The ability of an early detection of possible damage in a structure especially when subjected to severe external loadings
is a very important research topic. Damage in a structure usually comes with nonlinear and time-varying characteristics,
such as hysteresis, that lead to time-varying structural parameters. Identification of time-varying structural parameters is
necessary for assessing the safety of these damaged structures. A time-varying system identification technique using
wavelet multi-resolution analysis is proposed in this paper. Wavelet is well known for its ability to approximate and
represent arbitrary temporal functions. By expressing the time-varying parameters in a hysteretic structure using wavelet
multi-resolution models, the problem of identification of these time-varying parameters is transformed to a time-invariant
problem that depends on solving constant wavelet coefficients. An orthogonal forward regression algorithm is
then adopted to prune insignificant wavelet coefficients while estimating those significant ones. Examples of single- and
multi-degree-of-freedom hysteretic structures with different time-varying properties are given to demonstrate the
applicability and accuracy of the proposed approach.
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