Abstract
A novel non linear signal prediction method is presented using non linear signal analysis and deterministic chaos techniques in combination with Radial Basis Functions (RBF) Neural Networks for diode resonator chaotic circuits, used in industrial processes, as well as for Magnetic Resonance Spectroscopy (MRS) processes. The Time series analysis is performed by the method proposed by Grasberger and Procaccia, involving estimation of the correlation and minimum embedding dimension as well as of the corresponding Kolmogorov entropy. These parameters are used to construct the first stage of a one step / multistep predictor while an RBF Artificial Neural Network (ANN) is involved in the second stage to enhance prediction results. The novelty of the proposed two stage predictor lies on that the RBF ANN is employed as a second order predictor, that is, as an error predictor of the non-linear signal analysis stage application. This novel two stage predictor is evaluated through an extensive experimental study for both resonator circuits for industrial processes as well as for MRS signals in a preliminary stage of analysis. Different types of Neural Networks are compared as well.
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References
Lonngren, K.E.: Notes to accompany a student laboratory experiment on chaos. IEEE Transactions on Education 34(1) (February 1991)
Matsumato, T., Chua, L., Tanaka, S.: Simplest Chaotic Nonautonomous Circuit. Phys. Rev. A 30, 1155–1157 (1984)
Azzouz, A., Hasler, M.: Orbits of the R-L-Diode Circuit. IEEE Transaction on Circuits and Systems 37, 1330–1339 (1990)
Aissi, C.: Introducing chaotic circuits in an undergraduate electronic course. In: Proceedings of the 2002 ASEE Gulf-Southwest Annual Conference, The University of Louisiana at La-fayette, March 20-22, American Society for Engineering Education (2002); Copyright © 2002
de Moraes, R.M., Anlage, S.M.: Phys. Rev. E. 68, 26201 (2003)
Hanias, M.P., Giannaris, G., Spyridakis, A., Rigas, A.: Time series Analysis in chaotic di-ode resonator circuit. Chaos Solitons & fractals 27(#2), 569–573 (2006)
Grassberger, P., Procaccia, I.: Phys. Rev Lett. 50, 346–349 (1983)
Grassberger, P., Procaccia, I.: Physica D 9, 189 (1983)
Hanias, M.P., Karras, D.A.: On efficient multistep non-linear time series prediction in chaotic diode resonator circuits by optimizing the combination of non-linear time series analysis and neural networks. Engineering Applications of Artificial Intelligence 22(1), 32–39 (2009)
Mozdy, E., Newell, T.C., Alsing, P.M., Kovanis, V., Gavrielides, A.: Synchroniza-tion and control in a unidirectionally coupled array of chaotic diode resonators. Physical Review E 51(6), 5371–5376 (1995)
Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. Springer, New York (1996)
Takens, F.: Lecture Notes in Mathematics, vol. 898 (1981)
Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (1997)
Aasen, T., Kugiumtzis, D., Nordahl, S.H.G.: Computers and Biomedical Research 30, 95-116 (1997)
Fraser, A.M., Swinney, H.L.: Phys. Rev. A 33, 1134 (1986)
Fraser, A.M.: IEEE Transaction of Information Theory 35, 245 (1989)
Kononov, E.: Virtual Recurrence Analysis, Version 4.9 (2006), eugenek@ix.net.com.com
Haykin, S.: Neural Networks, a comprehensive foundation, 2nd edn. Prentice Hall, Englewood Cliffs (1999)
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Karras, D.A., Hanias, M.P. (2010). Improved Non Linear Time Series Forecasting Using Non Linear Analysis Techniques and RBF Neural Networks for MRS Signals and Chaotic Diode Resonator Circuits. In: Kim, Th., Yau, S.S., Gervasi, O., Kang, BH., Stoica, A., Ślęzak, D. (eds) Grid and Distributed Computing, Control and Automation. GDC CA 2010 2010. Communications in Computer and Information Science, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17625-8_25
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DOI: https://doi.org/10.1007/978-3-642-17625-8_25
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