Collaborative Research: Statistical Decision-Theoretic Methods for Robust Design Optimization

工程师们越来越多地依靠计算机模拟来开发新产品，如翼型，并了解新兴技术，如聚变胶囊。在实践中，这一过程充满了不确定性：制造的产品偏离了设计的产品；实际产品必须在各种操作条件下运行。稳健设计的问题是在制造和运行条件存在不确定性的情况下，优化复杂的、基于仿真的工程系统的问题。本研究项目将致力于开发严格的、易于计算的稳健设计方法。统计决策理论，特别是贝叶斯原理，为量化不确定性提供了一个概念性框架。将统计决策理论应用于稳健设计的尝试很少，而且处于当前工程实践的前沿；拟议的项目将通过开发更有效的计算方法来扩展这一前沿。将要开发的方法将在NASA兰利研究中心进行空气动力学设计优化问题的演示。这些问题为稳健设计方法的发展提供了理想的平台。除了我们对空气动力学设计的关注外，基于不确定性的设计方法具有广泛的应用前景，例如，在桑迪亚国家实验室测试的聚变胶囊的设计。潜在的好处包括增加了对分析工具的信心；减少了设计周期时间、风险和成本；越来越强大的设计；以及在确保可靠性的情况下改善了系统性能。来自数学、计算机科学和工程的本科生将参与这项研究。

Engineers increasingly rely on computer simulation to develop new products, such as, airfoils, and to understand emerging technologies, for instance, fusion capsules. In practice, this process is permeated with uncertainty: manufactured products deviate from designed products; actual products must perform under a variety of operating conditions. The problem of robust design is the problem of optimizing complex, simulation-based engineered systems in the presence of uncertainty about manufacturing and operating conditions.This research project will address the problem of developing rigorous, computationally tractable methods for robust design. Statistical decision theory, specifically the Bayes principle, provides a conceptual framework for quantifying the uncertainties. The application of statistical decision theory to robust design has been infrequently attempted and lies at the frontier of current engineering practice; the proposed project will extend that frontier by developing more efficient computational methods. The methods to be developed will be demonstrated on aerodynamic design optimization problems of vital interest at NASA Langley Research Center. These problems provide an ideal platform for the development of robust design methods. Beyond our focus on aerodynamic design, uncertainty-based design methods hold great promise for a wide range of applications, e.g., the design of fusion capsules tested at Sandia National Laboratories. The potential benefits include increased confidence in analysis tools; reductions in design cycle time, risk, and cost; increasingly robust designs; and improved system performance with ensured reliability. Undergraduates from across mathematics, computer science and engineering will be involved with this research.