A novel method termed rLSTM-AE is developed for the low-dimensional latent space identification of the stochastic dynamic systems with more than 1000 input random variables and the active learning-based dynamic reliability analysis. First, the long short-term memory network considers both the time-variant stochastic excitation and the time-invariant random variables is developed (rLSTM), which adopts the time-series excitation as the pertinent input feature and makes it available for the metamodeling of the high-dimensional stochastic dynamic systems. To circumvent the insufficient accuracy of deep neural networks for reliability analysis results from the limited observations, autoencoder (AE) is incorporated with the rLSTM (rLSTM-AE) and utilized to decompose the approximate extreme value space found by rLSTM onto a low-dimensional latent space. The dimension of the latent space is adaptively determined by a Gaussian process regression reconstruction error, which enables the Gaussian process regression with the similar accuracy as rLSTM regarding the extreme responses prediction. The proposed rLSTM-AE conducts the low-dimensional features extraction from the perspective of the output space decomposition and considers the time-dependent property of the dynamic systems. Finally, the detected latent variables can be combined with the active learning-based Gaussian process regression for the high-dimensional dynamic reliability analysis. One single-degree-of-freedom system and a reinforced concrete frame structure subjected to the stochastic excitation are investigated to validate the performance of the proposed method.

中文翻译：

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用于降维的 rLSTM-AE 及其在基于主动学习的动态可靠性分析中的应用

开发了一种称为 rLSTM-AE 的新方法，用于具有超过 1000 个输入随机变量的随机动态系统的低维潜在空间识别和基于主动学习的动态可靠性分析。首先，开发了同时考虑时变随机激励和时不变随机变量的长短期记忆网络（rLSTM），它采用时间序列激励作为相关输入特征，并使其可用于元建模高维随机动力系统。为了避免深度神经网络在有限观测值下的可靠性分析结果精度不足的问题，自动编码器（AE）与rLSTM（rLSTM-AE）相结合，用于将rLSTM找到的近似极值空间分解为低维潜在空间。空间。潜在空间的维数由高斯过程回归重建误差自适应确定，这使得高斯过程回归在极端响应预测方面具有与 rLSTM 相似的精度。所提出的rLSTM-AE从输出空间分解的角度进行低维特征提取，并考虑动态系统的时间相关特性。最后，检测到的潜在变量可以与基于主动学习的高斯过程回归相结合，进行高维动态可靠性分析。研究了随机激励下的一个单自由度系统和一个钢筋混凝土框架结构，以验证该方法的性能。