Limited samples wavelet network and its application for damage detection composites

Abstract

A new data processing method is proposed for the damage detection of anisotropic composite materials. The wavelet transform and its phase space property are discussed to illustrate how the signal features are represented in the time-frequency plane. The terms in the expansion of the wavelet series that have the same time-frequency property as the original signal are then obtained by comparing the time- frequency space of the signal with the phase space of the wavelet transform. For wavelet neural networks, the training process can be very slow because the number of terms in the wavelet series is often too large for a reasonable search. Here we apply the Gram-Schmidt orthogonal- ization to remove the redundant wavelets in the series using the characteristics of sampled data. Moreover, the values of the features corresponding to different damage types are obtained by linear equations. Experiments on the damage detection of composites with various size cracks and delamination are conducted to demonstrate the feasibility of the proposed method. They show that the reconstructed curves obtained by the proposed approach can well approximate the original sampled curves and that the features corresponding to different damage types are identified.