An uncertainty propagation analysis method considering multimodal random distribution

Abstract

<p indent=0mm>In practical engineering applications, random variables may follow a multimodal random distribution, such as damping characteristics of train shock absorber after long-term use and fatigue life of safety cut specimens after repair. Traditional uncertainty propagation analysis methods are mainly used for random variables following a unimodal distribution. Therefore, large errors will be produced when random variables follow a multimodal distribution. In this study, an uncertainty propagation analysis method considering a multimodal random distribution is proposed. First, the probability density function of input multimodal random variables is defined by the Gaussian mixture model; then, the high-order moments of response function are calculated using the efficient trivariate dimension reduction method, which effectively improves the computational efficiency of uncertainty propagation. Once again, the maximum entropy method is used to compute the probability density function of response, whereas an adaptive method based on entropy is used to determine the optimal order of statistical moments. Finally, four numerical examples are demonstrated to analyze the accuracy and efficiency of the proposed method in handling multimodal uncertainty propagation analysis.