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A phase space reconstruction method for getting instantaneous probability density function of nonlinear stochastic systems

International Conference on Applications of Statistics and Probability (12th : 2015 : Vancouver, B.C.)

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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This collection contains the proceedings of ICASP12, the 12th International Conference on Applications of Statistics and Probability in Civil Engineering held in Vancouver, Canada on July 12-15, 2015. Abstracts were peer-reviewed and authors of accepted abstracts were invited to submit full papers. Also full papers were peer reviewed. The editor for this collection is Professor Terje Haukaas, Department of Civil Engineering, UBC Vancouver.

Vancouver : University of British Columbia Library

10.14288/1.0076304

Non UBC

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/