Damage identification using 2-D discrete wavelet transform on extended operational mode shapes

In this paper a new scheme of damage detection and localisation is presented by implementing frequency response functions (FRFs) of damaged structure only. First damage sensitive shape signals are generated by taking the second order derivatives of the operational mode shapes at each frequency coordinate and then the anti-symmetric extension of each shape signal at the beginning and at the end of the signal is created to avoid boundary distortion phenomenon. In order to highlight the damage influence on shape signals, the shape signals are normalised with respect to the maximum value to adjust the amplitude difference between shape signals at different frequencies. It is illustrated that normalisation of shape signals significantly improves the damage localisation results. After normalising the shape signals, a two-dimensional (2-D) map of all shape signals is created and then is analysed by employing 2-D discrete wavelet transform (DWT). By performing 2-D DWT, three sets of horizontal, vertical and diagonal detailed wavelet coefficients will be obtained. It is demonstrated that amongst these three sets, horizontal detail coefficients are the most sensitive ones to any perturbation in the shape signals due to damage occurrence and, thus, are utilised to localise damage in this study.