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，如机翼，并了解新兴技术，如聚变舱。 在实践中，这个过程充满了不确定性：制造的产品偏离设计的产品;实际产品必须在各种操作条件下运行。 鲁棒设计问题是在制造和操作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、计算上易于处理的鲁棒设计方法。 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框架。 将统计决策理论应用于稳健设计的尝试并不多见，它处于当前工程实践的前沿;所提出的项目将通过开发更有效的计算方法来扩展这一前沿。所开发的方法将在NASA兰利研究中心的重大兴趣的气动设计优化问题上得到验证。这些问题为稳健设计方法的发展提供了一个理想的平台。 除了我们对空气动力学设计的关注，基于不确定性的设计方法在广泛的应用中具有很大的前景，例如，在桑迪亚国家实验室测试的融合胶囊的设计。 潜在的好处包括增加对分析工具的信心;减少设计周期时间、风险和成本;增加稳健的设计;以及在确保可靠性的情况下提高系统性能。来自数学、计算机科学和工程领域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.