On the reduction of required motions in the dynamic analysis using an optimization-based spectral matching

TL;DR

This paper introduces a spectral matching technique using unconstrained optimization and wavelet transform coefficients to effectively reduce the number of ground motions needed in dynamic analysis, maintaining accuracy.

Contribution

The study presents a novel spectral matching method employing wavelet coefficients and Levenberg-Marquardt optimization to significantly decrease required ground motions in seismic analysis.

Findings

Achieved over 80% reduction in required ground motions.

Improved spectral matching accuracy compared to conventional methods.

Matched signals preserve original shaking characteristics.

Abstract

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 case study model. In this regard, it has been found that we can reduce the number of required motions by more than 80% when matched motions are selected to be used as the seismic inputs for the dynamic analysis.