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Hierarchical Clustering of Materials With Defects Using Impact-Echo Testing

Signals obtained from impact-echo techniques can be used to detect and classify the defects in damaged materials. The defects change the wave propagation between the impact and the sensors producing particular spectrum elements, which define the feature vector. We propose a hierarchical clustering method that models the feature vector as a mixture of Gaussians (MoG) for every class and then merges different clusters using as a distance measure the symmetric Kullback–Leibler (KL) divergence. Since there is no closed-form solution to the KL divergence between MoGs, some approximations are introduced. We apply the hierarchical clustering algorithms to the signals obtained from real specimens made of aluminum alloy. The samples are classified into four classes according to the state: homogeneous (no defect), one hole, one crack, and multiple defects. We compare the performance of different approximations and discuss the dendrograms that are obtained. Similar kinds of defects are clustered first, and more importantly, the high-level hierarchy is able to distinguish between the defective and nondefective materials.