A greedy algorithm for wavelet-based time domain response spectrum matching

Abstract

U.S. Nuclear Regulatory Commission NUREG-0800, “Standard Review Plan,” Section 3.7.1, “Seismic Design Parameters,” Revision 4, describes acceptance criteria for seismic design time histories, including response spectrum matching and checking power spectral density functions. This paper is a focused introduction of a new algorithm developed for response spectrum matching, named as the Greedy Wavelet Method (GWM), which shows substantial advances in convergence characteristics over the RspMatch09 program. RspMatch09 is widely used by the nuclear industry and represents the results of multiple iterations of enhancement by international researchers since the basic method was first introduced in 1978. GWM modifies a seed acceleration time history by adding just one wavelet in each iteration, in contrast to RspMathc09 that adds a set of weighted wavelets, with the weights determined by solving an optimization problem in each iteration. GWM includes procedures to address two specific issues leading to convergence difficulties in response spectrum matching: The shape of the wavelets can be numerically distorted at high frequencies and the wavelet lead time previously recommended is not sufficiently long. These newly developed procedures made GWM unconditionally stable. For the benchmark problem, GWM was demonstrated to save 99.5% of the wavelets required by RspMatch09. We also implemented in GWM several advanced, interactive tools to perform baseline corrections and other related tasks. Examples provided in this paper are for demonstration purposes only.