Applying the Principal Component Analysis in the Problem of Analysis of the Specters of Free Oscillation

Abstract

This article addresses the main methods used for analysis, distribution, and classification of input data space. The main aspects of applying these methods are analyzed and determined. In this study it is found that the method of the principal components analysis (PCA) is the most suitable. Possible principal components analysis algorithms are described. A combination of these algorithms is used to distribute the input data in the analysis of signals and their spectra obtained by non-destructive testing after applying a free oscillations method. The article aims to study the possibility of reducing the vector of informative features after applying principal components analysis without losing the quality of recognition of the state of objects. The objects of study may be components of electric motors (shunt magnetic conductor), parts of aircraft made of composite materials and other structures that require analysis by non-destructive testing methods. Spectra taken during non-destructive testing by the method of free oscillations of samples of carbon fiber panels from defective and defect-free zones were studied. The analysis of three, five and ten harmonics was conducted and the maximum number of the principal components and the values of maximum dispersions of these components for the input values set of amplitudes were determined. The Mahalanobis distance was used to analyze the quality of the distribution of the input data space into classes (defect-free and defect zones of the sample). The quality of the separation of values from the damaged and undamaged zones of the sample into two classes was improved. Therefore, the use of principal component analysis, in this study, can increase the reliability of the recognition of the state of objects.