Volterra system identification using adaptive genetic algorithms

Abstract In this paper a floating point genetic algorithm (GA) for Volterra system identification is presented. The adaptive GA method suggested here addresses the problem of determining the proper Volterra candidates which leads to the smallest error between the identified nonlinear system and the Volterra model. This is achieved by using variable length GA chromosomes which encode the coefficients of the selected candidates. During the process of evolution the candidates with the least significant contribution in the error reduction process is removed. The proposed GA method detects the proper Volterra candidates and the associated coefficients in one single evolutionary process. The fitness function employed by the algorithm prevents irrelevant candidates from taking part of the final solution. Genetic operators are chosen to suit the floating point representation of the genetic data. As the evolution process improves and the method reaches a near-global solution, a local search is implicitly applied by zooming in the search interval of each gene by adaptively changing the boundaries of those intervals. The proposed algorithms has produced excellent results in modeling different nonlinear systems.

[1]  David E. Goldberg,et al.  The gambler''s ruin problem , 1997 .

[2]  Leehter Yao.  Genetic algorithm based identification of nonlinear systems by sparse Volterra filters , 1999, IEEE Trans. Signal Process..

[3]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[4]  Vu Duong,et al.  System identification by genetic algorithm , 2002, Proceedings, IEEE Aerospace Conference.

[5]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[6]  M. J. Korenberg,et al.  A robust orthogonal algorithm for system identification and time-series analysis , 1989, Biological Cybernetics.

[7]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[8]  Gary G. R. Green,et al.  Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network , 1994, Biological Cybernetics.

[9]  M. Tummala,et al.  Identification of Volterra systems with a polynomial neural network , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Sergio Benedetto,et al.  Nonlinear Equalization of Digital Satellite Channels , 1982, IEEE J. Sel. Areas Commun..

[11]  V. Marmarelis.  Identification of nonlinear biological systems using laguerre expansions of kernels , 1993, Annals of Biomedical Engineering.

[12]  W. Krenz,et al.  Interpretation of functional series expansions , 2006, Annals of Biomedical Engineering.

[13]  Zbigniew Michalewicz,et al.  Adaptation in evolutionary computation: a survey , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[14]  Vasilis Z. Marmarelis,et al.  Nonlinear analysis of renal autoregulation under broadband forcing conditions , 1993, Annals of Biomedical Engineering.

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.

[17]  David G. Messerschmitt,et al.  Nonlinear Echo Cancellation of Data Signals , 1982, IEEE Trans. Commun..

[18]  José A. Macías,et al.  Evolution of functional link networks , 2001, IEEE Trans. Evol. Comput..

[19]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[20]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[21]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[22]  Nirmal K. Bose,et al.  Quadratic-linear filters for signal detection , 1991, IEEE Trans. Signal Process..

[23]  M. Korenberg,et al.  Orthogonal approaches to time-series analysis and system identification , 1991, IEEE Signal Processing Magazine.