Seismic reliability analysis of nonlinear structures by active learning-based adaptive sparse Bayesian regressions

The Monte Carlo simulation (MCS) technique is quite simple in concept and the most accurate for seismic reliability analysis (SRA) of structures involving nonlinear seismic response analysis, considering the effect of the stochastic nature of earthquakes and the uncertainty of various structural parameters. However, the approach needs to execute several repetitive nonlinear dynamic analyses of structures. The metamodeling technique has emerged as a practical alternative in such a scenario. In SRA, the dual metamodeling approach is typically adopted to deal with the stochastic nature of earthquakes following a lognormal seismic response assumption. In contrast, a direct metamodeling approach of SRA can avoid such prior assumptions. Adaptive training near the limit state is important in the metamodeling-based SRA. However, its implementation is quite challenging for SRA due to the record-to-record variation of earthquakes. In this context, an adaptive sparse Bayesian regression-based direct metamodeling approach is developed for SRA, where an active learning-based algorithm is proposed for adaptive training of metamodels for approximating nonlinear seismic responses. As the sparse Bayesian regression is computationally faster than Kriging due to the sparsity involved in sparse Bayesian learning, the overall performance of the proposed approach is expected to be better than the adaptive Kriging-based SRA approach. The effectiveness of the proposed approach is illustrated by numerical examples.