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

0800117PI: missoum本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往往需要很长的计算时间。因为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，所以在寻找最佳解决方案时使用合理的方法来选择相关的设计配置是至关重要的。所提出的方法被称为显式设计空间分解，它将设计空间划分为区域，这些区域的边界根据变量明确定义，将“可接受”和“不可接受”的设计分开。这些边界是使用支持向量机（SVM）构建的，该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关系，这让设计师更有洞察力。此外，通过自适应地添加特定设计对应的相关样本，可以获得精确的基于svm的边界。这种方法有可能限制试错步骤并减少总计算时间。最后，显式边界对于诸如屈曲等不连续行为的问题是有用的，并且提供了一个简单的失效概率计算。总而言之，这种方法允许设计师在更少的设计迭代中获得更好、更可靠的设计。如果成功，本研究的结果将为以但不限于响应不连续和仿真时间长的非线性问题为特征的设计优化和不确定性下的设计提供一个总体框架（例如，耐撞性设计）。拟议方法的通用性将使其适用于传统工业（例如，汽车和航空航天）以及诸如生物医学装置设计等领域。如果成功的话，减少试错步骤将大大减少设计周期时间和成本。这项研究的结果将列入研究生课程，并通过技术出版物和报告加以传播。此外，这种方法有望对工业产生重大影响，从而简化设计流程和更好的产品。

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.