PCA Based Measures: Q-Statistic and T2-Statistic for Assessing Damages in Structures

This paper explores the use of Principal Component Analysis (PCA) based on T-2 and Q statistic formulation to detect and distinguish damages in structures. The structure used for this study is a blade of a turbine of an aircraft. This blade is excited using a shaker in one side and seven PZT's sensors are attached on the surface. A known signal is applied and the responses are analyzed. A PCA model is built using data from the undamaged structure. A mass is attached on the surface in four different positions. Data from the damaged structure tests are projected on the model. The principal components, Q-Residual and T-2-Hotelling's distances are analyzed. Q-residual 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-Hotelling's distance, is a measure of the variation in each sample within the PCA model.