Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32759
Cyclostationary Gaussian Linearization for Analyzing Nonlinear System Response under Sinusoidal Signal and White Noise Excitation

Authors: R. J. Chang

Abstract:

A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise are analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: Cyclostationary, Duffing system, Gaussian linearization, sinusoidal signal and white noise.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100729

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1941

References:


[1] A. A. Pervozvanskii, Random Processes in Nonlinear Control Systems, New York: Academic Press, 1965.
[2] P. Jung, “Periodically driven stochastic systems,” Physics Reports, vol. 234, nos. 4, 5, pp. 175-295, 1993.
[3] A. Jha and E. Nikolaidis, “Vibration of dynamic systems under cyclostationary excitations,” AIAA J., vol. 38, no. 12, pp. 2284-2291, 2000.
[4] K. Ellermann, “On the determination of nonlinear response distributions for oscillators with combined harmonic and random excitation,” Nonlinear Dynamics, vol. 42, pp. 305-318, 2005.
[5] W. A. Gardner, N. Antonio, and P. Luigi "Cyclostationarity: Half a century of research," Signal Processing, vol. 86, no. 4, pp. 639–697, 2006.
[6] A. B. Budgor, “Studies in nonlinear stochastic processes. III. Approximate solutions of nonlinear stochastic differential equations excited by Gaussian noise and harmonic disturbances,” J. Statistical Physics, vol. 17, no. 1, pp. 21-44, 1977.
[7] A. R. Bulsara, K. Lindenberg, and K. E. Shuler, “Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory,” J. Statistical Physics, vol. 27, no. 4, pp. 789-796, 1982.
[8] R. N. Yengar, “A nonlinear system under combined periodic and random excitation,” J. Statistical Physics, vol. 44, no. 5/6, pp. 907-920, 1986.
[9] A. H. Nayfeh and S. J., Serhan, Response statistics of non-linear systems to combined deterministic and random excitations, Int. J. Non-Linear Mechanics, vol. 25, no. 5, pp. 493-505, 1990.
[10] U. V. Wagner, On double crater-like probability density functions of a duffing oscillator subjected to harmonic and stochastic excitations,” Nonlinear Dynamics, vol. 28, pp. 343-355, 2002.
[11] H. Rong, G. Meng, X. Wang, Xu, W., and T. Fang, Response statistic of non-linear oscillator to combined deterministic and random excitation,” Int. J. Non-Linear Mechanics, vol. 39, pp. 871-878, 2004.
[12] Z. L. Huang, W. Q. Zhu, Y. Suzuki, “Stochastic averaging of non-linear oscillators under combined harmonic and white-noise excitations,” J. Sound and Vibration, vol. 238, no. 2, pp. 233-256, 2000.
[13] Y. J. Wu and W. Q. Zhu, “Stochastic averaging of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations,” J. Vibration and Acoustics, vol.130, 051004, pp. 1-19, 2008.
[14] Z. L. Huang and W. Q. Zhu, “Stochastic averaging of quasi-integrable Hamiltonian systems under combined harmonic and white noise excitations,” Int. J. Non-Linear Mechanics, vol. 39, pp. 1421-1434, 2004.
[15] J. Yu and Y. Lin, “Numerical path integration of a nonlinear oscillator subject to both sinusoidal and white noise excitations,” 5th Int. Conf. Stochastic Structural Dynamics; Advances in stochastic structural dynamics, Florida, USA, 2003, pp. 525-534.
[16] W. Xu, Q. He, T. Fang, and H. Rong, “Stochastic bifurcation in Duffing system subjected to harmonic excitation and in presence of random noise,” Int. J. Non-Linear Mechanics, vol. 39, pp. 1473-1479, 2004.
[17] U. V. Wagner and Wedig, W. V. “On the calculation of stationary solutions of multi-dimensional Fokker-Planck equations by orthogonal functions,” Nonlinear Dynamics, vol. 21, pp. 289-306, 2000.
[18] L. Socha, Linearization Methods for Stochastic Dynamic Systems, Berlin: Springer, 2008.
[19] R. J. Chang, “Two-stage optimal stochastic linearization in analyzing of non-linear stochastic dynamic systems,” Int. J. Non-Linear. Mechanics, vol. 58, pp. 295-304, 2014.