A multi-scale pseudo-force model in wavelet domain for identification of damage in structural components

Damage identification using wavelet-transform (WT)-processed vibration signals has been practiced over the years. In most studies, WT was used as an effective signal analysis tool to filter out noise and bring damage-incurred singularities into prominence. In spite of its proven effectiveness, such a processing is often carried out without theoretical footstones sustained by solid mechanics models, which are able to link characteristics of WT with features of damage. In the present work, a multi-scale pseudo-force model over wavelet domain was developed for vibration-based damage identification. By canvassing damage-caused local perturbance to dynamic equilibrium characteristics of a structural component, the underlying hypostasis of the model has explicit physical implication, addressing features of damage (e.g., a slot or a fine crack) and enabling a sophisticated solution to multi-scale modeling and identification of damage. In the model, WT was used as a multi-scale differential operator to acquire higher-order derivatives of equation of motion for characterizing damage of tiny dimension. The multi-scale nature brings additional benefits to enhance robustness of the detection under noisy measurement conditions. Without loss of generality, an EulerBernoulli beam component (EBC) was considered to facilitate understanding of the principle of the model. As proof-of-concept validation, a fine crack in an EBC was quantified using the model through numerical simulation and experiment. Satisfactory results have demonstrated the effectiveness of the model in evaluating fine damage and enhancing tolerance of the detection to measurement noise.