A time-variant uncertainty propagation analysis method for multimodal probability distributions

In practical engineering problems, scenarios frequently emerge where random parameters follow multimodal probability distributions. Traditional time-variant uncertainty propagation methods, originally designed for unimodal distributions, risk incurring significant inaccuracies when applied to such multimodal cases. To address this challenge this paper introduces a time-variant uncertainty propagation analysis framework tailored for multimodal probability distributions. Initially, the time-variant response function is discretized into a series of instantaneous response functions. Subsequently, an improved point estimation method is employed to compute high-order statistical moments and correlation coefficients of these instantaneous responses. Following this, the maximum entropy method is used to reconstruct the probability density function of each instantaneous response function from its derived statistical moments. The highest order of statistical moments is adaptively determined through entropy-based criteria to balance computational efficiency and accuracy. Ultimately, the validity and effectiveness of the proposed framework are demonstrated through three examples.