The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is inherently ill-posed. Conventional approaches address this problem through iterative optimization, typically representing signals as sums of exponentially decayed sinusoids, but these methods are computationally expensive and constrained by predefined basis functions. We propose a conditional variational autoencoder (CVAE) that learns a data-driven inverse mapping from SRS to acceleration time series. Once trained, the model generates signals consistent with prescribed target spectra without requiring iterative optimization. Experiments demonstrate improved spectral fidelity relative to classical techniques, strong generalization to unseen spectra, and inference speeds three to six orders of magnitude faster. These results establish deep generative modeling as a scalable and efficient approach for inverse SRS reconstruction.

翻译：冲击响应谱（SRS）被广泛用于表征单自由度（SDOF）系统对瞬态加速度的响应。由于从加速度时程到SRS的映射是非线性且多对一的，从目标谱重构时域信号本质上是一个不适定问题。传统方法通过迭代优化来解决此问题，通常将信号表示为指数衰减正弦波的和，但这些方法计算成本高昂，且受限于预定义的基函数。我们提出了一种条件变分自编码器（CVAE），它能够学习从SRS到加速度时间序列的数据驱动逆映射。一旦训练完成，该模型无需迭代优化即可生成与指定目标谱一致的信号。实验表明，相较于经典技术，该方法在谱保真度方面有所提升，对未见谱具有良好的泛化能力，且推理速度提高了三到六个数量级。这些结果确立了深度生成模型作为一种可扩展且高效的逆SRS重构方法。