Robust design optimization (RDO) is a valuable technique in the design of engineering structures as it can provide an optimum design solution that is relatively insensitive to input uncertainties. However, the nested double-loop estimation process required in RDO often results in significant computational costs. To address this issue, we propose an adaptive decoupled RDO method based on the Kriging surrogate model. This method transforms the nested double-loop estimation process into a traditional deterministic optimization procedure, thus reducing computational costs. Furthermore, a novel estimation expression for the performance standard deviation that can simultaneously reflect the uncertainties in both the prediction and the performance mean is established. The closed-form expressions of the performance mean and performance standard deviation under different design parameters are deduced, which are further implemented to the uncertainty propagation during the design optimization. Moreover, an adaptive framework is introduced to improve the computational accuracy of uncertainty propagation as well as optimization procedure to guarantee the estimation accuracy of RDO problems. Several numerical examples along with engineering cases are introduced to illustrate the effectiveness of the established adaptive decoupled adaptive RDO method, and the results demonstrate that the proposed method can effectively optimize the design of structures while reducing computational costs.

鲁棒设计优化（RDO）是工程结构设计中的一项有价值的技术，因为它可以提供对输入不确定性相对不敏感的最佳设计解决方案。然而，RDO 中所需的嵌套双环估计过程通常会导致巨大的计算成本。为了解决这个问题，我们提出了一种基于克里金代理模型的自适应解耦 RDO 方法。该方法将嵌套双环估计过程转变为传统的确定性优化过程，从而降低了计算成本。此外，建立了一种新的性能标准差估计表达式，可以同时反映预测和性能均值的不确定性。推导了不同设计参数下性能均值和性能标准差的闭式表达式，并进一步应用于设计优化过程中的不确定性传播。此外，引入了自适应框架来提高不确定性传播的计算精度，并引入优化程序来保证RDO问题的估计精度。通过几个数值算例和工程案例来说明所建立的自适应解耦自适应RDO方法的有效性，结果表明该方法可以有效优化结构设计，同时降低计算成本。在设计优化过程中进一步实现不确定性传播。此外，引入了自适应框架来提高不确定性传播的计算精度，并引入优化程序来保证RDO问题的估计精度。通过几个数值算例和工程案例来说明所建立的自适应解耦自适应RDO方法的有效性，结果表明该方法可以有效优化结构设计，同时降低计算成本。在设计优化过程中进一步实现不确定性传播。此外，引入了自适应框架来提高不确定性传播的计算精度，并引入优化程序来保证RDO问题的估计精度。通过几个数值算例和工程案例来说明所建立的自适应解耦自适应RDO方法的有效性，结果表明该方法可以有效优化结构设计，同时降低计算成本。