Statistical bilinearization in stochastic nonlinear dynamics

N. Wouw, van de; H. Nijmeijer; D.H. Campen, van

doi:10.1109/COC.2000.874266

Statistical bilinearization in stochastic nonlinear dynamics

N. Wouw, van de, H. Nijmeijer, D.H. Campen, van

Dynamics and Control

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

4 Citations (Scopus)

Abstract

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation

Original language	English
Title of host publication	Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings
Editors	F.L. Chernouskov, A.L. Fradkov
Place of Publication	Piscataway, NJ, USA
Publisher	Institute of Electrical and Electronics Engineers
Pages	394-399
ISBN (Print)	0-7803-6434-1
DOIs	https://doi.org/10.1109/COC.2000.874266
Publication status	Published - 2000

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10.1109/COC.2000.874266

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Wouw, van de, N., Nijmeijer, H., & Campen, van, D. H. (2000). Statistical bilinearization in stochastic nonlinear dynamics. In F. L. Chernouskov, & A. L. Fradkov (Eds.), Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings (pp. 394-399). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/COC.2000.874266

Wouw, van de, N. ; Nijmeijer, H. ; Campen, van, D.H. / Statistical bilinearization in stochastic nonlinear dynamics. Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings. editor / F.L. Chernouskov ; A.L. Fradkov. Piscataway, NJ, USA : Institute of Electrical and Electronics Engineers, 2000. pp. 394-399

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title = "Statistical bilinearization in stochastic nonlinear dynamics",

abstract = "A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation",

author = "{Wouw, van de}, N. and H. Nijmeijer and {Campen, van}, D.H.",

year = "2000",

doi = "10.1109/COC.2000.874266",

language = "English",

isbn = "0-7803-6434-1",

pages = "394--399",

editor = "F.L. Chernouskov and { Fradkov}, A.L.",

booktitle = "Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

}

Wouw, van de, N , Nijmeijer, H & Campen, van, DH 2000, Statistical bilinearization in stochastic nonlinear dynamics. in FL Chernouskov & AL Fradkov (eds), Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings. Institute of Electrical and Electronics Engineers, Piscataway, NJ, USA, pp. 394-399. https://doi.org/10.1109/COC.2000.874266

Statistical bilinearization in stochastic nonlinear dynamics. / Wouw, van de, N.; Nijmeijer, H.; Campen, van, D.H.
Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings. ed. / F.L. Chernouskov; A.L. Fradkov. Piscataway, NJ, USA: Institute of Electrical and Electronics Engineers, 2000. p. 394-399.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

TY - GEN

T1 - Statistical bilinearization in stochastic nonlinear dynamics

AU - Wouw, van de, N.

AU - Nijmeijer, H.

AU - Campen, van, D.H.

PY - 2000

Y1 - 2000

N2 - A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation

AB - A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original, nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation

U2 - 10.1109/COC.2000.874266

DO - 10.1109/COC.2000.874266

M3 - Conference contribution

SN - 0-7803-6434-1

SP - 394

EP - 399

BT - Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings

A2 - Chernouskov, F.L.

A2 - Fradkov, A.L.

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway, NJ, USA

ER -

Wouw, van de N , Nijmeijer H , Campen, van DH. Statistical bilinearization in stochastic nonlinear dynamics. In Chernouskov FL, Fradkov AL, editors, Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia ; proceedings. Piscataway, NJ, USA: Institute of Electrical and Electronics Engineers. 2000. p. 394-399 doi: 10.1109/COC.2000.874266

Statistical bilinearization in stochastic nonlinear dynamics

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