Damage assessment in composite plates using fractional wavelet transform of modal shapes with optimized selection of spatial wavelets

• Two-dimensional B-spline wavelets of fractional order were applied for the damage identification in composite plates.
• Heuristic optimization methods were used to tune the values of wavelets' parameters.
• Different types of single and multiple damages were analyzed for the first five modal shapes of the plates.
• In statistical sense, the best results of wavelets optimization were obtained using evolutionary algorithms.
• Proposed technique allows identifying the damage with high effectiveness.

Damage assessment is one of the crucial topics in the operation of structural elements made of polymers and polymeric composites. From the wide range of diagnostic methods and techniques the vibration-based damage evaluation seems to be effective, useful for application in industrial conditions and the low-cost. In order to improve the sensitivity of such class of methods the advanced signal processing techniques should be applied.` One of such techniques is the wavelet transform, which ensures the high sensitivity to the singularities in the measured vibration signals. The paper deals with a method for damage detection and localization in composite plates using the fractional discrete wavelet transform applied to the displacements of the modal shapes. The optimized selection of the parameters of spatial wavelets makes possible to improve the sensitivity of a proposed method. The presented studies cover the discussion on the various types of heuristic optimization algorithms that can be used for searching the best values of parameters of the fractional wavelet transform. The problem of selection of the most effective optimization algorithm, which allows to find the most suitable parameters of wavelets for the structural diagnostics of composite plates, is also considered. The method was tested on the data obtained from numerical experiments with various types of simulated single and multiple damages. Case studies were also conducted experimentally using non-destructive and non-invasive measurements of the displacements of modal shapes. The main advantages, difficulties and limitations of the presented method were discussed.