Reliability analysis of structures by multiple sparse polynomial chaos expansion based adaptive metamodel

The present study explores a polynomial chaos expansion (PCE) based adaptive metamodeling approach for reliability analyses using sparse PCE models from a pool of sparse regressors. In detail, each sparse PCE model predicts the model response from the candidate set, and a reduced subset is obtained using multiple sparse PCE model predictions. The local error is estimated using the variance of the predictions. Unlike adding important training data iteratively from the entire input space in the usual active learning approach, the present study adds data points during iteration from a moving reduced space. The reduced space enforces the learning function to select a point near the predicted limit state surface with the highest discordance among the different regressors. This makes the learning highly focused on choosing adaptive samples on the local region near the predicted limit state surface, leading to faster convergence for reliability estimates. The reliability results obtained by the proposed approach are compared with those obtained by the bootstrap resampling-based PCE Monte Carlo simulation (MCS) approach and PCE with active Kriging approach, considering the direct MCS-based results as the benchmark to demonstrate the effectiveness of the present approach.