System reliability analysis by combining structure function and active learning kriging model

Abstract Surrogate models are useful for reducing the computational burden in real applications. Structural reliability analyses based on active learning kriging models, such as efficient global reliability analysis (EGRA) and an active learning method to combine kriging and MCS (AK–MCS), have been widely proposed. However, these methods are mainly suitable for component reliability analyses. In general, the reliability analysis of practical engineering problems is mostly performed at the system level with multiple failure models. Two representative system reliability methods, i.e., an adaptation of the AK–MCS method for system reliability (AK–SYS) and system reliability analysis through active learning kriging model with truncated candidate region (ALK–TCR), are very useful for system reliability analysis with only random variables. However, these methods select training points from the perspective of component responses and are difficult to implement for complex systems. Therefore, the balance between applicability, accuracy and efficiency can be further improved. In this study, an efficient reliability method for structural systems with multiple failure modes is proposed to further extend the AK–SYS and ALK–TCR. A new learning function based on the system structure function, which efficiently take into account the influence of the different components and their logical arrangement through the use of the system's structure function, is developed to select the added points adaptively from the perspective of the system. Based on the proposed learning function, surrogate models are accurately constructed. Compared to AK–SYS and ALK–TCR, the proposed method has the following three main advantages: (1) the new learning function selects the added points from the perspective of the system to fully and directly utilize the predicted information of all the components; (2) the magnitude effect, which refers to the several orders of magnitude existing among the responses of components, have no influence on the proposed method; and (3) the proposed method is robust and has high applicability for complex systems. Four numerical examples are investigated to show the applicability and efficiency of the proposed method, and the results indicate that the proposed method is effective for system reliability analysis.