Q-statistic and T2-statistic PCA-based measures for damage assessment in structures

This article explores the use of principal component analysis (PCA) and T-2 and Q-statistic measures to detect and distinguish damages in structures. For this study, two structures are used for experimental assessment: a steel sheet and a turbine blade of an aircraft. The analysis has been performed in two ways: (i) by exciting the structure with low-frequency vibrations using a shaker and using several piezoelectric (PZT) sensors attached on the surface, and (ii) by exciting at high-frequency vibrations using a single PZT as actuator and several PZTs as sensors. A known vibration signal is applied and the dynamical responses are analyzed. A PCA model is built using data from the undamaged structure as a reference base line. The defects in the turbine blade are simulated by attaching a mass on the surface at different positions. Instead, a progressive crack is produced to the steel sheet. Data from sets of experiments for undamaged and damaged scenarios are projected into the PCA model. The first two projections, and the Q-statistic and T-2-statistic indices are analyzed. Q-statistic indicates how well each sample conforms to the PCA model. It is a measure of the difference or residual between a sample and its projection into the principal components retained in the model. T-2-statistic index is a measure of the variation of each sample within the PCA model. Results of each scenario are presented and discussed demonstrating the feasibility and potential of using this formulation in structural health monitoring.