Keywords: system identification, Haar wavelets, stiffness, damping.

In this paper, a technique for identifying the parameters of a structural system are proposed by using wavelet analysis. Wavelet analysis is a tool in the time frequency analysis of signals [1]. Wavelets are mathematical functions that decompose data into different frequency components, allowing each component to then be studied at a resolution suitable for its scale. Since wavelet analysis of data provides more information about the signals, this tool may be more effectively used for identification of dynamical system by using input and output signals [2,3,4].

The proposed formulations have been applied to linear single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. The formulation is based on the successive solution of linear simulations equations in the wavelet domain. The Haar discrete wavelet transform (DWT) has been used in this analysis.

The presented formulation scores over the other available ones as this can estimate both the stiffness and the damping with reasonable accuracy and is simple. For the purpose of illustration, the formulations presented here have been applied to a linear viscously damped SDOF and a two-bay, two-storey structures considered as a realistic example of an MDOF system. In the absence of any experimental data, numerical response data have been computed for a given input. The estimates of stiffness and damping match reasonably well with those used to compute the response data.

It has been concluded from the present studies that there is an optimal frequency parameter corresponding to a particular frequency band for which a smooth system parameter may be obtained. Considering higher or lower frequency bands may lead to too spiky fluctuations of parameters or a lack of data for identification, respectively. The formulation presented here may be further extended for the identification of non-linear SDOF and MDOF systems with suitable modifications and for identification with a reduced number of response states.

1

I. Daubechies, "Ten lectures on wavelets", Siam, 1992.

2

B. Basu, "Wavelet analysis for identification of stiffness degradation", Proceedings of the 7th International Conference on Maintenance and Renewal of Permanent Way; Power and Signalling; Structures and Earthworks, London, 2004.

3

B. Basu, "Identification of stiffness degradation in structures using wavelet analysis", Journal of Building and Constructional Materials, (in press), 2005. doi:10.1016/j.conbuildmat.2005.02.018

4

A. Chakraborty, B. Basu, "Identification of fundamental mode and mode shape of a bridge using continuous wavelet transform", Proceedings of the SECED Young Engineers Conference, Bath, 2005.

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