Predicting the Benefits of Topology Optimization

工程师的主要任务之一是通过计算机模拟来优化设计，即提高设计的性能。由于这可能既耗时又昂贵，工程师们面临着以下一组棘手的问题：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？人们能在不投入几天计算的情况下预测设计优化的好处吗？本项目将通过对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，允许工程师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。这使得设计者可以将有限的资源集中在最有希望的优化问题上，从而有可能显著提高工业竞争力。研究团队将在期刊和会议记录上发表研究结果；该团队还将向科学界发布结果软件。该团队将为高中生，包括代表不足的少数族裔学生，举办关于工程模拟和优化的工程研讨会。来自当地行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初出茅庐的工程师的影响，他们将接触到研究、工业经验和正规教育的独特结合。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好处的指标。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敏感场来估计。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。使用这个简单的概念，设计师可以做出合理的设计优化决策。本项目将解决以下问题：(1)帕累托最优概念能否应用于目前所考虑的结构力学问题以外的问题？(2)该概念能否用于对装配中的部件进行排序以进行设计优化？(3)如何推广这些概念以包括约束、多载荷情景和材料设计？(4)能否开发二阶和纠错策略以提高这些预测方法的效率？该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.