A Novel Structural Reliability Method on the Basis of Gaussian Mixture and Scaled Unscented Transformation

This paper proposes a novel method to capture efficiently the probability distribution of the limit state function (LSF) for structural reliability analysis. This method works by decomposing the probability distribution of the LSF into a Gaussian mixture and applying the scaled unscented transformation to approximate the required statistics for each mixture component. The number of mixture components is specified according to Akaike's information criterion. Because the required sample size grows linearly with the number of random inputs, little computational effort is required to recover the entire distribution of the LSF with precision. The effectiveness of the proposed method was validated through numerical examples, in which the results obtained from pertinent Monte Carlo simulations and other approaches are compared. The results demonstrated that the proposed method efficiently can yield accurate estimates of the probability distribution of the LSF in the entire range, and the probability of failure accordingly can be evaluated straightforwardly. Issues that need to be studied further were discussed.