Browse > Article
http://dx.doi.org/10.5000/EESK.2005.9.3.033

Parameter Identification of Nonlinear Dynamic Systems using Frequency Domain Volterra model  

Paik, In-Yeol (경원대학교 토목환경공학과)
Kwon, Jang-Sub (특허청 건설기술심사담당관실)
Publication Information
Journal of the Earthquake Engineering Society of Korea / v.9, no.3, 2005 , pp. 33-42 More about this Journal
Abstract
Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the $2^{nd}\;or\;3^{rd}$ order nonlinearity is dominant.
Keywords
dynamic system; frequency domain; Volterra model; higher order transfer function; nonlinear parameter estimation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Worden, K. and Tomlinson, G.R., Nonlinearity in Structural Dynamics: Detection, Identification and Modelling, Institute of Physics Publishing, UK, 2001
2 Kim, K. I., Powers, E. J., Ritz, C. P., Miksad, R. W. and Fischer, F. J., 'Modeling of the Nonlinear Drift Oscillations of Moored Vessels Subjected to Non-Gaussian Random Sea-Wave Excitation', IEEE Journal of Oceanic Engineering, Vol. OE-12, No.4., 1987, pp. 568-575
3 Kim, S. B., Powers, E. J., Miksad, R. W., Fischer, F. J., Hong, J. Y., 'Spectral Decomposition of Nonlinear TLP Sway Response to Non-Gaussian Irregular Seas,' Proceedings of the 21st Annual Offshore Technology Conference, OTC 6134, Houston, Tx, 1989
4 Paik, I. and Roesset, J. M., 'Use of quadratic transfer functions to predict response of tension leg platforms', Journal of Engineering Mechanics, ASCE, Vol. 122, No.9., 1996, pp. 882-889   DOI
5 Im, S. B. and Powers, E. J., 'A sparse thirdorder orthogonal frequency domain Volterra-like model,' Journal of Franklin Institute, Vol. 333 (B), No.3, 1996, pp. 385-412   DOI   ScienceOn
6 Sibetheros, I. A, Rijken, O. R. and Niedzwecki, J. M., 'Volterra series-based system analysis of random wave interaction with a horizontal cylinder,' Ocean Engineering, Vol. 27, 2000, pp. 241-270   DOI   ScienceOn
7 Bendat, J. S., Nonlinear System Analysis and Identification from Random Data, John Wiley & Sons, New York, 1990
8 Bedrosian, E. and Rice, S.O., 'The Output Properties of Volterra Systems (Nonlinear Sys-tems with Memory) Driven By Harmonic and Gaussian Inputs,' Proceedings of the IEEE, Vol. 59, No. 12, 1971, pp. 1688-1707
9 Borgman, L. E., 'Ocean Wave Simulation for Engineering Design,' Journal of Waterways and Harbors Division, ASCE, WW4, 95, 1969, pp. 557-583
10 Khan, A. A and Vyas, N. S., 'Non-linear parameter estimation using Volterra and Wiener theories,' Journal of Sound and Vibration, Vol. 221, No.5., 1999, pp. 805-821   DOI   ScienceOn
11 Schetzen, M., The Volterra and Wiener Theories of Nonlinear Systems, John Wiley, New York, 1980
12 IMSL FORTRAN numerical libraries
13 Nam, S. W. and Powers, E. J., 'Application of higher order spectral analysis to cubically nonlinear system identification,' IEEE Transaction on Signal Processing, Vol. 42, No.7., 1994, pp. 1746-1765   DOI   ScienceOn