Hyperdimensional Performance Maps for Engineering Design

设计工程师面临着确定如何修改设计变量以实现预期性能目标的挑战。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，并且很少有工具可用于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新的方法来表示复杂的高维，高度非线性的设计空间。 一个超维B样条对象（HyperMap）是适合从设计迭代（无论是模拟或实验）的数据，导致在一个系统中，性能指标的设计变量的变化。系统图用于探索设计空间，做出最佳设计决策，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、评估和优化过程中提供了优于竞争技术的计算优势。这项工作的广泛影响将是增强设计复杂系统的能力。 与工业和研究实验室的代表进行的讨论使我们相信，这项研究解决了复杂系统设计领域的真实的需求。 我们的计算方法代表了一个机会，介绍了一个科学的基础，以前的经验过程，并提供了一个基础的设计优化与相关的系统性能误差和不确定性的知识。 因此，我们希望这种方法也将为工程设计的学生提供教育效益，特别是通过使用复杂系统设计的工具。

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.