Efficient adaptive Kriging for system reliability analysis with multiple failure modes under random and interval hybrid uncertainty

In the field of the system reliability analysis with multiple failure modes,the advances mainly involve only random uncertainty.The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty(RI-HU).At present,there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability.This paper proposed an efficient Kriging model based on numerical simulation algorithm to solve the system reliability analysis under RI-HU.This method proposes a system learning function to train the system Kriging models of the system limit state surface.The convergent Kriging models are used to replace the limit state functions of the system multi-mode for identifying the state of the random sample.The proposed system learning function can adaptively select the failure mode contributing most to the system failure probability from the system and update its Kriging model.Thus,the efficiency of the Kriging training process can be improved by avoiding updating the Kriging models contributing less to estimating the system failure probability.The presented examples illustrate the superiority of the proposed method.

Safety lifetime analysis method for multi-mode time-dependent structural system

It is important to determine the safety lifetime of Multi-mode Time-Dependent Structural System(MTDSS). However, there is still a lack of corresponding analysis methods.Therefore, this paper establishes MTDSS safety lifetime model firstly, and then proposes a Kriging surrogate model based method to estimate safety lifetime. The first step of proposed method is to construct the Kriging model of MTDSS performance function by using extremum learning function. By identifying possible extremum mode of MTDSS, the performance function of MTDSS can be equivalently transformed into the one of Single-mode Time-Dependent Structure(STDS).The second step is to use the Advanced First Failure Instant Learning Function(AFFILF) to train the Kriging model constructed in the first step, so that the convergent Kriging model can identify the possible First Failure Instant(FFI) of STDS. Then safety lifetime can be searched quickly by dichotomy search. By using AFFILF, the minimum instant that the state is not accurately identified by the current Kriging model is selected as the training point, which avoids the unnecessary calculation which may be introduced into the existing First Failure Instant Learning Function(FFILF).In addition, the Candidate Sample Pool(CSP) reduction strategy is also adopted. By adaptively deleting the random candidate sample points whose FFI have been accurately identified by the current Kriging model, the training efficiency is further improved. Three cases show that the proposed method is accurate and efficient.