses, respectively. Comprehensive comparisons with crude Monte Carlo simulation, first order reliability method, and the adaptive active subspace-based heteroscedastic Gaussian process (AaS-hGP) method demonstrates the efficiency and accuracy of the proposed SALAS method, even in estimating rare event probabilities in high-dimensional stochastic spaces. • High-dimensional small failure probability estimation by sequential sampling. • Sequential Active Learning with Active Subspace (SALAS) is proposed. • Numerical demonstrations using Sobol function and typical engineering examples. • Accuracy and computational efficiency of SALAS is demonstrated.