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。工程设计师通常依赖预测模型来提供选择哪些设计方案的洞察力。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准确的近似，但可能非常昂贵，并且可能需要相当多的计算资源。另一方面，低保真度模型往往要快得多，因此可以用于在短时间内搜索大量的设计方案。该奖项支持基础研究，通过整合不同级别的多个模型来提高搜索效率。新的模型集成框架将使工程设计人员能够将快速和廉价的低保真模型与准确但更昂贵的高保真模型的优点联合收割机结合起来。这一领域的进展将导致以较低的成本开发更好的工程系统。 该研究将连接包括工程设计、数学科学和系统工程在内的多个学科，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经取得了重大进展，在不同的精度下集成多个模型的理论基础和实践方法仍有待于研究。这项研究将填补这一知识空白，开发一个理论和算法框架，两个关键组成部分：有序变换和最佳采样。该研究将建立一个新的有序设计空间使用低保真度模型创建的理论属性，并表明这些属性有利于有效的后续搜索优化设计。然后，将制定一个最佳抽样方法，以低成本有效地指导搜索，同时考虑到有序空间中的信息和低保真度模型中的偏差。扩展到多个低保真模型的好处也将被调查。

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.