Novel Kriging based learning function for system reliability analysis with correlated failure modes

Since some identical model inputs are contained in the limit state functions of different failure modes in system reliability analysis, these failure modes are correlated in general. However, the correlations of the failure modes are not considered in constructing the Kriging based learning function for system reliability analysis in most of current publications, which may damage the efficiency of system reliability analysis. To overcome this disadvantage, a novel Kriging based learning function for system reliability analysis is proposed in this paper by considering the correlations of the failure modes. At first, this paper derives the lower and upper bounds of the probability that the Kriging model misjudges the state (safety or failure) of the system with correlated failure modes at each candidate sample. Then, the reduction of the upper bound of misjudging probability is also deduced when adding a given candidate sample to the training set of a certain failure mode. Thereafter, a novel learning strategy is proposed by simultaneously selecting a new training sample and the corresponding updating failure mode to mostly reduce the upper bound of misjudging probability. Finally, several examples are employed to illustrate the performance of the proposed learning function in system reliability analysis.