Progressive damage detection based on multi-scale wavelet finite element model: numerical study

Taking advantage of the unique multi-scale and localization features of wavelet finite element model (WFEM), this study proposes a novel progressive damage detection approach. Dynamic equations of beam-type WFEM are first derived using the second-generation Hermite multiwavelet as shape functions. Then the procedure of WFEM-based progressive damage detection is elaborated, in which sub-element damage can be gradually identified through the model updating process with an objective function that combines measured frequencies and mode shapes. The scales of wavelets can be adaptively enhanced or reduced during the progress according to actual damage scenarios. Hence, the proposed approach can effectively minimize the number of degrees of freedom (DOFs) in WFEM, as well as the number of unknown variables to be updated. Numerical examples of a simply supported beam and a single-story frame are simulated with different damage scenarios. The results demonstrated that the proposed multi-scale WFEM-based damage identification approach could progressively identify the location, extent and severity of damage. Compared with the traditional method, the proposed method involves fewer DOFs and updating parameters in structural models, and fewer sensors in modal tests, and thus would considerably improve the efficiency of damage identification.