MODAL DECOMPOSITION AND SYNTHESIS OF RESPONSE SPECTRA USING KARHUNEN-LOÉVE TRANSFORM AND DISCRETE COSINE TRANSFORM

Abstract

 A method for mode decomposition and synthesis of velocity response spectra has been proposed using Karhunen-Loéve transform (KLT) . Eigenvalues and eigenvectors are solved for correlation matrix of the 101-dimensional feature vectors representing velocity response spectra calculated using a number of accelerograms. Next, the feature vectors are transformed to principal components using the orthogonal matrix composed of the eigenvectors. Several principal components are adopted to recompose the original response spectra without much loss of information. Illustrative examples using acceleration records observed in the 2011 Off the Pacific Coast of Tohoku Earthquake, Japan are shown. Modal synthesis using approximately three to twelve principal modes has been found to effective to recompose original response spectrum for damping ratio 5%. Less number of modes are required for damping ration 20%. It has been found that the orthogonal bases derived from KLT of all the ground motion records from nine major earthquakes can be modeled by simple cosine functions which can be universally used for discrete cosine transform (DCT).