Generation of Tri-Directional Spectra-Compatible Time Histories Coupling the Influence Matrix Method and Gram–Schmidt Orthogonalization

Abstract

This study presents a new approach for obtaining a set of tri-directional time histories compatible with target design spectra by modifying real recorded earthquake ground motions. The influence matrix method (IMM) based on eigenfunction expansion is improved for typical design response spectra with different shapes and employed in order to achieve accurate matching with the target design spectra. By applying the Gram–Schmidt orthogonalization in each iteration of the IMM procedure, the correlation coefficient between any two components can be guaranteed to be strictly zero. Hence, the generated three components in the orthogonal directions are statistically independent. The generated time histories satisfy the requirements of current codes and standards. Two examples are presented to illustrate the procedure and the superiority of the proposed method, with the maximum relative error between the generated time histories and target design spectra being less than 0.2% in [0.6, 100] Hz, and the code requirements being satisfied strictly.