.png){kind=icon}
.png){kind=icon}
Return
DR-PDEE-based Stochastic Dynamical Response Analysis for High-Dimensional Nonlinear Systems under Multiplicative Non-White Noise Excitation
.png){kind=icon}
PRE
AI
T
P
J
DOI：10.1016/j.probengmech.2026.103968.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Multiplicative stochastic excitation is important in modeling complex nonlinear dynamics across multiple fields. Further, random noise in physical systems is commonly not ideal white noise. It is noted that stochastic analysis of high-dimensional nonlinear systems, even under additive white noise, has been quite challenging for several decades. These issues are exacerbated in the case of multiplicative excitation and non-white excitation. To address these challenges, the dimension-reduced probability density evolution equation (DR-PDEE) is extended herein to determine the response probability density of such systems. The basic idea is to first augment the original system to a white noise excited higher-dimensional system, and then to reduce the system by the DR-PDEE. In this approach, the multiplicative non-white noise excitation is modelled by an analog filter with white noise input. The original dynamical system combined with the filter then forms an augmented higher-dimensional system driven by additive white noise. Next, the two-dimensional DR-PDEE is constructed for the joint process that combines the quantity of interest in the original system with a filter output, possessing a nonzero intrinsic diffusion function. Solving the DR-PDEE directly yields the probability density function (PDF) of the quantity of interest. Notably, it is found that, owing to the introduction of the analog filter, the original system driven by multiplicative non-white noise is converted into a problem involving additive white noise excitation. Thus, the intrinsic diffusion function in the corresponding DR-PDEE for the joint process becomes a known constant. This feature distinguishes the DR-PDEE for systems driven by multiplicative white noise, where the intrinsic diffusion functions are state-dependent. Thus, only the intrinsic drift functions in the DR-PDEE must be identified. These terms can be reliably estimated through a small number of representative deterministic analyses. An example is presented to validate the proposed method. The numerical example demonstrates that the DR-PDEE yields PDF solutions with high tail accuracy using only a limited number of deterministic analyses.
Journal
IF:
3.5
Papers:
1.7K
Citations:
4.1K
Organization
Cited Papers