In the context of structural system reliability, quantifying the relative importance of random input variables and failure modes is necessary for improving system reliability and simplifying the reliability-based design problems. We firstly introduce the reliability-based variable importance analysis (VIA) indices to structural systems for quantifying the individual, interaction and total effects of each random input variable on the system failure probability, and propose two new reliability-based mode importance analysis (MIA) indices for measuring the effects of each failure mode on the failure and safety of structural systems. Then, an active learning procedure, which combines the multiple response Gaussian process (MRGP) model and the Monte Carlo simulation (MCS), is introduced to efficiently and adaptively produce surrogate models for the failure surfaces of systems, and three learning functions are compared. Based on the well-established surrogate models, the system failure probability as well as the VIA and MIA indices are estimated without calling the limit state functions in addition. Results of six test examples demonstrate the significance of the VIA and MIA indices, and show that the developed MRGP-based methods are effective in estimating both the system failure probability and the proposed importance indices.
Wei, P., Liu, F., & Tang, C. (2018). Reliability and reliability-based importance analysis of structural systems using multiple response Gaussian process model. Reliability Engineering and System Safety, 175, 183–195. https://doi.org/10.1016/j.ress.2018.03.013