“Semi-empirical modeling of non-linear dynamic systems through identification of operating regimes and local models”
Authors: Tor A. Johansen and Bjarne A. Foss,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1995, Vol 16, No 4, pp. 213-232.
Keywords: Non-linear systems, system identification, fuzzy modeling, heuristic search algorithms
Abstract: An off-line algorithm for semi-empirical modeling of nonlinear dynamic systems is presented. The model representation is based on the interpolation of a number of simple local models, where the validity of each local model is restricted to an operating regime, but where the local models yield a complete global model when interpolated. The input to the algorithm is a sequence of empirical data and a set of candidate local model structures. The algorithm searches for an optimal decomposition into operating regimes, and local model structures. The method is illustrated using simulated and real data. The transparency of the resulting model and the exibility with respect to incorporation of prior knowledge is discussed.
PDF (3569 Kb) DOI: 10.4173/mic.1995.4.3
DOI forward links to this article:
[1] Bingfeng Gu and Yash P. Gupta (2008), doi:10.1016/j.isatra.2007.12.002 |
[2] K.P. Dharaskar and Y.P. Gupta (2000), doi:10.1205/026387600527725 |
[3] H.A.E. de Bruin and B. Roffel (1996), doi:10.1016/0959-1524(96)00003-0 |
[4] Ton C. Backx, Leo Huisman, Patricia Astrid and Ruud Beerkens (2008), doi:10.1002/9780470294772.ch2 |
[5] Ton C. Backx (1999), doi:10.1016/S1474-6670(17)57138-4 |
[6] Robert Haber and László Keviczky (1999), doi:10.1007/978-94-011-4481-0_1 |
[7] Robert Haber and László Keviczky (1999), doi:10.1007/978-94-011-4481-0_3 |
[1] H. Akaike (1969). Fitting autoregressive models for prediction, Ann. Inst. Stat. Math., 21:243-247, 1969 doi:10.1007/BF02532251
[2] J. C. Bezdek, C. Coray, R. Gunderson, J. Watson. (1981). Detection and characterization of cluster substructure, II. Fuzzy c-varieties and complex combinations thereof. SIAM J. Applied Mathematics, 40:352-372, 1981 doi:10.1137/0140030
[3] M. Carlin, T. Kavli, B. Lillekjendlie. (1994). A comparison of four methods for nonlinear data modeling, Chemometrics and Int. Lab. Sys., 23:163-178, 1994 doi:10.1016/0169-7439(93)E0080-N
[4] P. Craven G. Wahba. Smoothing noisy data with spline functions. (1979). Estimating the correct degree of smoothing by the method of generalized cross-validation, Numerical Math., 31:317-403, 1979.
[5] R. D. De Veaux, D. C. Psichogios, L. H. Ungar. (1993). A tale of two nonparametric estimation schemes: MARS and neural networks, In Proc. 4th Int. Conf. Artiffcial Intelligence and Statistics, 1993.
[6] J. H. Friedman. (1991). Multivariable adaptive regression splines, The Annals of Statistics, 19:1-141, 1991 doi:10.1214/aos/1176347963
[7] T. K. Ghose P. Ghosh. (1976). Kinetic analysis of gluconic acid production by pseudomonas ovalis, J. Applied Chemical Biotechnology, 26:768-777, 1976.
[8] R. A. Jacobs, M. I. Jordan, S. J. Nowlan, G. E. Hinton. (1991). Adaptive mixtures of local experts, Neural Computation, 3:79-87, 1991 doi:10.1162/neco.1991.3.1.79
[9] T. A. Johansen B. A. Foss. (1993). Constructing NARMAX models using ARMAX models, Int. J. Control, 58:1125-1153, 1993 doi:10.1080/00207179308923046
[10] T. A. Johansen B. A. Foss. (1993). State-space modeling using operating regime decomposition and local models, In Preprints 12th IFAC World Congress, Sydney, Australia, volume 1, pages 431-434, 1993.
[11] T. A. Johansen B. A. Foss. (1994). A dynamic modeling framework based on local models and interpolation - combining empirical and mechanistic knowledge and data, Submitted to Computers and Chemical Engineering, 1994.
[12] T. A. Johansen E. Weyer. (1995). Model structure identification using separate validation data - asymptotic properties, Submitted to the European Control Conference, Rome, 1995.
[13] R. D. Jones co-workers. (1991). Nonlinear adaptive networks: A little theory, a few applications, Technical Report 91-273, Los Alamos National Lab., NM, 1991.
[14] M. I. Jordan R. A. Jacobs. (1993). Hierarchical mixtures of experts and the EM algorithm, Technical Report 9301, MIT Computational Cognitive Science, 1993.
[15] T. Kavli. (1990). Nonuniformly partitioned piecewise linear representation of continuous learned mappings, In Proceedings of IEEE Int. Workshop on Intelligent Motion Control, Istanbul, pages 115-122, 1990.
[16] T. Kavli. (1993). ASMOD - An algorithm for adaptive spline modelling of observation data, Int. J. Control, 58:947-967, 1993 doi:10.1080/00207179308923037
[17] J. Larsen. (1992). A generalization error estimate for nonlinear systems, In Proc. IEEE Workshop on Neural Networks for Signal Processing, Piscataway, NJ, pages 29-38, 1992.
[18] L. Ljung. (1978). Convergence analysis of parametric identification methods, IEEE Trans. Automatic Control, 23:770-783, 1978 doi:10.1109/TAC.1978.1101840
[19] L. Ljung. (1987). System Identification: Theory for the User, Prentice-Hall, Inc., Englewood Cliffs, NJ., 1987.
[20] R. Murray-Smith. (1994). Local model networks and local learning, In Fuzzy Duisburg, pages 404-409, 1994.
[21] R. Murray-Smith H. Gollee. (1994). A constructive learning algorithm for local model networks, In Proceedings of the IEEE Workshop on Computer-Intensive Methods in Control and Signal Processing, Prague, Czech Republic, pages 21-29, 1994.
[22] M. Pottmann, H. Unbehauen, D. E. Seborg. (1993). Application of a general multimodel approach for identification of highly non-linear processes - A case study, Int. J. Control, 57:97-120, 1993 doi:10.1080/00207179308934380
[23] R. Shibata. (1976). Selection of the order of an autoregressive model by Akaike´s information criterion, Biometrica, 63:117-126, 1976 doi:10.1093/biomet/63.1.117
[24] A. Skeppstedt, L. Ljung, M. Millnert. (1992). Construction of composite models from observed data, Int. J. Control, 55:141-152, 1992 doi:10.1080/00207179208934230
[25] E. Sørheim. (1990). A combined network architecture using ART2 and back propagationfor adaptive estimation of dynamical processes, Modelling, Identification and Control.MIC, 11:191-199, 1990.
[26] P. Stoica, P. Eykhoff, P. Janssen, T. Söderström. (1986). Model-structure selection by cross-validation, Int. J. Control, 43:1841-1878, 1986 doi:10.1080/00207178608933575
[27] K. Stokbro, J. A. Hertz, D. K. Umberger. (1990). Exploiting neurons with localized receptive fields to learn chaos, J. Complex Systems, 4:603, 1990.
[28] M. Stone. (1974). Cross-validatory choice and assessment of statistical predictions, J. Royal Statistical Soc. B, 36:111-133, 1974.
[29] M. Sugeno G. T. Kang. (1988). Structure identification of fuzzy model, Fuzzy Sets and Systems, 26:15-33, 1988 doi:10.1016/0165-0114(88)90113-3
[30] T. Takagi M. Sugeno. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Systems, Man, and Cybernetics, 15:116-132, 1985.
[31] R. R. Yager D. P. Filev. (1993). Unified structure and parameter identification of fuzzy models, IEEE Trans. Systems, Man, and Cybernetics, 23:1198-1205, 1993 doi:10.1109/21.247902
[32] Y. Yoshinari, W. Pedrycz, K. Hirota. (1993). Construction of fuzzy models through clustering techniques, Fuzzy Sets and Systems, 54:157-165, 1993 doi:10.1016/0165-0114(93)90273-K
BibTeX:
@article{MIC-1995-4-3,
title={{Semi-empirical modeling of non-linear dynamic systems through identification of operating regimes and local models}},
author={Johansen, Tor A. and Foss, Bjarne A.},
journal={Modeling, Identification and Control},
volume={16},
number={4},
pages={213--232},
year={1995},
doi={10.4173/mic.1995.4.3},
publisher={Norwegian Society of Automatic Control}
};