Design optimization of complex engineering problems often involves multiple disciplines or subsystems that usually exist couplings or data interactions with each other. Multidisciplinary design optimization (MDO) is an advanced methodology to deal with such problems. Besides, uncertainty is a crucial factor affecting the performance of complex systems. Therefore, uncertain MDO (UMDO) is the focus of current engineering design research. This article proposes a novel (UMDO) method based on the conditional value at risk (CVaR) as a supplement and alternative scheme to traditional (UMDO) approaches. First, the number of multidisciplinary analyses of complex systems was reduced using collaboration models. Second, metamodels were constructed to simulate data interaction between multidisciplinary systems. Then, an approximate method for CVaR under uncertainty risk analysis was derived. A UMDO framework based on CVaR was constructed. The optimization process was driven by the gradient-based Monte Carlo simulation method. Finally, three different complexity examples verified the accuracy and efficiency of the proposed approach. Note to Practitioners —This article is motivated by the problem of optimization under uncertainty for complex multidisciplinary systems, but it is also applicable to other single-disciplinary uncertain optimizations. Existing uncertain multidisciplinary design optimization (UMDO) methods usually require complex multidisciplinary decoupling and uncertainty propagation analysis, which limits the application of complex system optimization methods. This article suggests a new method that uses the conditional value at risk (CVaR) analysis to quantify uncertain parameters and uses a collaboration model to decouple multidisciplinary systems. This method provides an effective new scheme for the optimization of complex systems under uncertainties. In this article, we describe mathematically the expression and approximation methods of CVaR analysis. We then show how to effectively decouple multidisciplinary systems through a collaboration model. Finally, a framework for UMDO is constructed. By applying this method to three examples, the results suggest that this method is feasible and effective. In future research, the problem of complex system optimization under mixed uncertainties of parameters and models will be investigated.

中文翻译：

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基于风险条件值的不确定的多学科设计优化新方法

复杂工程问题的设计优化通常涉及多个学科或子系统，这些学科或子系统之间通常存在耦合或数据交互。多学科设计优化（MDO）是解决此类问题的高级方法。此外，不确定性是影响复杂系统性能的关键因素。因此，不确定的MDO（UMDO）是当前工程设计研究的重点。本文提出了一种基于条件风险值（CVaR）的新颖（UMDO）方法，作为对传统（UMDO）方法的补充和替代方案。首先，使用协作模型减少了复杂系统的多学科分析数量。其次，构建元模型来模拟多学科系统之间的数据交互。然后，推导了不确定风险分析下的CVaR近似方法。构建了基于CVaR的UMDO框架。优化过程由基于梯度的蒙特卡洛模拟方法驱动。最后，三个不同的复杂度示例验证了所提方法的准确性和效率。执业者注意 —本文受复杂多学科系统不确定性下的优化问题的启发，但也适用于其他单学科不确定性优化。现有的不确定多学科设计优化（UMDO）方法通常需要复杂的多学科解耦和不确定性传播分析，这限制了复杂系统优化方法的应用。本文提出了一种新方法，该方法使用条件风险值（CVaR）分析来量化不确定参数，并使用协作模型来解耦多学科系统。该方法为不确定条件下的复杂系统优化提供了有效的新方案。在本文中，我们在数学上描述了CVaR分析的表达式和近似方法。然后，我们展示了如何通过协作模型有效地分离多学科系统。最后，构建了UMDO的框架。通过将该方法应用于三个实例，结果表明该方法是可行和有效的。在未来的研究中，将研究参数和模型混合不确定性下的复杂系统优化问题。