Reliability Analysis of Structures by Active Learning Enhanced Sparse Bayesian Regression

Abstract

Adaptive sampling near a limit state is important for metamodeling-based reliability analysis of structures involving an implicit limit state function. Active learning based on the posterior mean and standard deviation provided by a chosen metamodel is widely used for such adaptive sampling. Most studies on active learning-based reliability estimation methods use the Kriging approach, which provides prediction along with its variance. As with the Kriging approach, sparse Bayesian learning-based regression also provides posterior mean and standard deviation. Due to the sparsity involved in learning, it is expected to be computationally faster than the Kriging approach. Motivated by this, active learning-enhanced adaptive sampling-based sparse Bayesian regression is explored in the present study for reliability analysis. In doing so, polynomial basis functions, which do not involve free parameters, are chosen for the sparse Bayesian regression to avoid computationally expensive parameter tuning. The convergence of the proposed approach is attained based on the stabilization of 10 consecutive failure estimates. The effectiveness of the proposed adaptive sparse Bayesian regression approach is illustrated numerically with five examples.