Structural reliability analysis via dimension reduction, adaptive sampling, and Monte Carlo simulation

An improved reliability method, i.e., AL-AS-GPR-MCS, is developed taking advantage of active subspace (AS)-based dimension reduction technique, Gaussian process regression (GPR) surrogate model, active learning (AL)-based sampling strategy, and Monte Carlo simulation (MCS). In this method, the AL sampling strategy and the AS-based dimension reduction are incorporated into the GPR construction, allowing that the newly added sample in each iteration can be employed simultaneously to update the identified AS of original high-dimensional space and to refine the low-dimensional GPR model over the discovered AS. The failure probability is then estimated by the MCS using the constructed GPR model. In order to verify the versatility of the proposed method, four numerical examples are investigated, involving reliability analyses of both explicit performance functions and shear frame structures with implicit performance functions. It is revealed that satisfactory accuracy enhancement and computational cost savings are achieved by the AL-AS-GPR-MCS, since it is capable of discovering the latent AS of the original high-dimensional space which alleviates the curse of dimensionality, and refining the low-dimensional GPR construction within the discovered AS by the AL sampling strategy. Therefore, the proposed method is a powerful and promising tool for dealing with structural reliability problems with strong nonlinearities and high stochastic dimensions.