Time-dependent system reliability analysis using adaptive single-loop Kriging with probability of rejecting classification

In this paper, a new single-loop active learning Kriging method with probability of rejecting classification is proposed for solving time-dependent system reliability analysis problems. The proposed method aims at making full use of the response information of all potential failure time instants or failure modes to improve the sampling efficiency and algorithm interpretability. Firstly, the probability of rejecting classification of each candidate sample for single failure mode is derived based on the Kriging models that are used to approximate the performance functions. Then, both the joint probability of rejecting classification and cumulative probability of rejecting classification are constructed for time-dependent series system and time-dependent parallel system, respectively. Any potential failure information for multiple failure modes over the entire time interval is taken into account. On this basis, an effective active learning strategy is developed to identify the new training sample and the target Kriging model to be updated corresponding to a certain failure mode. The maximum real-time estimation error criterion for time-dependent system problem is utilized to stop refining Kriging models after fully exploiting the limit state surface. Finally, three examples are used to demonstrate the excellent efficiency and computational accuracy of the proposed method.

Automated summary

In this paper, a new single-loop active learning Kriging method with probability of rejecting classification is proposed for solving time-dependent system reliability analysis problems. The method makes full use of the response information of all potential failure time instants or failure modes to improve the sampling efficiency and algorithm interpretability. An effective active learning strategy is developed to identify the new training sample and the target Kriging model to be updated corresponding to a certain failure mode. The proposed method demonstrates excellent efficiency and computational accuracy in three examples.