Volterra Kernel Identification Using Triangular Wavelets

JVC/Journal of Vibration and Control

Volumn 10, Issue 4, 2004, Pages 597-622

  Prazenica, Richard J ^a   Kurdila, Andrew J ^b  

^a NASA DRYDEN FLIGHT RESEARCH CENTER   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Multiresolution analysis; Nonlinear system identification; Orthonormal wavelets; Triangular wavelets; Volterra series

Indexed keywords

AERODYNAMICS; ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; FLEXIBLE STRUCTURES; PREDICTIVE CONTROL SYSTEMS;

MULTIRESOLUTION ANALYSIS; NONLINEAR SYSTEM IDENTIFICATION; ORTHONORMAL WAVELETS; TRIANGULAR WAVELETS; VOLTERRA SERIES;

NONLINEAR SYSTEMS;

EID: 2342485991     PISSN: 10775463     EISSN: None     Source Type: Journal    
DOI: 10.1177/1077546041125809     Document Type: Article

References (28)

1. Bedrosian, E. and Rice, S. O., 1971, "The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs," Proceedings of the IEEE 59(12), 1688-1707.
2. Beylkin, G., Coifman, R., and Rokhlin, V., 1991, "Fast wavelet transforms and numerical algorithms," Communications on Pure and Applied Mathematics 44, 141-183.
3. Boyd, S. and Chua, L. O., 1985, "Fading memory and the problem of approximating nonlinear operators with Volterra series," IEEE Transactions on Circuits and Systems 32(11), 1150-1161.
4. Boyd, S., Tang, Y. S., and Chua, L. O., 1983, "Measuring Volterra kernels," IEEE Transactions on Circuits and Systems 30(8), 571-577.
5. Chen, Z., Micchelli, C., and Xu, Y., 1999, "A construction of interpolating wavelets on invariant sets," Mathematics of Computation 68(228), 1569-1587.
6. Cherry, J. A. and Snelgrove, W. M., 1998, "On the characterization and reduction of distortion in bandpass filters," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 45(5), 523-537.
7. Chon, K., Chen, Y., Holstein-Rathlou, N., and Marmarelis, V., 1998, "Nonlinear system analysis of renal autoregulation in normotensive and hypertensive rats," IEEE Transactions on Biomedical Engineering 45(3), 342-353.
8. Doyle, F. J. III, Pearson, R. K., and Ogunnaike, B. A., 2002, Identification and Control Using Volterra Models, Springer, London.
9. French, A. S., Sekizawa, S., Hoger, U., and Torkkeli, P., 2001, "Predicting the responses of mechanoreceptor neurons to physiological inputs by nonlinear system identification," Annals of Biomedical Engineering 19, 187-194.
10. Groetsch, C. W., 1993, Inverse Problems in the Mathematical Sciences, Vieweg, Wiesbaden.
11. Hansen, P. C., 1998, Rank Deficient and Discrete Ill-Posed Problems, SIAM, Philadelphia, PA.
12. Kurdila, A. J., Prazenica, R. J., Rediniotis, O., and Strganac, T., 2001, "Multiresolution methods for reduced-order models for dynamical systems," Journal of Guidance, Control, and Dynamics 24(2), 193-200.
13. Lee, Y. W. and Schetzen, M., 1965, "Measuring of the Wiener kernels of a non-linear system by cross-correlation," International Journal of Control 2(3), 237-254.
14. Mallat, S., 1998, A Wavelet Tour of Signal Processing, Academic Press, Boston, MA.
15. Marmarelis, V. Z., 1993, "Identification of nonlinear biological systems using Laguerre expansions of kernels," Annals of Biomedical Engineering 21, 573-589.
16. Marzocca, P., Librescu, L., and Silva, W. A., 2002, "Aeroelastic response of nonlinear wing sections using a functional series technique," AIAA Journal 40(5), 813-824.
17. Micchelli, C. and Xu, Y., 1994, "Using the matrix refinement equation for the construction of wavelets on invariant sets," Applied and Computational Harmonic Analysis 1, 391-401.
18. Nikolaou, M. and Mantha, D., 1998, "Efficient nonlinear modelling using wavelets and related compression techniques," in National Science Foundation Workshop on Nonlinear Model Predictive Control, Ascona, Switzerland, June 3-5.
19. Peddanarappagari, K. V. and Brandt-Pearce, M., 1998, Volterra series approach for optimizing fiber-optic communications system designs," Journal of Lightwave Technology 16(11), 2046-2055.
20. Prazenica, R., Lind, R., and Kurdila, A., 2003, "Uncertainty estimation from Volterra kernels for robust flutter analysis," Journal of Guidance, Control, and Dynamics 26(2), 331-339.
21. Reisenthel, P., 1999, "Prediction of unsteady aerodynamic forces via nonlinear kernel identification," in CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics, Williamsburg, VA.
22. Rugh, W. J., 1981, Nonlinear System Theory: The Volterra-Wiener Approach, Johns Hopkins University Press, Baltimore, MD.
23. Schetzen, M., 1980, The Volterra and Wiener Theories of Nonlinear Systems, Wiley, New York.
24. Silva, W., 1993, "Application of nonlinear systems theory to transonic unsteady aerodynamic responses," Journal of Aircraft 30(5), 660-668.
25. Silva, W. A., 1997, Discrete-Time Linear and Nonlinear Aerodynamic Impulse Responses for Efficient CFD Analyses, Ph.D. dissertation, The College of William & Mary, Williamsburg, VA.
26. Tan, L. and Jiang, J., 2001, "Adaptive Volterra filters for active noise control of nonlinear noise processes," IEEE Transactions on Signal Processing 49(8), 1667-1676.
27. Tsihrintzis, G. A. and Devaney, A. J., 2000, "A Volterra series approach to nonlinear traveltime tomography," IEEE Transactions on Geoscience and Remote Sensing 38(4), 1733-1742.
28. Wray, J. and Green, G., 1994, "Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network," Biological Cybernetics 71(3), 187-195.