Development of practical downsampling methods for nonlinear time history analysis of complex structures

Abstract

One of the main problems of nonlinear time history analysis is its high computational effort, especially in structures with large number of structural components, high-rise buildings and complex structural systems. The ground motions recorded in recent years also include more recorded points than in the past, which has also increased the required volume of calculations. In this paper, three downsampling methods for reducing calculation costs of nonlinear time history analysis are presented and their applicability is investigated through practical examples of complex structures. These methods include the discrete wavelet transform, the time step correction, and the wavelet time step correction which is introduced in this paper. The efficiency of these downsampling methods is investigated for near-fault and far-fault earthquake records, as well as for records on different soil types. A comprehensive study is performed on five sets of ground motions consisting of 20 records. Each record is filtered up to three stages using one half, one quarter, and one eighth of the number of the main record points. First the linear and nonlinear response spectra based on the original records and the approximate waves are investigated. Subsequently, to evaluate the performance of the methods on more complex structural systems, two three-dimensional structures of 6-story and 15-story are analyzed. The 6-story structure is equipped with viscous dampers, while the 15-story structure has seismic isolators. The results indicate that the wavelet time step correction method has better performance in most cases, compared to the other two methods. It is shown that careful consideration is needed when dealing with earthquake records with high frequency contents. In such situations, one filtering step for the discrete wavelet transform method and two filtering steps for the other two methods are recommended. Also, in practical applications, it is advisable to choose earthquake records exhibiting the least error based on the results of SDOF systems analyses. Employing this technique can significantly cut down computational effort (up to 90%), while maintaining an average error ranging from 1% to 2% for the wavelet time step correction method.