Most system identification methods are based on a time or frequency domain analysis of data that were measured in dynamic tests. In this article, an algorithm for the identification of a finite element model's parameters is presented that utilizes wavelet coefficients of the measured data and their integrals or derivatives, respectively. How the wavelet coefficients of derivatives and integrals can be related to each other by connection coefficients is shown. These relations are then applied within the proposed parameter identification algorithm. The performance of the method is demonstrated by means of numerical and experimental investigations.
Al-Khalidy, A. , Noori, M. , Hou, Z. , Yamamoto, S. , Masuda, A. and Sone, A. (1997). Health monitoring systems of linear structures using wavelet analysis. In: Chang, F.-K. (ed.). Structural Health Monitoring – Current Status and Perspectives, Proceedings of the International Workshop on Structural Health Monitoring, Stanford University, Stanford, CA, USA , 18–20 September, Lancaster, Basel: Technomic, pp. 164–175.
2.
Alonso, R.J. , Noori, M. , Duval, L.D. , Masuda, A. and Hou, Z. (2001). Damage detection for a nonlinear SDOF system under deterministic and random load . In: Proceedings of the 8th International Conference on Structural Safety and Reliability (ICOSSAR 2001) – CD-ROM, Newport Beach, CA, USA, 17–21 June, Rotterdam: A.A. Balkema.
3.
Avitable, P. , O'Callahan, J. and Milani, J. (1989). Comparison of system characteristics using various model reduction techniques . In: Proceedings of the 7th International Modal Analysis Conference (IMAC-VII), Las Vegas, Nevada, USA: Society for Experimental Mechanics, February, pp. 1109–1115 .
4.
Beylkin, G. and Torresani, B. (1996). Implementation of operators via filter banks; Hardy wavelets and autocorrelation shell. In: PAM Report 185 – Applied and Computational Harmonic Analysis, Vol. 3, pp. 164–185.
5.
Boller, C., Staszewski, W., Chang, F.-K., Ihn, J.-B. and Speckmann, H. (2001). Smart systems for in-service crack monitoring of aircraft components. In: Seeger, T. and Klee, S. (eds), 25 Jahre Fachgebiet Werkstoffmechanik an der TU Darmstadt, Vorträge des Festkolloquiums am 28. 09. 2001, Veröffentlichungen für Stahlbau und Werkstoffmechanik der Technischen Universität Darmstadt, Heft 65, Darmstadt, Technische Universitat Darmstadt, pp. 184–194.
6.
Chui, C.K. (1992). An Introduction to Wavelets. Wavelet Analysis and its Applications, Boston, San Diego, New York, London, Sydney, Tokyo, Toronto: Academic Press .
7.
Daubechies, I. (1992). Ten Lectures on Wavelets, Philadelphia: Society for Industrial and Applied Mathematics (SIAM).
8.
Ewins, D.J. (2000). Modal Testing: Theory, Practice and Applications, Engineering Dynamics Series, 2nd edn, Baldock, Hertfordshire, England: Research Studies Press Ltd.
9.
Ewins, D.J. and Inman, D.J. (eds) (2001). Structural Dynamics 2000: Current Status and Future Directions. Engineering Dynamics Series. Baldock, Hertfordshire, England: Research Studies Press Ltd.
10.
Ghanem, R. and Romes, F. (2000). A wavelet-based approach for the identification of linear time-varying dynamical systems . Journal of Sound and Vibration, 234(4), 555–576 .
11.
Ghanem, R. and Romes, F. (2001). A wavelet-based approach for model and parameter identification of non-linear systems . International Journal of Non-Linear Mechanics, 36(5), 835–859 .
12.
Hans, S. , Ibraim, E. , Pernot, S. , Boutin, C. and Lamarque, C.-H. (2000). Damping identification in multi-degree-of-freedom systems via a wavelet-logarithmic decrement – part 2: study of a civil engineering building . Journal of Sound and Vibration, 235(3), 375–403 .
13.
Heylen, W. , Lammens, S. and Sas, P. (1997). Modal Analysis Theory and Testing, Katholieke Universiteit Leuven-Departement Werktuigkunde, Leuven, Belgium .
14.
Hou, Z. , Noori, M. , Amand, R.S. , Hu, J. , Al-Khalidy, A. , Baker, M. , Yamamoto, S. , Masuda, A. and Sone, A. (1999). Damage detection using wavelet approach and its application for on-line health monitoring. In: Kobori, T. , Inoue, Y. , Seto, K. , Iemura, H. and Nishitani, A. (eds), Proceedings of the Second World Conference on Structural Control, Vol. 3, pp. 2351–2358, Kyoto, Japan: John Wiley & Sons .
15.
Kaiser, G. (1994). A Friendly Guide to Wavelets. Boston, Basel, Berlin: Birkhauser .
16.
Kyprianou, A. and Staszewski, W.J. (1999). On the cross wavelet analysis of duffing oscillator . Journal of Sound and Vibration, 228(1), 199–210 .
17.
Lamarque, C.-H. , Pernot, S. and Cuer, A. (2000). Damping identification in multi-degree-of-freedom systems via a wavelet-logarithmic decrement – part 1: theory . Journal of Sound and Vibration, 235(3), 361–374 .
18.
Mallat, S.G. (1989). A theory for multiresolution signal decomposition: The wavelet representation . IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693 .
19.
Markwardt, K. (2002). Systemanalyse und Parameteridentifikation mit Hilfe der schnellen Wavelet-Transformation. unpublished.
20.
Natke, H.G. (1992). Einführung in Die Theorie und Praxis der Zeitreihenund Modalanalyse. 3rd edn, Viehweg, Braunschweig, Wiesbaden.
21.
O'Callahan, J. (1989). A procedure for an improved reduced system (IRS) model . In: Proceedings of the 7th International Modal Analysis Conference (IMACVII), Las Vegas, Nevada, USA: Society for Experimental Mechanics, pp. 17–21 .
22.
O'Callahan, J. , Avitable, P. and Riemer, R. (1989). System equivalent reduction expansion process (SEREP). In: Proceedings of the 7th International Modal Analysis Conference (IMAC-VII) , Las Vegas, Nevada, USA: Society for Experimental Mechanics, pp. 29–37 .
23.
Resnikoff, H.L. and Wells, R.O. (1998). Wavelet Analysis: The Scalable Structure of Information, New York: Springer-Verlag .
24.
Ruzzene, A. , Fasana, L. , Garibaldi, L. and Piombo, B. (1997). Natural frequencies and dampings identification using wavelet transform: application to real data . Mechanical Systems and Signal Processing, 11(2), 207–218 .
25.
Staszewski, W.J. (1998). Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform . Journal of Sound and Vibration, 214(4), 639–658 .
26.
Staszewski, W.J. (2000). Wavelets for Mechanical and Structural Damage Identification. Monograph Series: Studia i Materialy, No. 510/1469/2000. Gdansk: Polish Academy of Science Press .
27.
Staszewski, W.J. and Cooper, J.E. (1997). Flutter data analysis using the wavelet transform . In: Jezequel, L. (ed.), New Advances in Modal Synthesis of Large Structures – Proceedings of the International Conference MV2, Lyon, France, 5-6 October 1995, Rotterdam/Brookfield: A.A. Balkema, pp. 203–214 .
28.
Sun, Z. and Chang, C.C. (2002). A wavelet packet based method for structural damage assessment . In: Proceedings of the 3rd World Conference on Structural Control, 7–12 April, Como, Italy: Wiley.
29.
Zabel, V. (2003). Applications of Wavelet Analysis in System Identification. PhD diss., Faculty of Civil Engineering, Bauhaus-University Weimar, Weimar.
