Principal Least Squares Canonical Correlation Analysis for damage quantification in aeronautic composite structures

Abstract

The Structural Health Monitoring (SHM) process is classically decomposed into four steps: damage detection, localization, classification and quantification. Here the focus is put on aeronautic composite structures and specifically on the damage quantification step. For SHM purpose, such structures are equipped with piezoelectric elements that can be used both as sensors and actuators. To quantify a detected damage, measurements are first performed in a reference state. Then, during the life cycle of the structure several measurements at unknown states are performed. Several damage indexes are then extracted from the difference between the reference and unknown states. This damage indexes matrix is the basis of any algorithms dedicated to the quantification step but still contains many more dimensions that just a quantification of damage size. The question raised here is the efficiency of dimension reduction algorithms in the damage indexes space for quantification purposes. Performances of simple direct regression (SDR), principal component analysis (PCA), partial least squares (PLS), canonical correlation analysis (CCA) and autoencoders (AE) are investigated for this purpose. It is shown that PCA, PLS and CCA are all able to discover a low-dimensional space within the damage indexes space that is linearly related with the physical damage size, and that average prediction errors of the order of ≃ 1% can be achieved by projecting data through that low-dimensional space.