This paper describes an automated localized modeling method to identify continuous nonlinear dynamic systems from their operating data. Using a method similar to finite element method’s automatic mesh generation, the input space is partitioned into overlapped regions that are small enough that a local model, such as a simple neural network, can approximate the data well in each region. Subsequently, adjacent regions are inspected to see if they can be represented well by a single local model to minimize the number of regions and local models needed to approximate a system. A nonlinear oscillator is used to test the proposed method, and the method was able to generate models that can simulate the system well. [S0022-0434(00)01902-X]
Issue Section:
Technical Briefs
1.
Cybenko
, G.
, 1989
, “Approximation by Superpositions of a Sigmoidal Function
,” Math. Control, Signals, Syst.
, 2
, No. 4
, pp. 303
–314
.2.
Funahashi
, K.
, 1989
, “On the Approximate Realization of Continuous Mappings by Neural Networks
,” Neural Networks
, 2
, pp. 183
–192
.3.
Hornik
, K.
, Stinchcombe
, M.
, and White
, H.
, 1989
, “Multilayer Feedforward Networks Are Universal Approximators
,” Neural Networks
, 2
, No. 5
, pp. 359
–366
.4.
McCulloch
, W. S.
, and Pitts
, W.
, 1943
, “A Logical Calculus of the Ideas Immanent in Nervous Activity
,” Bull. Math. Biophys.
, 5
, pp. 115
–133
.5.
Glauber
, R. J.
, 1963
, “Time-dependent Statistics of the Ising Model
,” J. Math. Phys.
, 4
, pp. 294
–307
.6.
Amit
, D.
, Gutfreund
, H.
, and Sompolinsky
, H.
, 1985
, “Spin-glass Models of Neural Networks
,” Phys. Rev. A
, 32
, pp. 1007
–1018
.7.
Moody
, J.
, and Darken
, C.
, 1989
, “Fast Learning in Networks of Locally-Tuned Processing Units
,” Neural Comput.
, 1
, pp. 281
–294
.8.
Gupta, M. M., and Qi, J., 1991, “On Fuzzy Neuron Models,” Proc. of Int’l Joint Conf. On Neural Networks ’91, 2, pp. 431–436.
9.
Ichihashi, H., 1991, “Learning in Hierarchical Fuzzy Models by Conjugate Gradient Method using Backpropagation Errors,” Proc. of Intelligent System Symposium, pp. 235–240.
10.
Berenji
, H. R.
, and Khedkar
, P.
, 1992
, “Learning and Tuning Fuzzy Logic Controllers through Reinforcements
,” Trans. Neural Networks
, 3
, No. 5
, pp. 724
–740
.11.
Ritter
, H. J.
, Martinez
, T. M.
, and Schuten
, K. J.
, 1989
, “Topology-conserving Maps for Learning Visuo-motor-coordination
,” Neural Networks
, 2
, No. 3
, pp. 159
–168
.12.
Principe
, J. C.
, Wang
, L.
, and Motter
, M. A.
, 1998
, “Local Dynamic Modeling with Self-organizing Maps and Applications to Nonlinear System Identification and Control
,” Proc. IEEE
, 86
, No. 11
, pp. 2240
–2258
.13.
Suganthan
, P. N.
, 1999
, “Hierarchical Overlapped SOM’s for Pattern Classification
,” IEEE Trans. Neural Netw.
, 10
, No. 1
, pp. 193
–196
.14.
George, P. L., 1991, Automatic Mesh Generation: Application to Finite Element Methods, Wiley, Chichester, New York.
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