Predicting the Benefits of Topology Optimization

工程师的主要任务之一是通过计算机仿真来优化设计，即提高设计的性能。由于这既耗时又昂贵，工程师们面临着以下一系列棘手的问题：是否值得优化给定的设计？通过计算机模拟，性能可以提高多少？一个人能预测设计优化的好处，而不投入几天的计算吗？该项目将通过预测模拟技术的基础研究来解决这些问题。将建立新的算法，使工程师能够在投入时间和精力进行详细调查之前快速预测设计优化的好处。通过允许设计师将有限的资源集中在最有前途的优化问题上，这有可能显著提高工业竞争力。研究小组将在期刊和会议论文集上发表研究结果；该团队还将向科学界发布最终的软件。该团队将为高中生（包括少数族裔学生）举办工程模拟和优化研讨会。来自当地工业和学生汽车项目的案例研究将被用作设计挑战。工业互动的更广泛影响是对崭露头角的工程师，他们将接触到独特的混合研究，工业经验和正规教育。在该项目中，帕累托最优距离的概念将被用作预测设计优化收益的度量。对于给定的设计，帕累托最优距离是到帕累托最优流形的一组轴向距离；这些距离将通过拓扑灵敏度场来估计。初步结果表明，这些帕累托最优距离确实可以用来估计设计优化的效益，即距离越大，效益越大。利用这个简单的概念，设计师可以对设计优化做出理性的决策。本项目将解决以下问题：(1)帕累托最优概念是否可以应用于迄今为止所考虑的结构力学问题之外的问题？(2)这个概念是否可以用于对装配中的零件进行排序以进行设计优化？(3)如何将这些概念推广到约束、多载荷场景和材料设计？(4)是否可以制定二阶和纠错策略来提高这些预测方法的有效性？该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

One of the primary tasks of engineers is to optimize designs, i.e., improve the performance of designs, through computer simulation. Since this can be time-consuming and expensive, engineers are faced with the following set of tough questions: Is it worth optimizing a given design? How much can the performance be improved through computer simulation? Can one predict the benefits of design optimization, without investing several days of computing? This project will address these questions through fundamental research on predictive simulation techniques. New algorithms will be established that will permit engineers to rapidly predict the benefits of design optimization, prior to investing time and effort into a detailed investigation. This has the potential to improve industrial competitiveness significantly by allowing designers to focus their limited resources on only the most promising optimization problems. The research team will publish the findings in journals and conference proceedings; the team will also release the resulting software to the scientific community. The team will conduct engineering workshops for high-school students, including underrepresented minority students, on engineering simulation and optimization. Case-studies from local industries and student-car projects will be used as design challenges. The broader impact of the industrial interaction is on budding engineers who will be exposed to a unique blend of research, industrial experience, and formal education.In the project, the concept of Pareto-optimal distances will be used as a metric for predicting the benefits of design optimization. The Pareto-optimal distances, for a given design, is a set of axis-aligned distances to the Pareto-optimal manifold; these distances will be estimated via the topological sensitivity field. Preliminary results indicate that these Pareto-optimal distances can indeed be used to estimate the benefits of design optimization, i.e., greater the distance, greater the benefit. Using this simple concept, designers can make rational decisions on design optimization. The following questions will be addressed in this project: (1) Can the Pareto-optimality concept be applied to problems beyond the structural mechanics problems considered thus far? (2) Can this concept be used to rank-order parts within an assembly for design optimization? (3) How can these concepts be generalized to include constraints, multi-load scenarios, and material design? (4) Can second-order and error-correction strategies be developed to improve the efficacy of these predictive methods?This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.