International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.13, No.2, Apr. 2021

Geometrical Framework Application Directions in Identification Systems. Review

Full Text (PDF, 1122KB), PP.1-20

Views:1   Downloads:0


Nikolay Karabutov

Index Terms

Framework;nonlinear dynamic system;phase portrait;structural identification;nonlinearity;structural identifiability;synchronizability;lag;Lyapunov exponent


The approaches review of the framework application in identification problems is fulfilled. It is showed that this concept can have different interpretations of identification problems. In particular, the framework is understood as a frame, structure, system, platform, concept, and basis. Two directions of this concept application are allocated: 1) the framework integrating the number of methods, approaches or procedures; b) the mapping describing in the generalized view processes and properties in a system. We give the review of approaches that are the basis of the second direction. They are based on the analysis of virtual geometric structures. These mappings (frameworks) differ in the theory of chaos, accidents, and the qualitative theory of dynamic systems. Introduced mappings (frameworks) are not set a priori, and they are determined based of the experimental data processing. The main directions analysis of geometrical frameworks application is fulfilled in structural identification problems of systems. The review includes following directions: i) structural identification of nonlinear systems; ii) an estimation of Lyapunov exponents; iii) structural identifiability of nonlinear systems; iv) the system structure choice with lag variables; v) system attractor reconstruction.

Cite This Paper

Nikolay Karabutov, "Geometrical Framework Application Directions in Identification Systems. Review", International Journal of Intelligent Systems and Applications(IJISA), Vol.13, No.2, pp.1-20, 2021. DOI: 10.5815/ijisa.2021.02.01


[1]B. Saha, K. Goebel, S. Poll, and J. Christopherson, “Prognostics methods for battery health monitoring using a Bayesian framework,” IEEE Trans. Instrum. Meas, vol. 58, no. 2, pp. 291–296, 2009. DOI: 10.1109/TIM.2008.2005965.

[2]G. Pillonetto, F. Dinuzzo, T. Chen, G. De Nicolao and L. Ljung, “Kernel methods in system identification, machine learning and function estimation: A survey,” Automatica, vol. 50, IS. 3, pp. 657-682, 2014. DOI.: 10.1016/j.automatica.2014.01.001

[3]R. Toth, B. M. Sanandaij, K. Poolla, T. L. Vincent, “Compressive system identification in the linear time-invariant framework,” 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA, December 12-15, 2011, pp. 783-790, 2012. DOI:10.1109/CDC.2011.6160383.

[4]R. Pintelon, and J. Schoukens, System Identification. A Frequency Domain Approach. Second Edition. Hoboken, New Jersey. Published by John Wiley & Sons, Inc. 2012. DOI: 10.1002/9781118287422.

[5]A. L. Varna, A. Swaminathan, M. Wu, “A Decision Theoretic Framework for Analyzing Binary Hash-based Content Identifi-cation,” DRM '08 Proceedings of the 8th ACM workshop on Digital rights management, pp. 67-76, 2008. DOI: 10.1145/1456520.1456532.

[6]F. Lauer, G. Bloch, R. Vidal, “A continuous optimization framework for hybrid system identification,” Automatica, vol. 47, is. 3, pp. 608-613, 2011. DOI : 10.1016/j.automatica.2011.01.020

[7]A. Iqbal, S. Aftab, I. Ullah, M.A. Saeed, and A. Husen, “ A classification framework to detect DoS attacks,” International Journal of Computer Network and Information Security, vol. 11, no. 9, pp. 40-47, 2019. DOI: 10.5815 / ijcnis.2019.09.05.

[8]H.M. Abdallah, A. Taha , M.M. Selim, “Cloud-based framework for efficient storage of unstructured patient health records,” International Journal of Computer Network and Information Security, vol. 11, no. 6, pp. 10-21, 2019. DOI: 10.5815/ijcnis.2019.06.02.

[9]L. Chen, K. S. Narendra, “Identification and Control of a Nonlinear Discrete-Time System Based on its Linearization: A Unified Framework,” IEEE transactions on neural networks, vol. 15, no. 3, pp. 663-673, 2004. DOI: 10.1109/TNN.2004.826206.

[10]T. Kurtoglu, I. Y. Tumer, “A Graph-Based Fault Identification and Propagation Framework for Functional Design of Complex Systems,” Journal of Mechanical Design, vol. 130, pp. 051401-8, 2008. DOI: 10.1007/978-94-017-9112-0_14.

[11]P.N. Papadopoulos, T. Guo, Member, J.V. Milanović, “Probabilistic Framework for Online Identification of Dynamic Behavior of Power Systems with Renewable Generation” IEEE Transactions on Power Systems, vol. 33, is. 1, pp. 45-54, 2017. DOI: 10.1109/TPWRS.2017.2688446.

[12]D. Roettgen, M. S. Allen, D. Kammer, and R. L. Mayes, “Substructuring of a Nonlinear Beam Using a Modal Iwan Framework, Part I: Nonlinear Modal Model Identification,” Dynamics of Coupled Structures, vol. 4, pp 165-178, 2017. DOI: 10.1007/978-3-319-54930-9_15.

[13]J.A. Carino, M. Delgado-Prieto, J.A. Iglesias, A. Sanchis, etc., “Fault Detection and Identification Methodology Under an In-cremental Learning Framework Applied to Industrial Machinery,” IEEE Access, 2018. DOI: 10.1109/ACCESS.2018.2868430.

[14]C.Y. Teh, Y. W. Kerk, K. M. Tay, and C. P. Lim, “On modelling of data-driven monotone zero-order TSK fuzzy inference systems using a system identification framework,” IEEE Transactions on Fuzzy Systems, 2018. DOI: 10.1109/TFUZZ.2018.2851258.

[15]S. Nagarajaiah, “Sparse and low-rank methods in structural system identification and monitoring,” X International Conference on Structural Dynamics (EURODYN 2017), Procedia Engineering, vol. 199, pp. 62–69, 2017. DOI: 10.1016/j.proeng.2017.09.153.

[16]S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos. Springer Science & Business Media, 2003. DOI: 10.1007/b97481.

[17]L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, and L.O. Chua, Methods of qualitative theory in nonlinear dynamics. Part II. World Scientific, 2001.

[18]A. Michel, K. Wang, B. Hu. Qualitative theory of dynamical systems. CRC Press, 2001. DOI.: 10.1201/9780203908297.

[19]Y.V. Pershin, and V.A. Slipko, Dynamical attractors of memristors and their networks. arXiv: 1808.07947, 2018.DOI: 10.1209/0295-5075/125/20002.

[20]J. Lü, S. Zhang, “Controlling Chen’s chaotic attractor using backstepping design based on parameters identification,” Chaos, Solitons & Fractals, vol. 32, is. 4, pp. 148–156, 2007. DOI.  10.1016/J.CHAOS.2005.11.045.

[21]C. Li, F. Min, “Multiple coexisting attractors of the serial–parallel memristor-based chaotic system and its adaptive generalized synchronization,” Nonlinear Dynamics, pp. 1-22, 2018. DOI: 10.1142/S0218126618500573.

[22]N. Karabutov, “Structural Methods of Design Identification Systems,” In Nonlinearity: Problems, Solutions and Applications. Volume 1. Ed. Ludmila Uvarova, Alexey B. Nadykto, Anatolii V. Latyshev. Nova Science Publishers Inc, pp. 233-274, 2017.

[23]N. Karabutov, Frameworks in identification problems: Design and analysis. Moscow: URSS/Lenand, 2018.

[24]N. Karabutov, “Structural methods of estimation Lyapunov exponents linear dynamic system,” International Journal of Intelligent Systems and Applications, vol. 7, no. 10, pp. 1-11, 2015. DOI: 10.5815/ijisa.2015.10.01.

[25]N. Karabutov, “About structural identifiability of nonlinear dynamic systems under uncertainty,” Global Journal of Science Frontier Research: (A) Physics and Space Science, vol. 18, is. 11, pp.  51-61, 2018. 

[26]F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, Theory of Lyapunov exponents and its application to problems of stability. Moscow: Nauka, 1966.

[27]N. Karabutov, “About Lyapunov exponents identification for systems with periodic coefficients,” Intelligent Systems and Ap-plications, vol. 10, no. 11, pp. 1-10, 2018. DOI: 10.5815/ijisa.2018.11.01.

[28]N.A. Bodunov, “Introduction to the theory of local parametrical identifiability,” Differential equations and management processes, no. 2, 2012.

[29]M.P. Saccomani, “Structural vs Practical identiability in system biology,” International Work-Conference on Bio informatics and Biomedical Engineering. IWBBIO 2013. Proceedings. Granada, 18-20 March, pp. 305-313, 2013. 

[30]O.-T. Chis, J.R. Banga, E. Balsa-Canto, “Structural identifiability of systems biology models: a critical comparison of methods,” PLOS ONE, vol. 6, is. 4, pp. 1-16, 2011. DOI: 10.1371/journal.pone.0027755

[31]J.D. Stigter, and R.L.M. Peeters, “On a geometric approach to the structural identifiability problem and its application in a water quality case study,” Proceedings of the European Control Conference 2007 Kos, Greece, July 2-5, pp. 3450-3456, 2007.

[32]Reference book on automatic control theory. Ed. A. A. Krasovsky. Moscow: Nauka, 1987.

[33]F. Takens, “Detecting strange attractors in turbulence,” Dynamical systems and turbulence. Lecture notes in mathematics / Eds. D.A. Rand, L.-S. Young. Berlin: Springer-Verlag, vol. 898, pp. 366-381, 1980. DOI: 10.1007/BFb0091924.

[34]A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano, “Determining Lyapunov exponents from a time series,” Physica 16D, no. 16, pp. 285–301, 1985. DOI: 10.1016/0167-2789(85)90011-9.

[35]M.T. Rosenstein, J.J. Collins, C.J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets Source,” Physica D, vol. 65, is. 1-2, pp. 117–134, 1993. 

[36]V.S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, L. Schimansky-Geier. Nonlinear dynamics of chaotic and sto-chastic systems. nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments. Second Edition. Springer, 2007. DOI: 10.1007/978-3-540-38168-6

[37]G.G. Malinetskiy, A.B. Potapov, Modern problems of nonlinear dynamics. Moscow: Editorial URSS, 2000.

[38] L.M. Pecora, L. Moniz, J. Nichols, T.L. Carroll, “A Unified approach to attractor reconstruction. Chaos,” An Interdisciplinary Journal of Nonlinear Science, vol. 17, 013110. 2007. DOI: 10.1007/978-1-4020-9143-8_1.

[39]E. Bradley, H. Kantz, Nonlinear time-series analysis revisited. arXiv:1503.07493v1, 2015. DOI: 10.1063/1.4917289.

[40]W. Liebert, K. Pawelzik, H.G. Schuster, “Optimal embedding of chaotic attractors from topological considerations,” Europhys, lett. 14, pp. 521, 1991. DOI:10.1209/0295-5075/14/6/004

[41]T. Buzug, G. Pflster, “Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behaviour of strange attractors,” Phys. Rev. A. 45, pp. 7073, 1992.

[42]A. Deshpande, Q. Chen, Y. Wang, Y.-C.G Lai, and Y. Do, “Effect of smoothing on robust chaos,” Physical review E 82, 026209 2010. DOI: 10.1103/PhysRevE.82.026209.

[43]L.A. Aguirre and C. Letellier, “Modeling nonlinear dynamics and chaos: A Review,” Mathematical Problems in Engineering, vol. 2009, no. 35 p. 2009. DOI: 10.1155/2009/238960.

[44]J. Johnston, Econometric methods. 2nd edition. New York: McGraw-Hill Book Company, 1972.

[45]B. Armstrong, “Models for the relationship between ambient temperature and daily mortality,” Epidemiology, vol. 17, no. 6, pp. 624-631, 2006. DOI: 10.1097/01.ede.0000239732.50999.8f.

[46]E. Malinvaud, Statistical methods in econometrics. 3d ed. Amsterdam: North-Holland Publishing Co. 1980.

[47]P.J. Dhrymes, Distributed Lags: Problems of Estimation and Formulation. San Francisco: Holden-Day, 1971.

[48]R. Solow, “On a family of lag distributions,” Econometrica, vol. 28, pp. 393-406, 1960.

[49]N.N. Karabutov, “Structural identification of static systems with distributed lags,” International Journal of Control Science and Engineering, vol. 2, no. 6, pp. 136-142, 2012. DOI: 10.5923/j.control.20120206.01.

[50]L. Achho, “Hysteresis Modeling and Synchronization of a Class of RC-OTA Hysteretic-Jounce-Chaotic Oscillators,” Universal journal of applied mathematics, vol. 1(2), pp. 82-85, 2013. DOI: 10.13189/ujam.2013.010207.

[51]H. Gao, L. Jézéquel, E. Cabrol, B. Vitry, “Characterization of a Bouc-Wen model-based damper model for automobile comfort simulation,” HAL Id: hal-02188563, 2019.

[52]W. G. Alghabbana, M. R. J. Qureshi, “Improved framework for appropriate components selection,” International Journal En-gineering and Manufacturing, vol. 1, pp. 18-24, 2014. DOI: 10.5815 / I IM 2014.01.03.