TY - JOUR

T1 - DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process

AU - Sun, T. T.

AU - Chen, J. B.

AU - Luo, Y.

AU - Lyu, J. H.

N1 - Publisher Copyright: © 2025 Elsevier B.V.

PY - 2025/5/5

Y1 - 2025/5/5

N2 - Accurately analyzing the probabilistic responses of high-dimensional nonlinear dynamical structures subjected to non-white and non-stationary stochastic excitations is a critical and challenging task. To address this issue, an efficient stochastic response analysis method is proposed by constructing an auxiliary diffusion process related to the non-white and non-stationary excitation process and incorporating it into the dimension-reduced probability density evolution equation (DR-PDEE). In the proposed method, the non-white stochastic excitation is represented through a spectral process with independent increments, and a white noise process associated with the excitation is constructed by modulating the amplitude of this spectral process to be a constant over the frequency domain. Subsequently, an auxiliary diffusion process is built by setting its governing equation driven by the constructed white noise, which guarantees that the auxiliary diffusion process has a non-zero intrinsic diffusion function and is correlated with the system response. The probability density function (PDF) of the response of interest for a high-dimensional nonlinear system can then be immediately obtained by solving the two-dimensional DR-PDEE, which governs the joint PDF of the response quantity and the constructed auxiliary diffusion process. The intrinsic drift functions in the DR-PDEE are expressed as the first-order conditional derivate moments, and a numerical scheme is developed to determine these terms based on the data from representative response trajectories. The proposed method guarantees that there are non-zero intrinsic diffusion functions in the corresponding DR-PDEE, which is realized without requiring a linear filter to simulate the non-white excitation from white noise, thus providing a broader scope of application. Several numerical examples, including linear and nonlinear multi-degree-of-freedom (MDOF) systems, are studied to illustrate the effectiveness of the proposed method. The stochastic excitations in these systems include stationary processes with power spectral densities (PSDs) that cannot be expressed as rational functions, as well as non-stationary processes characterized by the non-uniformly modulated evolutionary PSD (EPSD) model.

AB - Accurately analyzing the probabilistic responses of high-dimensional nonlinear dynamical structures subjected to non-white and non-stationary stochastic excitations is a critical and challenging task. To address this issue, an efficient stochastic response analysis method is proposed by constructing an auxiliary diffusion process related to the non-white and non-stationary excitation process and incorporating it into the dimension-reduced probability density evolution equation (DR-PDEE). In the proposed method, the non-white stochastic excitation is represented through a spectral process with independent increments, and a white noise process associated with the excitation is constructed by modulating the amplitude of this spectral process to be a constant over the frequency domain. Subsequently, an auxiliary diffusion process is built by setting its governing equation driven by the constructed white noise, which guarantees that the auxiliary diffusion process has a non-zero intrinsic diffusion function and is correlated with the system response. The probability density function (PDF) of the response of interest for a high-dimensional nonlinear system can then be immediately obtained by solving the two-dimensional DR-PDEE, which governs the joint PDF of the response quantity and the constructed auxiliary diffusion process. The intrinsic drift functions in the DR-PDEE are expressed as the first-order conditional derivate moments, and a numerical scheme is developed to determine these terms based on the data from representative response trajectories. The proposed method guarantees that there are non-zero intrinsic diffusion functions in the corresponding DR-PDEE, which is realized without requiring a linear filter to simulate the non-white excitation from white noise, thus providing a broader scope of application. Several numerical examples, including linear and nonlinear multi-degree-of-freedom (MDOF) systems, are studied to illustrate the effectiveness of the proposed method. The stochastic excitations in these systems include stationary processes with power spectral densities (PSDs) that cannot be expressed as rational functions, as well as non-stationary processes characterized by the non-uniformly modulated evolutionary PSD (EPSD) model.

KW - Diffusion process

KW - Dimension-reduced probability density evolution equation (DR-PDEE)

KW - High-dimensional nonlinear systems

KW - Intrinsic diffusion functions

KW - Non-stationary excitation

KW - Non-white noise excitation

UR - http://www.scopus.com/inward/record.url?scp=105004218414&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2025.118029

DO - 10.1016/j.cma.2025.118029

M3 - Article

AN - SCOPUS:105004218414

VL - 442

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 118029

ER -