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

Abstract

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, the weighting 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 considerably more robust, matching the target spectrum more faithfully. This is achieved while qualitatively maintaining the original signal's nonstationary statistics, such as general envelope, time location of large pulses, and variation of frequency content with time.

Significance of non-stationary characteristics of ground-motion on structural damage: shaking table study

“…In order to separate out the stationary and non-stationary characteristics of groundmotions, all of the ground-motions are matched to the mean response spectrum of FF ground-motions in FEMA P695 ( 2009) using the Reweighted Volterra Series Algorithm (RVSA) (Alexander et al 2014), which has been successfully used in a numerical exploration study by Kashani et al (2017a). In this study, we are using the same spectrally matched ground-motions that were used in the numerical study (Kashani et al 2017a).…”

“…More recently, Kashani et al (2017a) developed a novel numerical approach to quantify the impact of ground-motion types (near/far field, with/without pulses time-series), caused by the non-stationary content (time-varying parameters that are not captured by power spectral content alone), on the nonlinear dynamic response of RC bridge piers, including the effect of material cyclic degradation. They used the new algorithm (known as RVSA) developed by Alexander et al (2014) to generate a set of artificial spectrally equivalent ground-motions. They used the suggested far-field (FF), near-field without pulse (NFWP) and near-field pulse-like (NFPL) ground-motions in FEMA P695 (2009).…”

Dynamic interaction between adjacent buildings through nonlinear soil during earthquakes

“…The Reweighted Volterra Series Algorithm (RVSA) proposed by Alexander et al [43] is employed. This spectral matching process is stable and robust because it converges to any reasonable response spectrum for any suitable seed time-series and keeps the non-stationary characteristics (e.g.…”

Influence of non-stationary content of ground-motions on nonlinear dynamic response of RC bridge piers

“…With this in mind, the new algorithm (known as RVSA) developed by Alexander et al (2014) is employed to generate a set of artificial ground motions of equivalent spectral response. The groundmotion seeds are selected from the suggested far-field (FF), near-field without pulse (NFWP) and near-field pulse like (NFPL) ground motions in FEMA P695 (2009).…”