Tracking time-varying properties of hysteretic structure by wavelet multi-resolution analysis

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 timeinvariant 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