Online identification of linear time-varying stiffness of structural systems by wavelet analysis

An online identification of variation of stiffness in structural systems has been presented in this study. The proposed technique is based on wavelet analysis. The time-frequency characteristics of the wavelets have been used in the formulation of online identification. The basis function used is a modified version of the Littlewood-Paley wavelet. The bases generated from this wavelet at different scales have the advantage of non-overlapping frequency bands which has been utilized in the frequency tracking algorithm. Further, an algorithm for detection of variation in modes shapes in time-varying linear multi-degree-of-freedom (MDOF) systems has been developed. Several types of changes in stiffness, such as a sudden jump, a ramp (gradual) change, or a sudden change with subsequent restoration of stiffness have been considered as illustrative examples in case of single-degree-of-freedom (SDOF) and MDOF systems. It has been found that the proposed technique for wavelet based online identification is efficient in tracking different types of cases considered and has potential for application in adaptive control.