Model order reduction in subset simulations using the proper orthogonal decomposition.

The crude Monte Carlo method is computationally expensive. Hence, incorporating model order reduction methods enabling reliability analysis for high‐dimensional problems is necessary. However, this strategy may result in an inaccurate estimation of the probability of failure for rare events for two reasons. First, the model order reduction, represented by the proper orthogonal decomposition (POD) here, requires response information in the form of snapshots a priori. To capture the essential nonlinear response behavior, we propose to update the proper orthogonal modes using extreme events. Second, the crude Monte Carlo simulation requires many samples to estimate low failure probabilities reliably. To this end, subset simulation found wide application in reliability analysis to reduce computational effort. Following this strategy, the proposed samples gradually move toward the failure region. Thus, incorporating updates of the modes is particularly promising in evaluating samples from the current subset region. This contribution shows the computational efficiency of POD within subset simulations. We then propose to leverage the estimation of the probability of failure by updating the modes within each subset. [ABSTRACT FROM AUTHOR]