Identification of time-varying hysteretic structures using wavelet multiresolution analysis

In this paper, a wavelet multiresolution technique is proposed to identify time-varying properties of hysteretic structures. It is well known that arbitrary transient functions can be effectively and accurately approximated using wavelet multiresolution expansions due to wavelet's good time–frequency localization property. By decomposing the time-varying parameters with wavelet multiresolution expansion, a time-varying parametric identification problem can be transformed into a time-invariant non-parametric one. The identification in the time-invariant wavelet multiresolution domain can be achieved by choosing a wavelet basis function and performing a suitable parameter estimation technique. Since wavelet representation of arbitrary signal uses only a small number of terms, the orthogonal forward regression algorithm can be adopted for significant term selection and parameter estimation. Single and multiple degrees of freedom Bouc–Wen hysteretic structures with gradual and abrupt varying properties are used to illustrate the proposed approach. Results show that the wavelet multiresolution technique can identify and track the time-varying hysteretic parameters quite accurately. The effect of measurement noise is also studied. It is found that the presence of noise would affect more on the damping ratios and the Bouc–Wen parameters but less on the equivalent stiffness coefficients.