System response to random impulses

doi:10.1016/0022-460X(72)90119-8

Journal of Sound and Vibration

Volume 24, Issue 1, 8 September 1972, Pages 23-34

https://doi.org/10.1016/0022-460X(72)90119-8 Get rights and content

Abstract

An expression is obtained for the cumulant generating function of the multi-dimensional response of a linear system to Poisson distributed random impulses. It is shown that this result enables estimates to be made of the joint probability distribution of the response, when the latter is slightly non-Gaussian. As an application of the general theory, the evaluation of threshold statistics is considered in some detail and various modifications to the well-known Gaussian results are given.

An approach to the study of non-linear system response to random impulses is also developed; this leads to a generalization of the Fokker-Planck equation.

References (12)

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On the response of a simple oscillator to random impulses
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Application of nonstationary shot noise in the study of system response to a class of nonstationary excitation
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There are more references available in the full text version of this article.

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Citation Excerpt :
It is also called as the Kolmogorov-Feller equation [23]. The associated exact solution is too difficult to be obtained and most work has to be fulfilled by approximate methods, such as perturbation technique [24,25], Petrov-Galerkin method [26], cell-to-cell mapping (path integration) technique [27,28], finite difference method [29], exponential-polynomial closure (EPC) method [30,31] and stochastic averaging method [32,33]. Most of these methods have been applied to single-degree-freedom systems under Poisson impulses.
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System response to random impulses

Abstract

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Mathematical analysis of random noise

Bell System Technical Journal

Application of nonstationary shot noise in the study of system response to a class of nonstationary excitation

Journal of Applied Mechanics (series E)

Stochastic Processes