Mode Decomposition and Synthesis of Temporal Characteristics of Earthquake Motions using Karhunen-Loéve Expansion

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  • KL展開による地震動の経時特性のモード分解と合成

Abstract

<p>In the previous study, a 98-dimensional feature vector was proposed to represent temporal characteristics of a waveform of ground motion acceleration on the basis of its Husid plot. In this study, a method for mode decomposition and synthesis of the temporal characteristics was proposed using Karhunen-Loéve (KL) expansion. First, eigenvalues and eigenvectors are solved for variance-covariance matrix defined for the 98-dimensional feature vectors calculated using a number of accelerograms. Next, the feature vectors are transformed to principal components using the orthogonal matrix composed of the eigenvectors. Furthermore, inverse transformation is applied to several most principal components constituting the subspace in order to reduce the dimension of the original feature vectors with allowable loss of information. The kernel density estimation method is used to validate the envelope recomposed by mode synthesis. Illustrative examples for acceleration records observed in the 2011 Off the Pacific Coast of Tohoku Earthquake, Japan are shown. It is shown that three to six dimensional representation of the temporal characteristics can be generally achieved by using the orthonormal basis extracted by the KL expansion. On the other hand, principal components of higher order are required to describe the temporal characteristics of waveforms whose amplitude levels contain much fluctuations.</p>

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