Characterization of dynamic response using Principal Components Analysis

Principal Components Analysis (PCA) provides a simple approach to visualize the complicated dynamic response of a multi-degree-of-freedom system in terms of its principal modal responses. PCA is a technique used in statistics for the analysis of multivariate data. PCA was first developed by Pearson and was later independently developed by Hotelling. To illustrate the use of PCA, the eight-story moment-resistant frame was subjected to the Corralitos record of the 1989 Loma Prieta Earthquake. The chapter investigates similarities between PCA mode shapes and the elastic mode shapes and quantities derived from these shapes as a function of response intensity and structural system type. PCA is valuable for understanding higher mode interactions, the relevance of first-mode approximations of various response quantities, and for identifying important behavior during dynamic response, such as the development of weak story mechanisms.