Principal Components Analysis (PCA) is a method to extract the principal components (or modes) of response from recorded or computed response data, of systems exhibiting linear and/or nonlinear response. For linear systems, the PCA mode shapes coincide with the elastic mode shapes, if the nodal mass is uniformly distributed. For nonuniform mass distributions, the PCA modes are related to the elastic modes. The PCA technique is particularly valuable when applied to systems responding nonlinearly, because it identifies the "predominant mode" of response and the degree to which the response is in this mode. This paper illustrates the use of the PCA technique for estimating floor and interstory drifts for a 12-story moment-resistant steel frame responding to earthquake ground motions. Linear and nonlinear responses are considered, and the observed mode shapes and the accuracy of drift estimates are discussed. The interaction of modal amplitudes in time is considered in detail. The peak roof drift and interstory drifts are expressed as linear combinations of the PCA modes, and are represented graphically, together with the observed interaction response. A technique is described to determine peak values of these quantities by maximizing the drift functions relative to the observed modal interactions.
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