Inverse Synthesis of Shock Time Series from Shock Response Spectra Using Ensembles of Conditional Variational Autoencoders

Abstract

The shock response spectrum (SRS) characterizes the peak responses of single-degree-of-freedom systems to transient acceleration. Because the mapping from an acceleration time series (waveform) to its SRS is many-to-one, inverse synthesis seeks candidate waveforms consistent with a prescribed spectrum. We extend an earlier conditional variational autoencoder (CVAE) framework with a recurrent decoder that predicts multiscale wavelet coefficients and reconstructs waveforms through an inverse discrete wavelet transform. Individual models exhibit limited variability under latent sampling, motivating an ensemble of independently trained models spanning different mother wavelets and decomposition levels. Each member produces a separate candidate waveform for the same target SRS. Evaluation on four held-out benchmark datasets shows lower mean and median spectral errors for the illustrated wavelet model than for the earlier direct time-domain CVAE and a sum-of-decayed-sinusoids (SDS) baseline. A conditioning study examines frequency-grid and encoding choices. Comparisons with published inverse-SRS methods demonstrate superior performance across four holdout benchmark datasets (two operational shock datasets, one earthquake dataset, and one synthetic shock dataset) and competitive performance on synthetic targets reported by Brake. Single-model inference requires approximately 0.1-0.6 ms per waveform during batched inference compared with 5-8 s for SDS, excluding offline training. This low inference cost enables rapid generation of distinct SRS-compatible candidate waveforms across the ensemble, although their physical suitability requires assessment beyond spectral agreement.