An adaptive moment-based approach to uncertainty analysis considering multimodal random parameters

Multimodal random variables are widely encountered in practical engineering problems, such as the structural fatigue stress of a steel bridge accommodating both highway and railway traffic and the vibratory load experienced by a blade under stochastic dynamic excitations. Because of the error amplification effect caused by nonlinear response function in uncertainty propagation, traditional uncertainty analysis methods may yield large computational errors when multimodal distributions are involved. Herein, an uncertainty propagation method for multimodal distributions is proposed. First, the probability density function of multimodal random variables is modelled using a Gaussian mixture model. Second, the higher-order statistical moments of the response function are calculated through a bivariate dimension reduction method. Finally, the probability density function of the response function is computed using the maximum entropy method, and the desired statistical moment orders are means of an adaptive convergence framework. The effectiveness of the proposed method is demonstrated through two numerical examples and one engineering application.