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2015 | OriginalPaper | Chapter

Approximate Probability Density Function Solution of Multi-Degree-of-Freedom Coupled Systems Under Poisson Impulses

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Abstract

A solution procedure is proposed to approximate the probability density function (PDF) solution of high-dimensional non-linear systems under Poisson impulses. The PDF solution yields the generalized Fokker–Planck–Kolmogorov (FPK) equation. First a state-space-split method is proposed to reduce the high-dimensional generalized FPK equation to a low dimensional equation. After that, the exponential–polynomial closure method is further adopted to solve the reduced FPK equation for the PDF solution. In order to show the effectiveness of the proposed solution procedure, a two-degree-of-freedom coupled pitch–roll ship motion system and a 10-degree-of-freedom mass–spring–damper system are investigated, respectively. Compared to the simulated results, the proposed solution procedure is effective to obtain the PDF solution, especially in the tail region which is very important for reliability analysis.

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Metadata
Title
Approximate Probability Density Function Solution of Multi-Degree-of-Freedom Coupled Systems Under Poisson Impulses
Author
H. T. Zhu
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-07167-1_19

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