Application of Principal Component Analysis for Crack Detection in Turbine Blades

Abstract

In this work, Principal Component Analysis (PCA) is implemented for detecting cracks in gas turbine blades. The simulated problem involves a factory that produces blades in series, where some pieces exhibit cracks as a result of the manufacturing process. Based on black-and-white images of the blades, considered as pixel matrices, the goal is to identify defective pieces. The objective of the work is to develop an automated system capable of detecting these anomalies using PCA. The methodology applied includes the graphical simulation of N blade images, converting eachimage into a column vector, and forming a data matrix of M x N. Then, the eigenvectors and eigenvalues of the covariance matrix are calculated, selecting the most significant principal components. Finally, the data is projected into a new, lower-dimensional space, and decision boundaries are established to identify defective blades. The implemented method proved effective in detecting blades with cracks, allowing their separation for repair or disposal.