Application of PCA-SVD Validation Metric to Develop Calibrated and Validated Structural Dynamic Models

Abstract

Calibrated/validated models that can predict the dynamic response of a structure accurately need to be developed to avoid expensive testing. The quantification of margin and uncertainty using validation metric(s) provides the basis for calibrating/validating a model with respect to characterizing system response. The principle component analysis—singular value decomposition (PCA-SVD) validation metric uses SVD to quantify the margin and uncertainty. This method involves decomposing the spatial information into its singular values and vectors at each temporal point. The set of largest singular values of one data-set can be plotted against the other, which ideally should result in a straight line with unit slope and zero variance. The PCA-SVD validation metric is relatively easy to implement. It gives a clear indication of both the margin and the uncertainty by utilizing the dominant singular values. It also gives a clear indication of spatial correlation by utilizing the singular vectors associated with the dominant singular values. In this paper, an application of the PCA-SVD validation metric to develop calibrated/validated models of a rectangular steel plate structure is presented.