首页|Stochastic dynamic response analysis based on reduced dimension probability evolution equation under additive Gaussian white noise
Stochastic dynamic response analysis based on reduced dimension probability evolution equation under additive Gaussian white noise
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NETL
NSTL
Elsevier
The solution of derivate moments in reduced dimension probability evolution equation (RDPEE) is still a difficult task in current research, especially for complex systems. This paper introduces the cell renormalized method, which dissects state and probabilistic space, is applied to numerically calculate the derivate moments of cell-centered coordinates. Then, an efficient nonlinear regression method based on Bayesian inference named Gaussian process regression is used to obtained the continuous curve of derivate moments in state space. Eventually, by solving the RDPEE via path integral solution, the final probability distribution can be recovered without difficulty. To illustrate it, several numerical examples, which include uni-modal and multi-modal distributions, simple and complex dynamical systems, Markov and non-Markov cases, are all considered to validate the high accuracy and efficiency of proposed method.
Reduced dimension probability evolutionequationCell renormalized methodGaussian process regressionBayesian theoryFractional derivative
Jinheng Song、Jie Li
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College of Civil Engineering,Tongji University,1239 Siping Road,Shanghai 200092,PR China
College of Civil Engineering,Tongji University,1239 Siping Road,Shanghai 200092,PR China||State Key Laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai 200092,PR China
NETL
NSTL
Elsevier
