On the use of sparse Bayesian learning-based polynomial chaos expansion for global reliability sensitivity analysis

Global reliability sensitivity analysis determines the effects of input uncertain parameters on the failure probability of a system. Usually, the global reliability sensitivity analysis can be performed by the conventional Monte Carlo simulation (MCS) approach. However, the MCS approach requires a large number of model evaluations which limits MCS to apply for realistic problems. For that reason, a sparse polynomial chaos expansion (PCE) model is used in the present work based on a variational Bayesian (VB) inference. More specifically, the PCE coefficients are computed by the VB inference and the important terms in the PCE basis are selected by an automatic relevance determination (ARD) approach. Therefore, the VB inference is fully connected with the ARD approach. Global reliability sensitivity analysis is performed for some numerical examples using the sparse PCE model and all the results are compared with the MCS and the least angle regression (LARS)-based PCE model predicted results. The 95% confidence interval is also obtained by the VB approach to measure the prediction uncertainty. It is found that a very good result is obtained with the sparse PCE model using much less number of model evaluations as compared to the MCS approach. The accuracy of obtaining the PCE coefficients is higher by the VB inference than the LARS approach. Further, the required number of terms is small for the VB-PCE model and therefore, the number of PCE coefficients is also small.