Velocity divergence—Generalized adaptive probability density evolution method

This study proposes a novel velocity divergence-generalized adaptive probability density evolution method (VD-GAPDEM) for calculating the probability density function of the stochastic response process of stochastic structures under stochastic dynamic loads. First, based on the principle of probability conservation, the velocity divergence-generalized adaptive probability density evolution equation (VD-GAPDEE) is derived for a stochastic system that can effectively consider the shape and location changes of the joint transitional probability density of representative points (RPs) in the stochastic response process. Second, a novel VD-GAPDEM is proposed to solve the VD-GAPDEE directly using the point selection technique based on the generalized F discrepancy and the second-order Runge–Kutta method with a smoothing kernel method (Runge–Kutta-SKFAM). Furthermore, the differences and connections between VD-GAPDEM and the existing probability density evolution method are analyzed. Additionally, the high computational efficiency and accuracy of the proposed VD-GAPDEM are demonstrated through three typical examples of stochastic response analysis, involving stochastic systems subjected to stochastic dynamic loads.