Abstract Uncertainty inadvertently exists in various stages of engineering system design, development, and operating conditions. During the system design and development stages, a design engineer encounters the reliability and robustness measures of a dynamic uncertain system. Due to the existence of dynamic uncertainties, incorporating the time-dependent reliability of an engineering system in reliability based robust design optimization (RBRDO) is crucial. However, the time-dependent and highly non-linear performance functions present a new challenge to the RBRDO problem. This paper presents a multiobjective integrated framework and corresponding algorithms to handle a time-dependent RBRDO problem. The mean and coefficient of variation of the cost function are taken as a multiobjective problem that needs to be optimized to maximize the robustness without destabilizing the system performance. An evolutionary algorithm is employed to find the optimal design points. The performance functions used to estimate the time-dependent reliability are taken as dynamic probabilistic constraints. The dynamic probabilistic constraints are then converted into deterministic constraints by predicting the corresponding time-dependent reliability. A transfer learning based method integrated with the Kriging surrogate models is proposed to predict the time-dependent reliability for a given time interval. Various examples are used to demonstrate the effectiveness of the proposed approach.

中文翻译：

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一种有效的基于克里金法的基于时间依赖可靠性的基于进化算法的鲁棒设计优化方法

摘要 不确定性在工程系统设计、开发和运行的各个阶段不经意间就存在。在系统设计和开发阶段，设计工程师会遇到动态不确定系统的可靠性和鲁棒性措施。由于存在动态不确定性，将工程系统的时间相关可靠性纳入基于可靠性的鲁棒设计优化 (RBRDO) 至关重要。然而，时间相关和高度非线性的性能函数对 RBRDO 问题提出了新的挑战。本文提出了一个多目标集成框架和相应的算法来处理依赖于时间的 RBRDO 问题。成本函数的均值和变异系数被视为一个多目标问题，需要对其进行优化，以在不破坏系统性能的情况下最大限度地提高鲁棒性。采用进化算法来寻找最佳设计点。用于估计时间相关可靠性的性能函数被视为动态概率约束。然后通过预测相应的时间相关可靠性将动态概率约束转换为确定性约束。提出了一种与克里金代理模型集成的基于迁移学习的方法来预测给定时间间隔的时间相关可靠性。使用各种示例来证明所提出方法的有效性。采用进化算法来寻找最佳设计点。用于估计时间相关可靠性的性能函数被视为动态概率约束。然后通过预测相应的时间相关可靠性将动态概率约束转换为确定性约束。提出了一种与克里金代理模型集成的基于迁移学习的方法来预测给定时间间隔的时间相关可靠性。使用各种示例来证明所提出方法的有效性。采用进化算法来寻找最佳设计点。用于估计时间相关可靠性的性能函数被视为动态概率约束。然后通过预测相应的时间相关可靠性将动态概率约束转换为确定性约束。提出了一种与克里金代理模型集成的基于迁移学习的方法来预测给定时间间隔的时间相关可靠性。使用各种示例来证明所提出方法的有效性。然后通过预测相应的时间相关可靠性将动态概率约束转换为确定性约束。提出了一种与克里金代理模型集成的基于迁移学习的方法来预测给定时间间隔的时间相关可靠性。使用各种示例来证明所提出方法的有效性。然后通过预测相应的时间相关可靠性将动态概率约束转换为确定性约束。提出了一种与克里金代理模型集成的基于迁移学习的方法来预测给定时间间隔的时间相关可靠性。使用各种示例来证明所提出方法的有效性。