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Estimation of the Volterra functional series of a nonlinear system using frequency-response data

Estimation of the Volterra functional series of a nonlinear system using frequency-response data

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An algorithm is presented for the estimation of the parameters of the Volterra kernels of non-linear systems using a composite-frequency input signal. Transformations are presented between the Volterra and Wiener descriptions of nonlinear systems, which, together with an aperiodic model of Gaussian white noise, reveal the uniqueness of harmonics in the response spectrum. A periodic approximation to Gaussian white noise is proposed and is used in conjunction with a parameterised version of the kernel functions, derived from the examination of general nonlinear structures, in a parameter-estimation algorithm. The results of a simulation study are summarised.

References

    1. 1)
      • J.F. Barrett . The use of functionals in the analysis of non-linear physical systems. J. Electron. & Control , 567 - 615
    2. 2)
      • N. Wiener . (1958) , Nonlinear problems in random theory.
    3. 3)
      • J.F. Barrett . Hermite functional expansion and the calculation of output autocorrelation and spectrum for any time invariant system with noise input. J. Electron. & Control , 107 - 113
    4. 4)
      • Lawrence, P.J.: `Multifrequency testing of nonlinear systems', 1981, Ph.D. thesis, University of Wales Institute of Science and Thechnology.
    5. 5)
      • R.H. Flake . Volterra series representation of nonlinear systems. Trans. Amer. Inst. Elect. Eng. , 330 - 335
    6. 6)
      • George, D.A.: `An algebra of continuous systems', 50, Quarterly progress report, 1958, Res. Lab. Electron..
    7. 7)
      • Crum, L.A.: `Multi-dimensional Laplace transforms', 1971, Ph.D. thesis, Marquette University, Wisconsin.
    8. 8)
      • J.F. Barrett . The use of Volterra series to find the region of stability of a nonlinear differential equation. Int. J. Control , 209 - 216
    9. 9)
      • K.S. Narendra , P.G. Gallman . An iterative method for the identification of nonlinear systems using the Hammerstein model. IEEE Trans. , 546 - 550
    10. 10)
      • N. Ream . Nonlinear identification using inverse-repeat M-sequences. Proc. IEE , 1 , 213 - 218
    11. 11)
      • Cosgriff, R.L.: `Application of set theory in zero memory nonlinear stochastic problems', Proc. Nat. Elect. Conf., 1965, chicago, 21, p. 666–670.
    12. 12)
      • Lawrence, P.J., Rogers, G.J.: `Recursive identification for systems models of the transfer function type', Proceedings of 5th IFAC symposium on identification and system parameter estimation, 1979, Darmstadt .
    13. 13)
      • D.W. Marquardt . An algorithm for least squares estimation of nonlinear parameters. J. Soc. Ind. & Appl. Math. , 431 - 441
    14. 14)
      • R. Fletcher , C.H. Reeves . Function minimization by congugate gradients. Comput. J.
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