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TECHNICAL PAPERS

Energy-Based Stochastic Estimation for Nonlinear Oscillators With Random Excitation

[+] Author and Article Information
J. B. Roberts, M. Vasta

School of Engineering, University of Sussex, Falmer, Brighton, East Sussex BN1 9QT, UK

J. Appl. Mech 67(4), 763-771 (Aug 14, 2000) (9 pages) doi:10.1115/1.1330546 History: Received June 23, 1999; Revised August 14, 2000
Copyright © 2000 by ASME
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References

Masri,  S. F., and Caughey,  T. K., 1979, “A Nonparametric Identification Technique for Nonlinear Dynamic Problems,” ASME J. Appl. Mech., 46, pp. 433–447.
Chassiakos,  A. G., Masri,  S. F., Smyth,  A. W., and Caughey,  T. K., 1998, “On-Line Identification of Hysteretic Systems,” ASME J. Appl. Mech., 65, pp. 194–203.
Yasuda,  K., Kamiya,  K., and Komakine,  M., 1997, “Experimental Identification Technique of Vibrating Structures With Geometrical Nonlinearity,” ASME J. Appl. Mech., 64, pp. 275–280.
Unbehauen,  H., and Rao,  G. P., 1990, “Continuous Time Approaches to System Identification—A Survey,” Automatica, 26, pp. 23–35.
Feng,  M. Q., Kim,  J.-M., and Xue,  H., 1998, “Identification of a Dynamic System Using Ambient Vibration Measurements,” ASME J. Appl. Mech., 65, pp. 1010–1021.
Roberts,  J. B., Dunne,  J. F., and Debonos,  A., 1992, “Estimation of Ship Roll Parameters in Random Waves,” ASME J. Offshore Mech. Arct. Eng., 114, pp. 114–121.
Roberts,  J. B., Dunne,  J. F., and Debonos,  A., 1994, “Stochastic Estimation Methods for Nonlinear Ship Roll Motion,” Prob. Eng. Mech., 9, pp. 83–93.
Roberts,  J. B., Dunne,  J. F., and Debonos,  A., 1995, “A Spectral Method for Estimation of Nonlinear System Parameters for Measured Response,” Prob. Eng. Mech., 10, pp. 199–207.
Roberts, J. B., Dunne, J. F., and Debonos, A., 1996, “Parameter Estimation for Randomly Excited Non-linear Systems: A Method Based on Moment Equations and Measured Response Histories,” Proceedings of the IUTAM Symposium on Advances in Non-linear Stochastic Mechanics, A. Naess and S. Krenk, eds., Trondheim, Norway, July 1995, Kluwer, Dordrecht, The Netherlands, pp. 361–372.
Battaini, M., and Roberts, J. B., 1977, “Moment and Spectral Methods for Stochastic Parameter Estimation of Multi-Degree of Freedom Systems,” Proceedings of the ESREL ’97 International Conference on Safety and Reliability, Vol. 2, G. Guedes Soares, ed., Lisbon, Portugal, Pergamon, Oxford, UK, pp. 1323–1330.
Vasta,  M., and Roberts,  J. B., 1998, “Stochastic Parameter Estimation of Non-linear Systems Using Higher-Order Spectra,” J. Sound Vib., 213, pp. 201–221.
Roberts,  J. B., and Vasta,  M., 2000, “Parametric Identification of Systems With Non-Gaussian Excitation Using Measured Response Spectra,” Prob. Eng. Mech., 15, pp. 59–71.
Krenk,  S., and Roberts,  J. B., 1999, “Local Similarity in Nonlinear Random Vibration,” ASME J. Appl. Mech., 66, pp. 225–235.
Roberts,  J. B., and Vasta,  M., 2000, “Markov Modelling and Stochastic Estimation for Nonlinear Ship Rolling in Irregular Seas,” Phil. Trans. R. Soc. Lond. A., 358, pp. 1917–1941.
Roberts,  J. B., and Spanos,  P. D., 1986, “Stochastic Averaging: An Approximate Method of Solving Random Vibration Problems,” Int. J. Non-Linear Mech., 21, pp. 111–134.
Roberts,  J. B., 1982, “A Stochastic Theory for Nonlinear Ship Rolling in Irregular Seas,” J. Ship Res., 26, pp. 229–245.
Roberts, J. B., and Vasta, M., 1999c, “Response of Nonlinear Oscillators to Nonwhite Random Excitation Using an Energy Based Method,” Proceedings of the IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics, Chennai, India, to be published by Kluwer Academic Publishers.
Gardiner, C. W., 1985, Handbook of Stochastic Methods, Springer-Verlag, Berlin.
Stratonovitch, R. L., 1963, Topics in the Theory of Random Noise, Vol. 1 and 2, Gordon and Breach, New York.

Figures

Grahic Jump Location
(a) Three-dimensional plot of Jd versus a⁁ and b⁁; (b) contour plot of Jd versus a⁁ and b⁁; (c) scatter plots of the estimates of the linear and nonlinear damping parameters, for two different excitation levels, showing the intersection of the regression lines; (d) enlarged plot of part of Fig. 3(b); (e) scatter plots of the estimates of the linear and nonlinear stiffness parameters, for two different excitation levels, showing the intersection of the regression lines
Grahic Jump Location
(a) Comparison of estimated energy values with the exact values, (b) scatter plot of the estimates of the linear and nonlinear stiffness parameters
Grahic Jump Location
(a) Variation of the slope of the diffusion coefficient with Δt, (b) comparison between the estimated and true variation of the diffusion coefficient with energy level, (c) comparison between the estimated variation and true variation of the drift coefficient with energy level, (d) comparison between the estimated and true damping function variation with energy level, (e) estimated histogram of the energy, (f ) comparison between estimates of the input power spectrum and the true spectrum, (g) variation with frequency of the standard deviation of the estimates of the input power spectrum, (h) variation of the frequency of free undamped oscillation with energy level, (i) scatter plot for the estimates of the linear and nonlinear damping parameters

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