This paper proposes an effective and robust decoupled approach for addressing reliability-based design optimization (RBDO) problems. The method iteratively performs a parallel constrained Bayesian optimization (PCBO) with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) sequentially updated through an enhanced active learning-based reliability evaluation process. During the deterministic optimization process, the PCBO integrates with a trust region approach that considers a collection of simultaneous local optimization runs, each guided by an independent Gaussian process (GP) model. The trust region approach leverages a well-established selection strategy in reinforcement learning, known as the multi-armed bandit, to allocate samples across local trust regions and decide which local optimization runs to continue. In particular, batched Thompson sampling is adopted as an acquisition function to determine the optimal design by selecting a batch of candidate points from local trust regions via sampling from the posterior of the independent GP models, with the batch evaluations executed in parallel. In the reliability analysis, the GP model estimates, from the optimal design offered by the PCBO, the spectrum of LSFs under random parameters, and hence allows an efficient failure probability estimation through a cross-entropy (CE) method with Gaussian mixture (GM) clustering without direct performance function evaluations. By leveraging information from the GM clustering, an enhanced active learning mechanism is developed to strategically refine the GP model by generating multiple informative points in the clustered regions with the largest uncertainty and high-reliability sensitivity, thus improving the accuracy of failure probability predictions. Eventually, an invertible cross-entropy (iCE) method is proposed to decouple the reliability analysis from the optimization process, enabling the update of the new MPP assigned for the PCBO to identify the new optimal design. The proposed method significantly alleviates computational costs for both deterministic design optimization and reliability analysis and quickly converges to the optimal RBDO design. Three numerical examples are provided to illustrate the efficiency and robustness of the proposed approach in addressing the RBDO problem.

中文翻译：

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通过批量 Thompson 采样进行并行约束贝叶斯优化，并增强主动学习过程，以实现基于可靠性的设计优化

本文提出了一种有效且稳健的解耦方法，用于解决基于可靠性的设计优化 （RBDO） 问题。该方法迭代执行并行约束贝叶斯优化 （PCBO），其确定性参数基于最可能点 （MPP） 支撑极限状态函数 （LSF），通过增强的基于主动学习的可靠性评估过程依次更新。在确定性优化过程中，PCBO 与信任域方法集成，该方法考虑一组同步的局部优化运行，每个运行都由独立的高斯过程 （GP） 模型指导。信任区域方法利用强化学习中成熟的选择策略（称为多臂老虎机）在本地信任区域之间分配样本，并决定继续运行哪些本地优化。特别是，采用批量 Thompson 采样作为采集函数，通过从独立 GP 模型的后验采样，从局部信任区域中选择一批候选点来确定最佳设计，同时并行执行批量评估。在可靠性分析中，GP 模型根据 PCBO 提供的最佳设计估计随机参数下 LSF 的频谱，因此允许通过交叉熵 （CE） 方法和高斯混合 （GM） 聚类进行有效的故障概率估计，而无需直接的性能函数评估。 通过利用来自 GM 聚类的信息，开发了一种增强的主动学习机制，通过在不确定性最大和高可靠性敏感性的聚类区域中生成多个信息点来战略性地改进 GP 模型，从而提高故障概率预测的准确性。最终，提出了一种可逆交叉熵 （iCE） 方法，将可靠性分析与优化过程解耦，从而能够更新分配给 PCBO 的新 MPP 以确定新的最优设计。所提出的方法显著降低了确定性设计优化和可靠性分析的计算成本，并迅速收敛到最优 RBDO 设计。提供了三个数值示例来说明所提出的方法在解决 RBDO 问题方面的效率和稳健性。