A reliability analysis method based on analytical expressions of the first four moments of the surrogate model of the performance function

For efficiently and accurately analyzing the reliability of structure, the analytical expressions of the first four moments of output are deduced by the Bayesian Monte Carlo method, on which the analytical failure probability can be directly obtained by employing the existing high-order moment standardization technique and the Edgeworth expansion. By use of the proposed procedure, the failure probability of structure can be estimated by an analytical expression without introducing additional errors. Also, only the training points are needed to gain the analytical expressions of the first four moments. Several examples involving numerical test and engineering application are introduced to illustrate the accuracy and the efficiency of the proposed method for reliability analysis of structure.