Damage detection in time-varying beam structures based on wavelet analysis

Existing system identification methods are mostly dealing with local changes that are time-invariant. However, the process of local change in a real structure caused by damage is mostly time-varying, which can be modeled with a change in the physical parameters such as structural stiffness and damping. An identification algorithm for a time-varying beam system is proposed based on wavelet analysis. The response signal is firstly decomposed using the Daubechies wavelet scaling function. The governing differential equation of a structure is then transformed into a set of linear equations based on the orthogonality property of the scaling functions in a wavelet space. Finally, the proposed algorithm is illustrated with studies on a cantilever beam structure. The precision of identification with respect to different wavelet scales is investigated and discussed. Numerical results demonstrate that the proposed method can identify smoothly, periodically and abruptly time-varying physical parameters with excellent accuracy.