Abstract
New methodology of adaptive monitoring and evaluation of complicated dynamic data is introduced. The major objectives are monitoring and evaluation of both instantaneous and long-term attributes of complex dynamic behavior, such as of chaotic systems and real-world dynamical systems. In the sense of monitoring, the methodology introduces a novel approach to quantification and visualization of cognitively observed system behavior in a real time without further processing of these observations. In the sense of evaluation, the methodology opens new possibilities for consequent qualitative and quantitative processing of cognitively monitored system behavior. Techniques and enhancements are introduced to improve the stability of low-dimensional neural architectures and to improve their capability in approximating nonlinear dynamical systems that behave complex in high-dimensional state space. Low-dimensional dynamic quadratic neural units enhanced as forced dynamic oscillators are introduced to improve the approximation quality of higher dimensional systems. However, the introduced methodology can be universally used for adaptive evaluation of dynamic behavior variability also with other neural architectures and adaptive models, and it can be used for theoretical chaotic systems as well as for real-word dynamical systems. Simulation results on applications to deterministic, however, highly chaotic time series are shown to explain the new methodology and to demonstrate its capability in sensitive and instantaneous detections of changing behavior, and these detections serve for monitoring and evaluating the level of determinism (predictability) in complex signals. Results of this new methodology are shown also for real-world data, and its limitations are discussed.
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References
Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer, New York (1996)
Grassberger, P., Procaccia, I.: Characterisation of Strange Attractors. Physical Review Letters 65, 346 (1983)
Eckmann, J.-P., Kamphorst, O., Ruelle, D.: Recurrence Plots of Dynamical Systems. Europhysics Letters, 973–979 (1987)
Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence-Plot-Based Measures of Complexity and their Application to Heart-Rate-Variability Data. Physical Review E66, 66(2), 026702.1–026702.8 (2002)
John, D., Catherine, T.: MacArthur Research Network on Socioeconomic Status and Health (1997), http://www.macses.ucsf.edu/Research/Allostatic/notebook/heart.rate.html (retrieved 02/2008)
Zitek, P., Bila, J., Kuchar, P.: Blood Circularion Model Establishing Heart Rate Variability as Control Performance. In: Computational Intelligence for Modelling, Control &Automation, Vienna, Austria, pp. 305–310. IOS Press, Amsterdam (1999)
Bila, J., Zitek, P., Kuchar, P., Bukovsky, I.: Heart Rate Variability: Modelling and Discussion. In: Proceedings of International IAESTED Conference on Neural Networks, Pittsburgh, USA, pp. 54–59 (2000) ISBN 0-88986-286-9
Bila, J., Bukovsky, I., Oliviera, T., Martins, J.: Modeling of Influence of Autonomic Neural System to Heart Rate Variability. In: IASTED International Conference on Artificial Intelligence and Soft Computing ~Asc 2003~, Banff, Canada, pp. 345–350 (2003) ISSN: 1482-7913, ISBN: 0-88986-367-9
Vitkaj, J.: Analysis of Chaotic Signals by Means of Neural Networks. [PhD. Thesis] (in Czech), Faculty of Mechanical Engineering, Czech Technical University in Prague, Czech Republic (2001)
Bila, J., Ulicny, D.: Analysis of Chaotic Signals: Non-linear Methods versus Neural Networks. In: Proceedings of 3rd International Carpathian Control Conference, vol. 1, pp. 481–486. VSB-TUO, Ostrava (2002)
Gupta, M.M., Liang, J., Homma, N.: Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. IEEE Press and Wiley-Interscience, John Wiley & Sons, Inc., Chichester (2003)
Bukovsky, I., Redlapalli, S., Gupta, M.M.: Quadratic and Cubic Neural Units for Identification and Fast State Feedback Control of Unknown Non-Linear Dynamic Systems. In: Fourth International Symposium on Uncertainty Modeling and Analysis ISUMA 2003, pp. 330–334. IEEE Computer Society, Maryland (2003) ISBN 0-7695-1997-0
Hou, Z.-G., Song, K.-Y., Gupta, M.M., Tan, M.: Neural Units with Higher-Order Synaptic Operations for Robotic Image Processing Applications. Soft Computing - A Fusion of Foundations, Methodologies and Applications ISSN 1432-7643 (Print) 1433–7479 (Online) 11(3), 221–228 (2007)
Bukovsky, I.: Modeling of Complex Dynamical systems by Nonconventional Artificial Neural Architectures and Adaptive Approach to Evaluation of Chaotic Time Series, Ph.D. Thesis, Faculty of Mechanical Engineering, Czech Technical University in Prague (in English, defended September 7 (2007) supervisor Bila, J., supervisor-specialist Gupta, M. M, http://www.fs.cvut.cz/~bukovsky/ivo.htm )
Bukovsky, I., Hou, Z.-G., Bila, J., Gupta, M.M.: Foundation of Nonconventional Neural Units and their Classification. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI) 2(4), 29–43 (2008)
Bukovsky, I., Anderle, F., Smetana, L.: Quadratic Neural Unit for Adaptive Prediction of Transitions among Local Attractors of Lorenz System. In: IEEE International Conference on Automation and Logistics, Qingdao, China (2008), ISBN 978-1-4244-2503-7
Bukovsky, I., Bila, J.: Adaptive Evaluation of Complex Time Series using Nonconventional Neural Units. In: ICCI 2008, The 7th IEEE International Conference on Cognitive Informatics, California, USA (2008) ISBN 9781424425389
Cannas, B., Cincotti, S.: Hyperchaotic Behaviour of two Bi-directionally Coupled Chua’s Circuits. International Journal of Circuit Theory and Applications 30, 625–637 (2002)
PhysioBank: MIT-BIH Arrhythmia Database, http://www.physionet.org/physiobank/database/mitdb/ (retrieved in April 2001)
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Bukovsky, I., Bila, J. (2010). Adaptive Evaluation of Complex Dynamical Systems Using Low-Dimensional Neural Architectures. In: Wang, Y., Zhang, D., Kinsner, W. (eds) Advances in Cognitive Informatics and Cognitive Computing. Studies in Computational Intelligence, vol 323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16083-7_3
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DOI: https://doi.org/10.1007/978-3-642-16083-7_3
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