Abstract Earthquake disaster records demonstrate that the influence of aftershocks (ASs) needs to be considered in structural seismic design and performance assessment, owing to the additional damage caused by them. To study the failure mechanism of a structure undergoing a sequence earthquake (i.e., mainshock–aftershock (MS–AS)), a clear understanding of the correlation between the intensity measures (IMs) of an MS–AS is important. However, the above correlation has not yet been systematically studied. Previously, some researchers have investigated the correlation between the individual IMs of an MS–AS separately by a Copula function based on an assumption that all the IMs of the MS (AS) are independent. However, the IMs are actually related, owing to their definition. Concurrently, deep learning (particularly the generation models) can be used to reveal the potential connections between data without any assumptions. Moreover, these models can present the conditional probability distribution of data by adding specific conditions. This study aims to build a conditional generative adversarial network (CGAN) model to simulate the IMs of an AS of an MS–AS, which can not only reflect the correlation between the corresponding IMs of the MS–AS but also that between the IMs used. The performance of this model is ascertained based on residual analysis, and the IM AS predictability is tested using real records. This study selects 972 MS–AS ground motions from the Next Generation Attenuation-West2 (NGA-West2) database, randomly dividing them into 80% and 20% and using as the training set and testing set, respectively. The results show that the CGAN model can predict the IMs of ASs with good accuracy. Moreover, the ground motion prediction equation (GMPE) by Abrahamson et al. (ASK14) is selected to compare with the CGAN model, and it is exhibited that the CGAN model matches the as-recorded IMs of ASs better that the former. All these results demonstrate that the proposed CGAN model is a promising and reliable approach for IM prediction of an AS.

中文翻译：

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用于模拟余震强度测量的条件生成对抗网络模型

摘要 地震灾害记录表明，余震会造成额外的破坏，因此在结构抗震设计和性能评估中需要考虑余震的影响。为了研究经历序列地震（即主震-余震 (MS-AS)）的结构的破坏机制，清楚地了解 MS-AS 的强度测量 (IM) 之间的相关性很重要。然而，上述相关性尚未得到系统研究。此前，一些研究人员基于 MS (AS) 的所有 IM 都是独立的假设，通过 Copula 函数分别研究了 MS-AS 的各个 IM 之间的相关性。然而，由于它们的定义，IM 实际上是相关的。同时，深度学习（尤其是生成模型）可用于在没有任何假设的情况下揭示数据之间的潜在联系。而且，这些模型可以通过添加特定条件来呈现数据的条件概率分布。本研究旨在建立条件生成对抗网络（CGAN）模型来模拟 MS-AS 的 AS 的 IM，该模型不仅可以反映 MS-AS 的相应 IM 之间的相关性，还可以反映所使用的 IM 之间的相关性。 . 该模型的性能是基于残差分析确定的，并且使用真实记录测试了 IM AS 的可预测性。本研究从 Next Generation Attenuation-West2 (NGA-West2) 数据库中选取 972 个 MS-AS 地震动，随机分为 80% 和 20%，分别作为训练集和测试集。结果表明，CGAN模型可以很好地预测AS的IM。此外，Abrahamson 等人的地面运动预测方程（GMPE）。(ASK14) 被选择与 CGAN 模型进行比较，表明 CGAN 模型比前者更好地匹配 AS 记录的 IM。所有这些结果表明，所提出的 CGAN 模型是一种有前途且可靠的 AS IM 预测方法。