On the Influence of Reference Mahalanobis Distance Space for Quality Classification of Complex Metal Parts Using Vibrations

Mahalanobis distance (MD) is a well-known metric in multivariate analysis to separate groups or populations. In the context of the Mahalanobis-Taguchi system (MTS), a set of normal observations are used to obtain their MD values and construct a reference Mahalanobis distance space, for which a suitable classification threshold can then be introduced to classify new observations as normal/abnormal. Aiming at enhancing the performance of feature screening and threshold determination in MTS, the authors have recently proposed an integrated Mahalanobis classification system (IMCS) algorithm with robust classification performance. However, the reference MD space considered in either MTS or IMCS is only based on normal samples. In this paper, an investigation on the influence of the reference MD space based on a set of (i) normal samples, (ii) abnormal samples, and (iii) both normal and abnormal samples for classification is performed. The potential of using an alternative MD space is evaluated for sorting complex metallic parts, i.e., good/bad structural quality, based on their broadband vibrational spectra. Results are discussed for a sparse and imbalanced experimental case study of complex-shaped metallic turbine blades with various damage types; a rich and balanced numerical case study of dogbone-cylinders is also considered.
Keywords: Mahalanobis–Taguchi system (MTS); integrated Mahalanobis classification system (IMCS); Mahalanobis distance space; feature selection; classification; binary particle swarm optimization; nondestructive testing; vibrations