Dynamic Systems; Nonlinearity; Nonlinear System Identification; Expert Systems
Abstract :
[en] The identification of nonlinear dynamic systems is increasingly becoming a necessary part of vibration testing and there is significant research effort devoted to it. However, as the current methodologies are still not suitable for the identification of general nonlinear systems the subject is very rarely introduced to undergraduate students. In this paper, recent progress in developing an expert approach to nonlinear system identification is used in order to demonstrate the subject within the context of an undergraduate course or as an introductory tool for postgraduate students. The demonstration is based around a software package of an Expert System designed to apply systematically a wide range of identification approaches to the system under investigation. It is shown that the software can be used to demonstrate the need for nonlinear system identification, the complexity of the procedure, the possibility of failure and the good chances of success when enough physical information about the system is available.
Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Intéractions fluide structure et aérodynamique expérimentale
Vio, Gareth Arthur; University of Liverpool > Department of Engineering
Language :
English
Title :
Demonstrating the identification of nonlinear vibrating systems to undergraduate students
Publication date :
2007
Journal title :
International Journal of Mechanical Engineering Education
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Bibliography
S. S. Rao, Mechanical Vibrations, 4th edition (Pearson Prentice Hall, International Edition, 2004).
S. Chen and S. A. Billings, 'Representations of non-linear systems: the NARMAX model', International Journal of Control, 49(3) (1989), 1013-1032. (Pubitemid 20610988)
M. Simon and G. R. Tomlinson, 'Use of the Hilbert transform in modal analysis of linear and nonlinear structures', Journal of Sound and Vibration, 96(4) (1984), 421-436. (Pubitemid 15454919)
G. Palm and B. Popel, 'Volterra representation and wiener-like identification of nonlinear systems: scope and limitations', Quarterly review of Biophysics, 18 (1985), 135-164.
S. F. Masri and T. K. Caughey, 'A nonparametric identification technique for nonlinear dynamic problems', Journal of Applied Mechanics, 46 (1979), 433-447.
G. Dimitriadis, G. A. Vio and D. Shi, 'Development of an expert system for the identification of nonlinear vibrating systems', International Conference on Recent Advances in Structural Dynamics, Southampton, UK, July 2006.
G. Dimitriadis, G. A. Vio and J. E. Cooper, 'Identification of non-linear dynamic systems using an expert approach', 47th AIAA Structures, Structural Dynamics and Materials Conference, Rhode Island, USA, April 2006.
G. Dimitriadis, G. A. Vio and D. Shi, 'An expert system for the identification of nonlinear dynamical systems', International Conference on Intelligent Computing, ICIC 2006, Kunming, China, August 2006.
G. Dimitriadis, G. A. Vio and D. Shi, 'An expert system for the identification of nonlinear dynamical systems', In D. S. Huang, K. Li and G. W. Erwin (eds), Intelligent Computing, Vol. 4113 of Lecture Notes in Computer Science (Springer-Verlag, Berlin/Heidelberg, 2006), pp. 1263-1268. (Pubitemid 44532552)
L. Ljung, System Identification: Theory for the User (Prentice Hall, Englewood Cliffs, NJ, 1987).
R. Grimshaw, Nonlinear Ordinary Differential Equations (Blackwell Scientific, Oxford, 1990).
D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems, 3rd edition (Oxford University Press, Oxford, 1999).
K. S. Mohammad, K. Worden and G. R. Tomlinson, 'Direct parameter estimation for linear and nonlinear structures', Journal of Sound and Vibration, 152 (1991), 471-499.
S. F. Masri, H. Sassi and T. K. Caughey, 'Nonparametric identification of nearly arbitrary nonlinear systems', Journal of Applied Mechanics, 49 (1982).
G. Dimitriadis, 'Experimental validation of the constant level method for identification of nonlinear multi degree of freedom systems', Journal of Sound and Vibration, 258(5) (2002), 829-845. (Pubitemid 41100809)
P. A. Atkins, J. R. Wright and K. Worden, 'An extension of force appropriation to the identification of non-linear multi-degree of freedom systems', Journal of Sound and Vibration, 237(1) (2000), 23-43.
D. E. Adams and R. J. Allemang, 'A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback', Mechanical Systems and Signal Processing, 14 (2000), 637-656.
C. M. Richards and R. Singh, 'Identification of multi-degree-of-freedom non-linear systems under random excitations by the "reverse path," spectral method', Journal of Sound and Vibration, 213 (1998), 673-708.
D. M. Storer and G. R. Tomlinson, 'Recent developments in the measurement and interpretation of higher order transfer functions from non-linear structures', Mechanical Systems and Signal Processing, 7 (1993), 173-189.
V. Lenaerts, G. Kerschen and J. C. Golinval, 'ECL benchmark: application of the proper orthogonal decomposition', Mechanical Systems and Signal Processing, 17(1) (2003), 237-242.
K. Worden and G. R. Tomlinson, Nonlinear Vibrations (Sheffield University Press, Sheffield, 2000).
S. Chen, S. A. Billings and W. Luo, 'Orthogonal least squares methods and their applications to non-linear system identification', International Journal of Control, 50(5) (1989), 1873-1896. (Pubitemid 20636409)
M. F. Platten, J. R. Wright, K. Worden, J. E. Cooper and G. Dimitriadis, 'Non-linear identification using a genetic algorithm approach for model selection'. In Proceedings of the 23rd International Modal Analysis Conference, Orlando, Florida, USA, February 2005.
C. M. Fonseca and P. J. Fleming, 'Nonlinear system identification with multiobjective genetic algorithms', in Proceedings of the 13th World Congress of IFAC, San Francisco, California, USA, 1996.
K. Rodriguez-Vazquez, C. M. Fonseca and P. J. Fleming, 'Multiobjective genetic programming: a nonlinear system identification application', in J. R. Koza (ed.), Late Breaking Papers at the 1997 Genetic Programming Conference, Stanford University, CA, USA, 1997, pp. 207-212.
G. Dimitriadis and G. A. Vio, 'Nonlinearity characterization for nonlinear dynamic system identi-fication using an expert approach', in Proceedings of the 29th International Conference on Noise and Vibration Engineering, Leuven, Belgium, September 2006.
J. B. Allen and L. R. Rabiner, 'A unified approach to short-time Fourier analysis and synthesis', Proc. IEEE, 65(11) (1977), 1558-1564.
N. E. King and K. Worden, 'A rational polynomial technique for calculating Hilbert transforms', in Proceedings of the 6th International Conference on Recent Advances in Structural Dynamics, Southampton, UK, 1997, pp. 1056-1065.
G. Dimitriadis and J. E. Cooper, 'A method for identification of non-linear multi-degree-of-freedom systems', Proceedings Journal of the Institute of Mechanical Engineers, Part G, 212 (1998), 287-298.
L. Fox and I. Parker, Chebyshev Polynomials in Numerical Analysis (Oxford University Press, Oxford, 1968).
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