Obtaining Spectrum Matching Time Series Using a Reweighted Volterra Series Algorithm (RVSA)

In this paper, we introduce a novel algorithm for morphing any accelerogram into a spectrum matching one. First, the seed time series is re-expressed as a discrete Volterra series. The first-order Volterra kernel is estimated by a multilevel wavelet decomposition using the stationary wavelet transform. Second, the higher-order Volterra kernels are estimated using a complete multinomial mixing of the first-order kernel functions. Finally, theweighting of every term in this Volterra series is optimally adapted using a Levenberg–Marquardt algorithm such that the modified time series matches any target response spectrum. Comparisons are made using the SeismoMatch algorithm, and this reweighted Volterra series algorithm is demonstrated to be considerablymore robust,matching the target spectrummore faithfully. This is achievedwhile qualitatively maintaining the original signal’s nonstationary statistics, such as general envelope, time location of large pulses, and variation of frequency content with time.