Improving Search Efficiency in Engineering Design by Integrating Multiple Models at Different Fidelities

本研究的目的是提高工程设计中的搜索效率。工程设计人员通常依靠预测模型来洞察应该选择哪些设计方案。在这个过程中，他们还必须决定使用哪些模型，平衡模型保真度和计算成本。高保真模型通常提供更精确的近似，但可能非常昂贵，并可能需要大量的计算资源。另一方面，低保真模型往往要快得多，因此可以在短时间内搜索大量的设计备选方案。该奖项支持通过整合不同保真度的多个模型来提高搜索效率的基础研究。新的模型集成框架将使工程设计人员能够将快速且廉价的低保真模型的好处与准确但更昂贵的高保真模型结合起来。这一领域的进展将导致以更低的成本开发更好的工程系统。这项研究将跨越工程设计、数学科学和系统工程等多个学科，并有助于开发新的跨学科课程，增强工程专业学生的教育体验。尽管多尺度设计和多学科设计优化已取得重大进展，但集成不同保真度的多个模型的理论基础和实践方法仍有待研究。这项研究将通过开发一个包含两个关键组成部分的理论和算法框架来填补这一知识空白：序数变换和最优抽样。这项研究将建立使用低保真模型创建的新的有序设计空间的理论性质，并表明这些性质有助于后续高效地搜索优化设计。然后，将开发一种最优抽样方法，以低成本高效地指导搜索，同时考虑有序空间中的信息和低保真模型中的偏差。还将调查扩展到多个低保真模型的好处。

The goal of this research is to improve search efficiency in engineering design. Engineering designers usually rely on predictive models to provide insight into which design alternatives to select. In this process, they must also decide which models to use, balancing model fidelity and computation cost. High-fidelity models usually provide a more accurate approximation but may be very costly and may require considerable computational resources. Low-fidelity models on the other hand tend to be much faster and can therefore be used to search through a large number of design alternatives in a short time. This award supports fundamental research to improve the search efficiency by integrating multiple models at different fidelities. The new model integration framework will enable engineering designers to combine the benefits of both fast and inexpensive low-fidelity models with accurate but more expensive high-fidelity models. Progress in this area will lead to the development of better engineered systems at a lower cost. The research will bridge several disciplines including engineering design, mathematical science and systems engineering, and contribute to the development of a new interdisciplinary curriculum enhancing the educational experience of engineering students.Although significant advances have been made in multiscale design and multidisciplinary design optimization, the theoretical foundation and practical approaches for integrating multiple models at different fidelities still remains to be investigated. This research will fill this knowledge gap by developing a theoretical and algorithmic framework with two key components: ordinal transformation and optimal sampling. The research will establish theoretical properties of a new ordinal design space created using a low-fidelity model and show that these properties facilitate efficient subsequent search for optimized designs. An optimal sampling method will then be developed to guide the search efficiently, at low-cost, taking into account both the information in the ordinal space and the bias in the low-fidelity model. The benefit of the extension to multiple low-fidelity models will also be investigated.