Moment Method with Box–Cox Transformation for Structural Reliability

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Abstract
Structural reliability analysis involving highly nonnormally distributed performance functions or relatively small failure probabilities is still a challenging problem in engineering practice. To overcome these problems, this paper developed the moment method combined with Box–Cox transformation. A new criterion is proposed to select the optimal Box–Cox transformation parameter that makes the transformed performance functions approximately normally distributed. This criterion was established based on the minimum distance between the pair of the skewness and kurtosis of the transformed performance function and that of a normal random variable, in which the statistical moments of the transformed performance function are evaluated from the point-estimate method. The failure probability was evaluated using a third-order moment reliability index. The accuracy and efficiency of the proposed method were demonstrated through several numerical examples, including structural reliability analysis with correlated random variables; stochastic processes; and nonnormal, nonlinear, and implicit performance functions.

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