An improved method, termed as the AL-DLGPR-PDEM, is presented to address high-dimensional reliability problems. The novelty of this work lies in developing a complete framework for combining the deep learning (DL) architectures, serving as the utility of dimension reduction, and the Gaussian process regression (GPR), resulting in the so-called DLGPR model. First, the parameters of both the DL and the GPR are inferred using a joint-optimization scheme, rather than the traditional two-step, separate-training scheme. Second, the network configuration of the DLGPR is optimally determined by using a grid-search procedure involving cross-validation, instead of an empirical setting manner. On this basis, the DLGPR is adaptively refined via an active learning (AL)-based sampling strategy, so as to gain the desired DLGPR using as fewer training samples as possible. Eventually, the finalized DLGPR is evaluated at the whole representative point set, thereby the probability density evolution method (PDEM) is conducted accordingly. Two numerical examples are investigated. The first one tackles with the static reliability analysis of a planner steel frame, where the case of small failure probabilities is also considered; the second one addresses the dynamic reliability analysis of the steel frame under fully non-stationary stochastic seismic excitation. Comparisons against other existing reliability methods are conducted as well. Results demonstrate that the proposed AL-DLGPR-PDEM achieves a fair tradeoff between accuracy and efficiency for dealing with high-dimensional reliability problems in both static and dynamic analysis examples.

提出了一种改进的方法，称为AL-DLGPR-PDEM，用于解决高维可靠性问题。这项工作的新颖之处在于，开发了一个完整的框架，用于将深度学习（DL）架构（作为降维的效用）与高斯过程回归（GPR）结合起来，从而形成了所谓的DLGPR模型。首先，使用联合优化方案而不是传统的两步，单独训练方案来推断DL和GPR的参数。其次，通过使用涉及交叉验证的网格搜索程序而不是经验设置方式来最佳地确定DLGPR的网络配置。在此基础上，通过基于主动学习（AL）的采样策略对DLGPR进行自适应调整，以便使用尽可能少的训练样本来获得所需的DLGPR。最终，在整个代表点集上评估最终的DLGPR，从而据此进行概率密度演化方法（PDEM）。研究了两个数值示例。第一个解决方案是对规划钢框架的静态可靠性分析，其中还考虑了小故障概率的情况。第二篇是在完全非平稳随机地震激励下对钢框架的动力可靠性分析。还与其他现有的可靠性方法进行了比较。结果表明，所提出的AL-DLGPR-PDEM在静态和动态分析示例中均能在精度和效率之间取得合理的权衡，以解决高维可靠性问题。