Multiclass feature selection using computational homology for Lamb wave–based damage characterization

We investigate a new approach for characterizing class separability based on topological measures for use with identifying flaw severity in plates. Multi-mode Lamb waves are propagated across a flat-bottom hole of varying depth. Lamb wave tomography reconstructions are first generated to locate and size the flaw at each depth. As the flaw depth increases, scattering and mode conversion effects dominate the raw time-domain signals, obscuring information about flaw severity. Pattern classification provides an alternate means for processing the ultrasonic waveforms to identify flaw severity. High-dimensional feature spaces are generated from the Lamb wave signals using the dynamic wavelet fingerprinting technique. In order to achieve high classification accuracy, an optimal feature space is required. An intelligent feature selection routine is explored here that identifies favorable class distributions in multidimensional feature spaces using computational homology theory. Betti numbers and formal classification accuracies are calculated for each feature space subset to establish a correlation between the topology of the class distribution and the corresponding classification accuracy.