Time-Variant Reliability Analysis for a Complex System Based on Active-Learning Kriging Model

Abstract

The active-learning Kriging (ALK)–based time-variant system reliability analysis has been widely concentrated. Unfortunately, the current time-variant system reliability methods are mostly focused on the series system, parallel system, or series-parallel system; thus, they cannot efficiently deal with the time-variant reliability problem of a complex system such as bridge system, network system, and so on. In view of this issue, the paper proposes an efficient time-variant reliability method for a complex system by introducing the structure function into the ALK-based time-variant reliability analysis. Firstly, similar to the ALK-based time-variant system reliability method, some extreme values corresponding to the initial input samples are optimized, and thus the initial extremum response surface is constructed based on the Kriging model. Then, considering the epistemic uncertainty of the Kriging predictions, the predicted response of system structure function under a particular input sample is viewed as a random variable, and its mean and variance are computed based on the minimal cut sets of a complex system. Lastly, considering the aleatory uncertainty between the different candidate samples, the point corresponding to the maximum prediction variance is selected, the most important component is decided by introducing the structure importance, and its extreme value is correspondingly optimized to update the initial extremum response surface. The stopping criterion is also provided in this paper and the effectiveness of the proposed method is illustrated by several examples.