Hyperdimensional Performance Maps for Engineering Design

设计工程师面临的挑战是确定如何修改设计变量以实现预期的性能目标。对于高度复杂的情况，必须同时考虑的性能标准的数量远远超过了人类工程师可以轻松考虑的数量。这些性能标准通常是大量设计变量的高度非线性函数，很少有工具可以帮助工程师管理这样的设计空间。本研究的目的是提供一种表示复杂高维、高度非线性设计空间的新方法。超维b样条对象（HyPerMap）适合于设计迭代（模拟或实验）的数据，从而形成一个将性能指标与设计变量的变化联系起来的系统。系统图用于探索设计空间，做出最优设计决策，并了解不确定性对决策的影响。此外，基于b样条的HyPerMap结构在生成、进化、评估和优化方面比竞争技术具有计算优势。这项工作的广泛影响将是提高设计复杂系统的能力。与工业和研究实验室代表的讨论使我们确信，这项研究解决了复杂系统设计领域的实际需求。我们的计算方法为之前的经验过程提供了科学基础，并为相关系统性能误差和不确定性的设计优化提供了基础。因此，我们期望该方法也将为工程设计专业的学生提供教育效益，特别是通过使用复杂系统设计的结果工具。

Design engineers are challenged with determining how to modify design variables in order to realize desired performance goals. For highly complex situations, the number of performance criteria that must be simultaneously considered far exceeds the number that a human engineer can comfortably contemplate. These performance criteria are typically highly non-linear functions of a large number of design variables, and few tools are available to assist engineers in managing such design spaces. The objective of this research is to provide a new method for representing complex high-dimension, highly non-linear design spaces. A hyperdimensional B-spline object (HyPerMap) is fit to data from design iterations (either simulations or experiments), resulting in a system that relates performance indices to variations in design variables. The system map is used to explore the design space, make optimal design decisions, and understand the impact of uncertainty on decisions. Furthermore, the B-spline based HyPerMap structure offers computational advantages over competing techniques during generation, evolution, evaluation, and optimization.The broad impact of this work will be an enhanced ability to design complex systems. Discussions with representatives from industry and research laboratories have convinced us that this research addresses a real need in the area of complex systems design. Our computational approach represents an opportunity to introduce a scientific foundation to a previously experiential process and to provide a basis for design optimization with knowledge of the associated system performance error and uncertainty. Thus, we expect the approach will also provide educational benefits for students of engineering design, particularly through the use of the resulting tools for complex systems design.