Abstract
This paper introduces a wavelet-based linearization method to estimate the single-degree-of-freedom (SDOF) nonlinear system response based on the traditional equivalent linearization technique. The mechanism by which the signal is decomposed and reconstructed using the wavelet transform is investigated. Since the wavelet analysis can capture temporal variations in the time and frequency content, a nonlinear system can be approximated as a time dependent linear system by combining the wavelet analysis technique with well-known traditional equivalent linearization method. Two nonlinear systems, bilinear hysteretic system and Duffing oscillator system, are used as examples to verify the effectiveness of the proposed wavelet-based linearization method.
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References
Mason, A.B.J.: Some Observations on the Random Response of Linear and Nonlinear Dynamical Systems. Ph. D. Dissertation, Calif. Inst. of Tech. Pasadena (1997)
Isidori, A.: Nonlinear Control Systems- An Introduction. Springer, New York (1989)
Grizzle, J.W., Kokotovic, P.V.: Feedback linearization of Sampled Data Systems. IEEE Trans. Auto. Control 33, 857–859 (1988)
Hedrick, J.K., Girard, A.: Feedback Linearization Theory and Application. Springer, New York (2005)
Kryov, N.N., Bogoliubov, N.N.: Introduction to Nonlinear Mechanics. Princeton University, Princeton (1947)
Booton Jr., R.C.: Nonlinear Control Systems with Random Inputs. IRE Trans. Circuit Theory CT-I (1), 9–17 (1954)
Agrawal, O.D.: Application of Wavelets in Modeling Stochastic Dynamic Systems. Journal of Vibration and Acoustics 120, 763–769 (1998)
Iwan, W.D., Mason Jr., A.B.: Equivalent Linearization for Systems Subjected to Non-stationary Random Excitation. International Journal of Nonlinear Mechanics 15, 71–82 (1980)
Chui, C.K.: Wavelet Analysis and Its Applications. An Introduction to Wavelets, vol. 1. Academic Press, Inc., New York (1992)
Chui, C.K.: Wavelet: A Tutorial in Theory and Applications. Academic Press, New York (1992)
Grochenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser (2001)
Grossmann, A., Morlet, J.: Decomposition of Hardy Functions into Square Integral Wavelets of Constant Shape. SIAM Journal of Mathematical Analysis 15, 723–736 (1984)
Grossmann, A., Kronland-Martinet, R., Morlet, J.: Reading and Understanding Continuous Wavelet Transform. In: Combes, J.M., Grossmann, A., Tchamitchian, P. (eds.) Wavelet Time-Frequency Methods and Phase Space, pp. 2–20. Springer, Berlin (1989)
Kobayash, M.: Wavelets and their applications. SIAM, Philadelphia (1998)
Walker, J.: A Primer on Wavelets and their Scientific Applications. Chapman & Hall CRC, New York (1999)
Dobson, S., Noori, M., Hou, Z., Dimentberg, M.: Direct Implementation of Stochastic Linearization for SDOF Systems with General Hysteresis. Structure Engineering and Mechanics 6(5), 473–484 (1998)
Asano, K., Iwan, W.D.: An Alternative Approach to the Random Response of Bilinear Hysteretic Systems. Earthquake Engineering and Structural Dynamics 12, 229–236 (1998)
Xie, W.F., Fu, J., Yao, H., Su, C.-Y.: Neural Network Based Adaptive Control of Piezoelectric Actuator with Unknown Hysteresis. International Journal of Adaptive Control and Signal Processing 23, 30–54 (2009)
Basu, B., Gupta, V.K.: Seismic Response of SDOF Systems by Wavelet Modeling of Non-stationary Processes. Journal of Engineering Mechanics (ASCE) 124(10), 1142–1150 (1998)
Newland, D.E.: An Introduction to Random Vibrations, Spectral & Wavelet Analysis. Longman Scientific & Technical, New York (1993)
Roberts, J.B., Spanos, P.D.: Random Vibration and Statistical Linearization, Mineola, New York (1990)
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Ma, XM., Xie, WF., Keshmiri, M., Mohebbi, A. (2012). Wavelet-Based Linearization for Single-Degree-Of-Freedom Nonlinear Systems. In: Su, CY., Rakheja, S., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2012. Lecture Notes in Computer Science(), vol 7506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33509-9_10
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DOI: https://doi.org/10.1007/978-3-642-33509-9_10
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