Efficient Stochastic Response Analysis of High-Dimensional Nonlinear Systems under Complex Non-White Excitation via DR-PDEE involving Auxiliary Diffusion Process

Engineering structures are typically high-dimensional nonlinear systems, which has led to long-standing challenges in their stochastic response analysis under random excitations. This challenge is further intensified when the excitation applied to the system consists of complex non-white stochastic processes. The dimension-reduced probability density evolution equation (DR-PDEE) has shown considerable promise in addressing this issue. In previous research, applying the DR-PDEE to non-white excitation problems requires constructing linear filters in advance, which is usually a difficult task in particular for excitations with non-rational function shaped power spectral density. To facilitate the application of the DR-PDEE to problems involving generic stochastic excitations, an efficient stochastic response analysis method is developed by integrating the DR-PDEE with an auxiliary diffusion process. In this method, an excitation-correlated white noise process is constructed by sharing the random phases of the non-white excitation imposed on the high-dimensional structure. This constructed white noise is then applied to a low-dimensional system whose response forms the auxiliary diffusion process. The selection of this low-dimensional system is further discussed, and guidelines are provided for practical implementation. By coupling the response of interest of the structure with this auxiliary diffusion process, a two-dimensional DR-PDEE is established, ensuring the existence of the diffusion term without designing a linear filter. This approach enables efficient stochastic response analysis of high-dimensional nonlinear structures subjected to non-white excitations characterized by arbitrary power spectral densities. Numerical examples involving excitations with irrational power spectral densities, non-uniformly modified evolutionary spectra, and physical random excitation models illustrate the accuracy and effectiveness of the proposed method.