In this paper, a genetic-algorithm-based non-linear autoregressive with exogenous inputs system identification (GANARXSI) algorithm was developed to identify non-linear systems and was successfully applied to both non-linear continuous-time and discrete-time systems with acceptable accuracy. This algorithm can achieve robustness and efficiency in identifying complex non-linear systems. The effects of different combinations of operators of genetic algorithms are also studied and an operator of truncate mutation was proposed to improve greatly the convergence rate in identification process. An identified non-linear coupled liquid-level system is used to evaluate the performance of the algorithm. An experimental verification is carried out in a dynamometer engine test cell and the identified engine model during the I/M240 driving cycle is also used to validate the proposed methodology. After testing the algorithm for different complex non-linear systems, the GANARXSI algorithm proved to be a practical technique of identification for non-linear systems.
LeontaritisI. J.BillingsS. A.Input-output parametric models for non-linear systems. Part I: Deterministic non-linear systems. Int. J. Control, 1985, 41 (2), 303–328.
2.
LeontaritisI. J.BillingsS. A.Input-output parametric models for non-linear systems. Part II: Stochastic non-linear systems. Int. J. Control, 1985, 41 (2), 329–344.
3.
BillingsS. A.ChenS.KorenbergM. J.Identification of MIMO non-linear systems using a forward-regression orthogonal estimator. Int. J. Control, 1989, 49 (6), 2157–2189.
4.
ChenS.BillingsS. A.GrantP. M.Nonlinear system identification using neural networks. Int. J. Control, 1990, 51 (6), 1191–1214.
5.
NarendraK. S.ParthasarathyK.Identification and control of dynamic systems using neural network. IEEE Trans. Neural Network, 1990, 1 (1), 4–26.
6.
LiC. J.JeanY. C.Genetic algorithm in identifying nonlinear auto regressive with exogenous input models for nonlinear systems. In Proceedings of the American Control Conference, 1993, pp. 2305–2309.
7.
GoldbergD. E.Genetic Algorithms in Search, Optimization, and Machine Learning, 1989 (Addison-Wesley, Reading, Massachusetts).
8.
HollandJ. H.Adaptation in Natural and Artificial Systems: An Introductory Analysis with Application to Biology, Control, and Artificial Intelligence, 1993 (MIT Press, Cambridge, Massachusetts).
9.
MarmarelisP. Z.MarmarelisV. Z.Analysis of Physiological Systems. The White Noise Approach, 1978 (Plenum, New York).
10.
BillingsS. A.Identification of nonlinear systems—a survey. Proc. Instn Electr. Engrs, Part D, 1980, 127 (6), 272–284.
11.
KorenbergM.BillingsS. A.LiuY. P.McllroyP. J.Orthogonal parameter estimation algorithm for non-linear stochastic systems. Int. J. Control, 1988, 48 (1), 193–210.
12.
BakerJ. E.Reducing bias and inefficiency in the selection algorithm. In Proceedings of the Second Annual Conference onGenetic Algorithms, Cambridge, Massachusetts, 1987, pp. 14–21.
13.
DebK.GoldbergD. E.An investigation of niche and species formation in genetic function optimization. In Proceedings of the Third International Conference onGenetic Algorithms, 1989, pp. 42–50.
14.
GrefenstetteJ. J.BakerJ. E.How genetic algorithms work: A critical look at implicit parallelism. In Proceedings of the Third International Conference onGenetic Algorithms, 1989, pp. 20–27.
15.
BackT.HoffmeisterF.Extended selection mechanisms in genetic algorithms. In Proceedings of the Fourth International Conference onGenetic Algorithms, San Diego, California, 1991, pp. 92–99.
16.
De JongK. A.An analysis of the behavior of a class of genetic adaptive systems. Doctoral dissertation, University of Michigan, Ann Arbor, Michigan, 1975.
17.
DavisL.Applying adaptive algorithms to epistatic domains. In Proceedings of the Ninth International Joint Conference onArtificial Intelligence, Los Angeles, California, 1985, pp. 162–164.
18.
GoldbergD. E.LingleR.Alleles, loci, and the traveling salesman problem. In Proceedings of the International Conference onGenetic Algorithms and Their Applications, Pittsburgh, Pennsylvania, 1985, pp. 154–159.
19.
OliverI. M.SmithD. J.HollandJ. H.A study of permutation crossover operators on the traveling salesman problem. In Proceedings of the Second International Conference onGenetic Algorithms, 1987, pp. 224–230.
20.
LouisS. J.RawlinsG. J. E.Designer genetic algorithms in structure design. In Proceedings of the Fourth International Conference onGenetic Algorithms, 1991, pp. 53–60.
21.
PottsJ. C.GiddensT. D.YadavS. B.The development and evaluation of an improved genetic algorithm based on migration and artificial selection. IEEE Trans. Systems, Man, Cybernetics, 1994, 24 (1), 73–82.
22.
FlocktonS. J.WhiteM. S.Pole-zero system identification using genetic algorithms. In Proceedings of the Fifth International Conference onGenetic Algorithms, July 1993, pp. 531–535.
23.
KristinssonK.DumontG. A.System identification and control using genetic algorithms. IEEE Trans. Systems, Man, Cybernetics, 1992, 22 (5), 1033–1046.
24.
IbaH.KuritaT.GarisH. D.SatoT.System identification using structured genetic algorithms. In Proceedings of the Fifth International Conference onGenetic Algorithms, July 1993, pp. 279–286.
25.
TanK. C.LiY.Evolutionary system identification in the time domain. Proc. Instn Mech. Engrs, Part I, Journal of Systems and Control Engineering, 1997, 211 (14), 319–323.
26.
LuhG.-C.Identification of an internal combustion engine model by nonlinear multi-input multi-output system identification. PhD dissertation, Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio, June 1994.
27.
FakhouriS. Y.Identification of the Volterra kernels of nonlinear systems. Proc. Instn Electr. Engrs, Part D, 1980, 127 (6), 296–304.
28.
LeontaritisI. J.BillingsS. A.Experimental design and identifiability for nonlinear systems. Int. J. Systems Sci, 1987, 18 (1), 189–202.
