Abstract
The problem of estimating unknown parameters in a non-linear randomly excited dynamic system, when the excitation is unmeasurable, is considered. It is shown that, if the excitation is modelled stochastically as a Gaussian process, with a prescribed spectral form, it is possible to estimate the parameters from response data alone using either moment equations or a spectral input-output relationship. When applied to simulated data for a particular non-linear oscillator, as an example, it is found that the use of moment equations leads to a very good estimation of the stiffness parameters but is incapable of yielding estimates of the absolute level of damping. However the latter can be found accurately by applying a spectral relationship. Improvements in the accuracy of estimation for the damping parameters, and the input intensity, are achieved by using a theoretical expression for the distribution of the energy envelope of the response in combination with statistical linearisation.
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References
Debonos, A. (1993) Estimation of Non-linear Ship Roll Parameters using Stochastic Identification Techniques. D.Phil. Thesis, University of Sussex.
Gawthrop, P. J., A. Kountzeris, A. & Roberts, J.B. (1988) Parametric Identification of Non-linear Ship Roll Motion from Forced Roll Data. J. Ship Research, 32,101–111.
Kountzeris, A., Roberts, J.B. & Gawthrop, P.J. (1991) Estimation of Ship Roll Parameters from Motion in Irregular Seas. Trans. Royal Institution of Naval Architects, 132,253–266.
Roberts, J.B. (1982) A Stochastic Theory for Non-linear Ship Rolling in Irregular Seas, J. Ship Research, 26, 229–245.
Roberts, J.B. and Dacunha, N.M.C. (1985) The Roll Motion of a Ship in Random Beam Waves: Comparison between Theory and Experiment. J. Ship Research, 29,112–126
Roberts, J. B., Dunne, J.F. & Debonos, A. (1992) Estimation of Ship Roll Parameters in Random Waves. ASME J. Offshore Mechanics and Arctic Engineering, 114, 114–121.
Roberts, J.B., Dunne J.F. & A. Debonos, A. (1994) Stochastic Estimation Methods for Non-linear Ship Roll Motion. Probabilistic Engineering Mechanics 9, 83–93.
Roberts, J.B., Dunne, J.F. and A. Debonos, A. (1995) A Spectral Method for Estimation of Non-linear System Parameters from Measured Response. Probabilistic Engineering Mechanics (to be published).
Roberts, J. B. & Spanos, P.D. (1986) Stochastic Averaging: An Approximate Method for Solving Random Vibration Problems. International Journal of Non-linear Mechanics, 21, 111–134.
Roberts, J. B. & Spanos, P.D. (1990) Random Vibration and Statistical Linearization. J. Wiley & Sons, Chichester, UK.
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© 1996 Kluwer Academic Publishers
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Roberts, J.B., Dunne, J.F., Debonos, A. (1996). Parameter Estimation for Randomly Excited Non-Linear Systems. In: Naess, A., Krenk, S. (eds) IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. Solid Mechanics and its Applications, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0321-0_34
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DOI: https://doi.org/10.1007/978-94-009-0321-0_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6630-3
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