Efficient approach for dynamic reliability analysis based on uniform design method and Box-Cox transformation

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This paper proposes a novel approach for dynamic reliability analysis of uncertain structures subjected to non-stationary stochastic excitations. This approach calculates the first-passage probabilities by evaluating the transformed extreme value distribution (TEVD) instead of the original extreme value distribution (EVD). The Box-Cox transformation is first used to symmetrize the extreme value, and then the generalized Gaussian distribution (GGD) is suggested to approximate the main body and tails of the TEVD. An absolute skewness minimization criterion is proposed to find the optimal Box-Cox transformation parameter. Furthermore, the random-function spectral representation method (RFSRM) and uniform design method (UDM) are successfully combined to estimate the first four central moments of the transformed extreme value with a small sample size. Two numerical examples involving linear and nonlinear shear-frame structures under nonstationary ground motions are investigated. The results indicate that the proposed method can be used for dynamic reliability analysis with high accuracy and efficiency.