Implementation of machine learning techniques into the Subset Simulation method

Abstract

A hybrid reliability analysis procedure that combines the advantages of the Subset Simulation method, the application of surrogate models and clustering techniques is proposed to efficiently assess the failure probability of complex structural systems that may exhibit multiple failure modes. The proposed procedure, herein called SS-KK, integrates the Kriging surrogate modeling technique, K-means clustering algorithm into the original Subset Simulation (SS) method. The approach is found to not only improve the efficiency of the Subset Simulation method in finding the reliability of a structural system but to also help identify the important failure modes and controlling random variables. This information is important to aid engineers optimize the structural design process by focusing on the critical failures modes and design variables.The method consists of first constructing a relatively coarse global Kriging model at each subset level of SS by applying an appropriate active learning strategy. Subsequently, the initial global Kriging model is partitioned into several local Kriging models that coincide with the important failure modes identified by the K-means clustering algorithm. This partitioning, which helps identify the important failure modes, also gives a better representation of the entire failure region leading to improved estimates of the system reliability. Finally, FORM is implemented for each local Kriging to rank the importance of each identified failure mode based on its Hasofer-Lind reliability index and to use the associated design point and sensitivity coefficients to identify the most critical random variables.Several examples extracted from the available literature are analyzed to illustrate the advantages of the proposed SS-KK methodology and demonstrate its accuracy and efficiency.