Exploration and visualization of design spaces with applications to negative stiffness metamaterials




Morris, Clinton Benjamin

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Engineering design problems are commonly hierarchical and multilevel which requires coordination between models at each scale. If the models are computationally expensive or highly nonlinear, such as many materials design applications, identification of an optimal design may be exceptionally difficult. Alternatives to optimization-based methods include set-based methods that classify and track sets or ensembles of high performance designs. By relaxing the requirement for an optimal design, it is often possible to identify promising, high performance regions of the design space efficiently. Bayesian network classifiers (BNCs) are such an approach that can identify these regions of promising designs in the presence of nonlinear relationships and mixed variables. When manufacturing the promising designs identified by the BNC approach, the intended design may not match the physical embodiment due to manufacturing variations. These variations may alter the performance of the design leading to unsatisfactory results and products. To facilitate selection of not only high performance but reliably manufacturable designs, a method for incorporating manufacturing variation, modeled as a joint probability distribution is presented for the BNC approach. The approach utilizes a dual classification strategy that identifies regions of design that are likely to perform well within statistical confidence. These design regions can be high dimensional in which it becomes very difficult to identify and visualize clusters of promising designs. This leads to a lack of understanding of the design space. To enhance the designer’s knowledge of the design space, this work presents a method, based on spectral clustering, that can identify high performance regions in a high dimensional space. Furthermore, a method for visualizing each individual design region is presented that is accomplished by incorporating t-Distributed Stochastic Neighbor Embedding. Through the accomplishment of these three tasks—incorporating manufacturing variation, clustering, and visualizing—a novel design methodology will be developed which will then be applied to identify satisfactory designs for a negative stiffness metamaterials design problem which will be manufactured and tested.


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