On the Use of Principal Component Analysis for Parameter Identification and Damage Detection in Structures

In this lecture, an approach based on principal component analysis (PCA) is considered for three purposes, namely damage detection, structural health monitoring and identification of nonlinear parameters in structural dynamics. The key idea of PCA is to reduce a large number of measured data to a much smaller number of uncorrelated variables while retaining as much as possible of the variation in the original data.
The first problem to which PCA is applied here is the damage detection problem. When applied to vibration measurements, it can be shown that the basis of eigenvectors (called the proper orthogonal modes) span the same subspace as the mode-shape vectors of the monitored structure. Thus the damage detection problem may be solved using the concept of subspace angle between a reference subspace spanned by the eigenvectors of the initial (undamaged) structure and the subspace spanned by the eigenvectors of the current (possibly damaged) structure.
The second problem concerns structural health monitoring of civil engineering structures when environmental effects (e.g. the influence of the variation of the ambient temperature) have to be removed from the structural changes. In this case, PCA may be applied on identified modal features (e.g. the natural frequencies) to separate the changes due to environmental variations from the changes due to damage sources.
The third problem is related to the estimation of nonlinear parameters using model updating techniques. In this case, the most interesting property of PCA is that it minimizes the average squared distance between the original signal and its reduced linear representation. When applied to nonlinear problems, PCA gives the optimal approximating linear manifold in the configuration space represented by the data. The linear nature of the method is appealing because the theory of linear operators is still available. However, it should be borne in mind that it also exhibits its major limitation when the data lie on a nonlinear manifold.