On the reduction of the number of required motions in the dynamic analysis using a refined spectral matching

This study aims to show the efficiency of a proposed spectral matching technique for the reduction of required ground motions in the dynamic time history analysis. In this non-stationary spectral matching approach, unconstrained optimization is employed to adjust the signal to match a target spectrum. Adjustment factors of discrete wavelet transform (DWT) coefficients associated with the signals are then considered as decision variables and the Levenberg-Marquardt algorithm is employed to find the optimum values of DWT coefficients. This matching algorithm turns out to be quite effective in the spectral matching objective, where matching at multiple damping ratios can be readily achieved. First, the efficiency of the spectral matching procedure is investigated in a case study earthquake record and then compared with two conventional spectral matching methods. Results show considerable improvement in the matching accuracy which is accompanied by minimal changes in shaking characteristics of the original signal. In addition, it is shown that earthquake records matched with the proposed method can noticeably reduce the essential number of ground motions that are normally required for the dynamic analysis of a concrete dam as well as a shear wall system being considered here as the case study models. In this regard, it has been found that the number of required motions can be reduced by more than 80% when matched motions are selected to be used as the seismic inputs for the dynamic analysis.