Evaluation of Moments of Performance Functions Based on Efficient Cubature Formulation

Abstract

Estimation of statistical moments of performance functions is one of the main topics in structural reliability analysis by moment methods. It is possible to apply the well-developed multiple-dimensional cubature formulas to assess such statistical moments. In this paper, a new criterion is proposed to fulfill the aim. Several efficient cubature formulas are firstly revisited. Then, a new criterion is proposed to select “the best” cubature formula that gives the most accurate statistical moments of performance functions. This criterion is established based on the marginal moments of input random variables. The cubature formula that provides the smallest difference between the estimated values and the exact values of marginal moments is determined as the adopted one for statistical moments of performance functions. Several numerical examples are presented to illustrate the effectiveness of the proposed criterion, in which Monte Carlo simulations are employed for comparison.

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