The research objective of this award is to develop methods that enable the product design space to be modeled so that promising regions can be identified and developed. Every product has a design space associated with the choices made during design. Often, these choices are made with limited or changing information and thus the resulting design may not lie in the best region of the design space. By modeling the design space, information about design tradeoffs and opportunities for technological innovation can be identified and used to improve the design of the product. This research focuses on the tasks of accurately modeling the design space with available data, recognizing the regions within the design space that contain the most promising designs, and applying multi-objective optimization techniques to select the best designs from these regions. Deliverables include the development of algorithms to support adaptive data collection and the handling of data from multiple sources, methods that characterize and can identify promising regions within the design space, and the integration of optimization methods within a software system that supports multi-objective optimization problems.
If successful, the results of this research will provide opportunities to dramatically reduce the time it takes to design a new product while improving the quality of product designs developed with these methods. These methods will be general enough to be applied to a wide range of product design problems. Results from this research will be widely disseminated through professional meetings and conferences and through publication in disciplinary journals. Collaborations with industrial partners to evaluate these methods on real-world problems are anticipated and the undergraduate and graduate students involved in the project will benefit from their exposure to an emerging design technology.
Almost everything around us is the product of a complex design process that we are only beginning to understand. As we develop our understanding of design as an activity; we become more capable of producing better designs that are more responsive to the needs of their users. The capability to analyze and predict the performance of a design, using the fundamental principles of science and mathematics is central to the process of design for engineers. Yet, it is far easier to define useful analysis than it is to solve many of these analysis problems. When faced with this challenge, one alternative is to solve a simpler approximation to the problem at hand. These surrogate problems, if similar to the original problem, still enable engineers to understand how changes to the design will affect the ultimate performance and satisfaction of the users. This grant has supported the development of a surrogate modeling technique based on Non Uniform Rational B-splines (NURBs), a mathematical representation common in computer graphics. This research focused on applying these surrogate representations to robust multiple-objective optimization problems subject to probabilistic uncertainties which are common in design. NURBs-based surrogate models have a unique underlying structure that can be represented mathematically as a graph. Within this graph, it is possible to encapsulate the performance of the design and the robustness of particular solutions. Performance can be expressed many ways, but fundamentally relates to the ability of the design to satisfy a particular set of design needs and is thus a "local" property specific to a particular design. Robustness on the other hand is a measure of how similar design solutions perform in comparison to the original design solution, and is thus regional in nature. Since no two products are perfect copies of each other, and variation is a natural manufacturing limitation, all designs must exhibit both performance and robustness. The best designs balance the demands of performance with those of robustness. The graph formulation that emerges from a NURBs-based metamodel enables both characteristics to be compared in a design problem, allowing the engineer to arrive at the best tradeoff between performance and robustness or what is known as a robust optimal design. These designs can be identified for design problems composed of continuous, mixed continuous-discrete and discrete variables. Previous approaches to finding robust optimal designs were more computationally demanding and were limited to continuous variables despite the fact that many design problems incorporate discrete variables (e.g. finite part sizes or material types). This intellectual leap has already led to a new understanding of what it means to be a robust design solution, and is defined with a sound mathematical basis and is supported by numerous well known algorithms. As a result, this approach to surrogate modeling exhibits considerable computational efficiency, which makes it attractive for many design challenges. Preliminary applications have examined biomechanical analysis of medical issues in the knees and backs, the characterization of complex engineering materials such as composites, real-time augmentation of construction processes, and intelligent autonomous agent-based control of robotic and co-robotic systems. In these studies, surrogate model approaches have reduced computation times from days to minutes or even seconds for the complex analyses necessary to improve these technologies. As this approach matures, it may enable rapid characterization of medical issues, enhancing the treatment of individuals suffering from knee and back pain while reducing costs; new materials enabling higher performance engineering design solutions and superior engineering capabilities to utilize these new materials in designs; highways that are built more efficiently and last longer; and robotic systems that can collaborate with humans in complex unstructured environments. These applications are just the beginning of what is now possible. Finally, this grant has directly impacted more than 1400 students in the last four years, including several graduate students who are now contributing to the biomedical, manufacturing and defense industries; several undergraduates who gained research experience working on the software supporting this research; and finally, a substantial number of students who have seen the results of this research contribute to their cutting edge coursework and engineering experiences.
