Estimators for Structural Damage Detection Using Principal Component Analysis

Structural damage detection is an important issue in conservation. In this research, principal component analysis (PCA) has been applied to the temporal variation of modal frequencies obtained from a dynamic test of a scaled steel structure subjected to different damages and different temperatures. PCA has been applied in order to reduce, as much as possible, the number of variables involved in the problem of structural damage detection. The aim of the PCA study is to determine the minimum number of principal components necessary to explain all the modal frequency variation. Three estimators have been studied: T2 (the square of the vector norm of the projection in the principal component plan), Q (the square of the norm of the residual vector), and the variance explained. In the study, the results related to the undamaged structure needed one principal component to explain the modal frequency variation. However, the high damage configurations need five principal components to explain the modal frequency. The T2 and Q estimators have been arranged in order of increasing damage for all the performed experimental tests. The results indicate that these estimators could be useful to detect damage and to distinguish among a range of intensities of structural damage.