Computational methods for modeling and design of complex engineering systems under uncertainty

基于计算的设计开始成为许多工程领域的标准，高保真模型现在越来越多地用于支持工业设计实践中的决策。尽管在这一领域取得了重大进展，但仍有许多挑战有待克服，以充分实现基于计算的设计工作流程的潜力，以加速复杂系统的设计。主要挑战之一是计算成本。随着对高保真模型的不断推动，即使在大规模并行计算机上，对各种设计方案/概念的评估在计算上也是不可行的。另一个挑战来自于这样一个事实，即不确定性在工程系统的数学建模和表征中无处不在。现有的方法在处理不确定性时可能在计算上是禁止的，例如，当工程师希望使用高保真模型预测性能统计数据和/或决定可以帮助减轻不确定性影响的参数设置时。这两个挑战加剧了复杂的现实世界的工程系统的计算机模型，往往是参数化的大量的设计变量和不确定的参数。在计算建模和设计优化中，特别是在存在不确定性的情况下，迫切需要可扩展且有效的算法来解决高维问题。拟议的研究计划将解决这些重要的挑战和重点的主要研究课题是：（i）新颖的数据驱动和基于Galerkin/Petrov-Galerkin投影的算法，用于构建高维参数化系统的实时仿真器沿着严格的误差估计能力，（ii）低秩张量分解策略，用于有效地处理高维问题，（iii）在不确定性下快速计算计算工程决策分析的算法，这将使工程师能够获得更深入的见解并允许近实时决策，以及（iv）用于异构多核计算机集群的并行软件工具。这些领域的突破是克服与不确定性设计相关的计算挑战和开发下一代沉浸式协作环境的关键，用于复杂工程系统的多学科分析和稳健设计。特别关注的应用领域包括燃气涡轮机系统/部件级设计、气动外形设计和多学科飞机设计。拟议的研究计划将大大提高并找到申请人正在进行的研究合作伙伴关系中的应用，这些合作伙伴关系涵盖计算科学和工程领域的各种主题，以及与燃气涡轮机发动机全球领导者普惠加拿大公司的合作。

Computation-based design is starting to become the norm in many engineering sectors and high-fidelity models are now increasingly used to support decision making in industrial design practice. Despite the significant progress that has been made in this area, a number of challenges remain to be overcome in order to fully realize the potential of computation-based design workflows to accelerate complex systems design. One of the main challenges is computational cost. With the increasing push towards high-fidelity models, evaluation of a wide range of design alternatives/concepts can be computationally infeasible even on massively parallel computers. Another challenge arises from the fact that uncertainty is ubiquitous in the mathematical modeling and characterization of engineering systems. Existing approaches can be computationally prohibitive when dealing with uncertainty, e.g., when engineers wish to predict performance statistics using a high-fidelity model and/or decide on parameter settings that can help mitigate the impact of uncertainty. These two challenges are exacerbated by the fact that computer models of complex real-world engineering systems are often parametrized in terms of a huge number of design variables and uncertain parameters. There is a pressing need for scalable and efficient algorithms to tackle high-dimensional problems in computational modeling and design optimization, especially in the presence of uncertainty. The proposed research program will address these important challenges and the main research topics of focus are: (i) novel data-driven and Galerkin/Petrov-Galerkin projection based algorithms for constructing real-time emulators of high-dimensional parametrized systems along with rigorous error estimation capabilities, (ii) low-rank tensor decomposition strategies for efficiently dealing with high-dimensional problems, (iii) algorithms for rapid calculation of decision analytics for computational engineering under uncertainty that will enable engineers to gain deeper insights and allow near real-time decision making, and (iv) parallel software tools for heterogeneous multicore computer clusters. Breakthroughs in these areas are key to overcoming the computational challenges associated with design under uncertainty and developing the next generation of immersive collaborative environments for multidisciplinary analysis and robust design of complex engineering systems. The application areas of particular focus include gas turbine system/component level design, aerodynamic shape design and multidisciplinary aircraft design. The proposed research program will greatly enhance and find applications in the applicant's ongoing research partnerships that cover various topics in computational science and engineering as well as collaboration with Pratt & Whitney Canada who is a global leader in gas turbine engines.