Principal Component and Independent Component Regression for Predicting the Responses of Nonlinear Base Isolated Structures
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Peak base displacement is one of the most important quantities in the design of base-isolated buildings. During the preliminary stages of design, a nonlinear time-history analysis is often not possible or too expensive, and hence reliable measures for predicting peak base displacement must be obtained through other means. In this study, regression models are developed in order to predict the peak displacement using a series of intensity measures (IMs) as model inputs. This thesis utilizes two methods for this purpose, Principal Component Regression (PCR) and a newly proposed method known as Sorted-Input Independent Component Regression (SI-ICR). In the framework of PCR and SI-ICR, the problem that exists due to correlation of IMs is addressed, which allows the transformation of correlated components into uncorrelated ones. This step is followed by dimensionality reduction of the components that do not contribute significantly to the explained variance of the original data set. A regression model using only one IM, peak ground velocity (PGV), is also developed to compare the advantages of using multiple IMs as opposed to one. Prediction results are presented and compared to simulation results for building models with increasing degree of complexity, starting with a two degree of freedom uniaxial case to a twelve degree of freedom biaxial model. It is concluded that PCR and SI-ICR significantly outperform the PGV model with PCR slightly outperforming SI-ICR. PCR is regarded as a more suitable and practical regression method for predicting the responses of nonlinear base isolated structures.