Time-varying damage detection in beam structures using variational mode decomposition and continuous wavelet transform

Civil engineering structures in operation are likely to suffer damage. During the service life, structural damage evolves gradually from minor to severe. However, most current studies focus on damage localization and quantification of damage severity, and hence little attention has been paid to the detection of time-varying damage. This paper aims to propose a new approach for tracking the damage evolution of beam structures. In this approach, the wavelet threshold method is used at first to denoise the response signal. After that, the variational mode decomposition (VMD) is introduced to decompose the denoised response signal into several mono-components adaptively. A proposed index of wavelet total energy change (WTEC) is then applied to the new decomposed signals to localize damages of beam structures. On a basis of this, a time-varying damage index called wavelet energy change ratio (WECR) is established via the continuous wavelet transform and time window techniques and then applied to the response at the damaged position for tracking damage evolution. The proposed method is verified via a numerical example of a simply supported beam (its length and area of cross section are 5 m and 0.04 m2, respectively) with a sudden and a linear stiffness reduction under 1940 El Centro ground acceleration record. In addition, an experiment on a 10-meters-long steel bridge with abrupt stiffness reduction under a moving load is investigated to demonstrate the effectiveness and accuracy of the proposed time-varying damage detection method. The results show that the index of WTEC is able to localize damages of beam structures effectively whatever they are a single damage position or multiple damage positions. Moreover, the damage evolution can be tracked by the proposed index of WECR accurately even though random noises and end effects pose a great impact on the time-varying damage detection results.