Abstract Structural failures caused by a strong earthquake may induce a large number of casualties and huge socioeconomic losses. To design a structure that can withstand such earthquake events, it is essential to accurately estimate the nonlinear structural responses caused by strong ground motions. As a replacement of an onerous and complex nonlinear time history analysis, simple regression-based equations have been widely adopted in routine engineering practices. It is, however, noted that the response prediction is deterministic, which cannot quantify the variabilities stemming from the nonlinear behavior of the structural system, i.e. varying seismic demands given the same earthquake intensity value. In addition, it is well known that the accuracy of prediction based on the regression-based equations is limited. In order to quantify such uncertainties and improve the prediction accuracy, this paper proposes a probabilistic deep neural network model based on a Bayesian deep learning method. By introducing a loss function which is proportional to the negative log likelihood of the Gaussian distribution function, the mean and variance of the structural responses can be obtained. This assessment is important especially for earthquake engineering applications because of large randomness in the input ground motion details and their significant impact on the structural responses. Moreover, using the proposed probabilistic deep neural network model, one can estimate seismic fragilities of the structural system efficiently. Thorough numerical investigations are carried out to demonstrate the proposed method. The supporting source code and data are available for download at http://ERD2.snu.ac.kr .

中文翻译：

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使用深度学习方法对地震响应进行概率评估

摘要 强震引起的结构破坏可能造成大量人员伤亡和巨大的社会经济损失。为了设计能够承受此类地震事件的结构，必须准确估计由强地面运动引起的非线性结构响应。作为繁琐复杂的非线性时程分析的替代，基于简单回归的方程已广泛应用于常规工程实践中。然而，需要注意的是，响应预测是确定性的，它不能量化源自结构系统非线性行为的可变性，即在给定相同地震强度值的情况下变化的地震需求。此外，众所周知，基于回归方程的预测精度是有限的。为了量化此类不确定性并提高预测精度，本文提出了一种基于贝叶斯深度学习方法的概率深度神经网络模型。通过引入与高斯分布函数的负对数似然成正比的损失函数，可以获得结构响应的均值和方差。这种评估对于地震工程应用尤其重要，因为输入地震动细节具有很大的随机性及其对结构响应的重大影响。此外，使用所提出的概率深度神经网络模型，可以有效地估计结构系统的地震脆弱性。进行了彻底的数值研究以证明所提出的方法。