An innovative DoE strategy of the kriging model for structural reliability analysis

Abstract

An innovative strategy of the design of experiments (DoE) is proposed to reduce the number of calls of the performance function in the kriging-based structural reliability analysis procedure. Benefitting from the local uncertainty provided by the kriging model and the joint probability density function of performance function values of untried points derived in this research, the epistemic variance of the target failure probability is calculated approximately. The variance is treated as the accuracy measurement of the estimated failure probability. The next best point is defined as the untried point that can minimize the variance of failure probability in the sense of expectation which is computed by Gauss–Hermite quadrature. The basic idea of the proposed strategy is to refresh the current DoE by adding the next best point into it. The candidate points of the next best one are randomly generated by Markov chain Monte Carlo method from the kriging-based conditional distribution. A structural reliability analysis procedure is introduced to apply the proposed DoE strategy, whose stopping criterion is constructed mainly on the basis of the coefficient of variation of failure probability. To validate the efficiency of the proposed DoE strategy, three examples are analyzed in which there are explict and implict performance function. And, the analysis results demonstrate the outperformance of the innovative strategy.