Adaptive Kriging model has gained growing attention for its effectiveness in reducing the computational costs in time-dependent reliability analysis (TRA). However, the existing methods struggle to identify critical sample regions, leverage parallel computational resources, and assess the value for sample trajectories, thus restricting improvement in accuracy and efficiency. To address the challenges, this study proposes a time series clustering adaptive enhanced method (TSCM). TSCM first employs the time series clustering technique to partition the sample region efficiently. A novel time-dependent Kriging occurrence learning function is then introduced to account for both the uncertainty of sample trajectories and its influence on the approximated limit state boundary. Subsequently, an adaptive sampling strategy is developed to select training samples in parallel, guided by an uncertainty-based assessment of sample regions. After that, a time-dependent error-based stopping criterion is introduced to determine the training stage and terminate the update process. Finally, TSCM is extended to time-dependent reliability-based design optimization problems. Several numerical examples and an engineering case study demonstrate the superior computational efficiency and accuracy of the proposed method.

中文翻译：

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用于瞬态可靠性分析和设计优化的时间序列聚类自适应增强方法

自适应克里金模型因其在降低瞬态可靠性分析 （TRA） 计算成本方面的有效性而受到越来越多的关注。然而，现有方法难以识别关键样本区域、利用并行计算资源和评估样本轨迹的价值，从而限制了准确性和效率的提高。为了应对这些挑战，本研究提出了一种时间序列聚类自适应增强方法 （TSCM）。TSCM 首先采用时间序列聚类技术来有效地对样本区域进行分区。然后引入了一种新的瞬态 Kriging 发生学习函数来解释样本轨迹的不确定性及其对近似极限状态边界的影响。随后，开发了一种自适应采样策略，以基于不确定性的样本区域评估为指导，并行选择训练样本。之后，引入一个与时间相关的基于错误的停止标准，以确定训练阶段并终止更新过程。最后，TSCM 扩展到基于时间依赖可靠性的设计优化问题。几个数值算例和一个工程实例分析证明了所提出的方法具有卓越的计算效率和准确性。