Explicit Design Space Decomposition with Adaptive Sampling for Design Optiimization and Uncertainty Quantification

这个奖项的研究目标是开发一种方法，帮助设计师和工程师在不确定的情况下优化复杂的产品。由于非线性行为的存在，车辆或发动机等复杂系统的设计通常需要非常长的计算时间。由于优化需要反复调用模拟代码(例如，崩溃分析)来调查多维设计空间，因此使用合理的方法来选择相关的设计配置以寻找最佳解决方案至关重要。提出的方法称为显式设计空间分解，将设计空间划分为区域，这些区域的边界是根据变量明确定义的，这些区域的边界区分了“可接受”和“不可接受”的设计。这些边界是使用支持向量机(支持向量机)构建的，支持向量机能够定义多维、不相交和非凸区域。通过设计空间的区域和系统的特定行为之间的直接对应，这为设计者提供了洞察力。此外，通过自适应地添加与特定设计相对应的相关样本，可以获得准确的基于支持向量机的边界。这种方法有可能限制反复尝试的步骤并减少总的计算时间。最后，显式边界对于具有不连续行为(如屈曲)的问题很有用，并提供了一种直接计算失效概率的方法。如果成功，研究结果将为不确定的非线性问题下的设计优化和设计提供一个通用的框架，这些非线性问题的特征是响应不连续和模拟时间长(例如耐撞性设计)。拟议方法的一般性将使其适用于传统行业(例如汽车和航空航天)以及生物医学设备设计等领域。减少试错步骤，如果成功，将大大减少设计周期和成本。这项研究的结果将纳入研究生课程，并通过技术出版物和演示文稿进行传播。此外，这一方法预计将对工业产生重大影响，从而简化设计流程并提供更好的产品。

0800117PI: MissoumThe research objective of this award is to develop a method to aid designers and engineers in optimizing complex products under uncertainty. The design of complex systems such as a vehicle or an engine often requires very long computational times due to the presence of nonlinear behaviors. Because optimization requires repeated calls to a simulation code (e.g., crash analysis) to investigate a multi-dimensional design space, it is critical to use a sound methodology to select relevant design configurations in the search for the best solutions. The proposed approach, referred to as explicit design space decomposition, partitions the design space into regions whose boundaries, which are defined explicitly in terms of the variables, separate "acceptable" and "unacceptable" designs. These boundaries are constructed using a Support Vector Machine (SVM) which is able to define multi-dimensional, disjoint, and non-convex regions. This gives insight to the designer through a direct correspondence between regions of the design space and specific behaviors of a system. In addition, accurate SVM-based boundaries can be obtained by adaptively adding relevant samples corresponding to specific designs. This approach has the potential to limit trial-and-error steps and reduce the total computational time. Finally, explicit boundaries are useful for problems with discontinuous behaviors such as buckling and provide a straightforward calculation of probabilities of failure. All in all, this approach allows the designer to reach better and more reliable designs in fewer design iterations.If successful, the results of this research will provide a general framework for design optimization and design under uncertainty of nonlinear problems characterized by, but not limited to, discontinuous responses and long simulation times (e.g., design for crashworthiness). The generality of the proposed approach will make it applicable to traditional industries (e.g., automobile and aerospace) as well as fields such as the design of biomedical devices. The reduction of trial-and-error steps will, if successful, drastically reduce design cycle times and cost. The results of this research will be included in graduate coursework and disseminated through technical publications and presentations. In addition, this approach is expected to have a significant impact on industry, resulting in streamlined design processes and better products.