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A phase space reconstruction method for getting instantaneous probability density function of nonlinear stochastic systems Jiang, Zhong-ming; Li, Jie
Dynamic response analysis of non-linear structures involving random parameters has been an important and challenging problem for a long time. A variety of theoretical and numerical methods have been studied for engineering purpose. As a newly developed method, the probability density evolution method (PDEM) is capable of capturing the instantaneous probability density function (PDF) of stochastic dynamic responses of structures. In this paper, a new method named “phase space reconstruction method” (PSRM) is introduced. By this method, the instantaneous PDF of dynamic responses of highly non-linear systems can be obtained effectively. Some examples, including a Riccati oscillator, a SDOF oscillator, and a Van der Pol oscillator, are investigated. The results demonstrate the applicability and accuracy of PSRM in getting the solution of the generalized density evolution equation (GDEE) .
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