The cell renormalized method for the solution of KF equation and RDKF equation under additive Poisson white noise

Poisson white noise is frequently occurring in various engineering applications. Consequently, solving the stochastic dynamic response of structures subjected to Poisson white noise excitation constitutes a crucial research challenge. In this paper, using the Kolmogorov–Feller (KF) and reduced-dimensional KF (RDKF) equations, a highly efficient numerical approach is proposed for determining the probability distribution of the response. The process begins by generating Poisson white noise using stochastic harmonic function and subsequently computing the dynamic response of the structure. The cell renormalized method is then employed to compute the derivate moments at the centers of each cell. Following this, Gaussian Process Regression (GPR) is utilized to model the continuous derivate moments curve or surface within the state space. Finally, the path integral solution is applied to solve the KF and RDKF equations, ultimately yielding the desired probability distribution of the structural response. To highlight the advantages of the proposed methodology, a series of numerical examples, including one and two dimensional scenarios, linear and nonlinear systems, are all employed to substantiate the applicability of proposed method.