Dimensionality reduction of ultrasonic array data for characterization of inclined defects based on supervised locality preserving projection.

Ultrasonic arrays are increasingly used for inspection of the structural components in non-destructive testing (NDT) applications. The ultrasonic array data can be processed to form high-resolution images for detection and localization of defects. Alternatively, the scattering matrix can be extracted from the full matrix of array data and used for defect characterization if the defect size is small (i.e., comparable to an ultrasonic wavelength). This paper studies the dimensionality reduction problem of scattering matrix databases. In particular, we focus on accurate characterization of inclined defects for which previous approaches based on principal component analysis (PCA) yielded high characterization uncertainty. We propose a supervised approach based on locality preserving projection (LPP) and introduce noise constraints to the objective function of LPP. In simulation, the proposed approach is shown to produce a well-resolved defect manifold for 45°ellipses. Characterization results obtained using the simulated noisy measurements of four 60°ellipses confirm the performance improvement of LPP over PCA. In experiments, three 60°ellipses and two surface-breaking cracks have been characterized. On average, the root-mean-square (RMS) sizing error given by the LPP approach is 39.0% lower compared to PCA for the ellipses and 11.1% lower for the surface-breaking cracks.