Orthogonal Signal Decomposition Coupled with Bayes and Puzzy Discriminant Classifiers for Ultrasonic Flaw Detection

The performance of an ultrasonic flaw detection system is valued by its success in differentiating flaw echoes from those scattered by microstructures (e.g. grain scattering or clutter). In order to successfully detect and classify the target echoes from background noise, an effective feature extracting method and a robust decision process are required. In this study, we present a comparative evaluation of three orthogonal signal decomposition methods: constant B (bandwidth); constant E (energy); and constant Q (i.e., ratio of bandwidth to center frequency), spanning the entire frequency band of the signal. An efficient method of implementing orthogonal decomposition using the Haar filter is presented in this paper. Orthogonal decomposition of the signal offers feature vectors suitable for classification and signal evaluation. The differences observed in the probability density function of clutter and the flaw echoes resulting from orthogonal decomposition are utilized to design the Bayes and fuzzy discriminant classifiers for flaw detection. These classifiers show good sensitivities in detecting flaw echoes in the presence of strong clutter where the signal-to-noise ratio is about zero dB. In this paper we present a mathematical derivation for these techniques and experimental results to demonstrate their application in ultrasonic nondestructive testing.