The Application of Polynomial Response Surface and Polynomial Chaos Expansion Metamodels within an Augmented Reality Conceptual Design Environment

Koehring, Andrew
Major Professor
Eliot Winer
Committee Member
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Mechanical Engineering
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Mechanical Engineering

The engineering design process consists of many stages. In the conceptual phase, potential designs are generated and evaluated without considering specifics. Winning concepts then advance to the detail design and high fidelity simulation stages. At this point in the process, very accurate representations are made for each design and are then subjected to rigorous analysis. With the advancement of computer technology, these last two phases have been very well served by the software community. Engineering software such as computer-aided design (CAD), finite element analysis (FEA), and computational fluid dynamics (CFD) have become an inseparable part of the design process for many engineered products and processes. Conceptual design tools, on the other hand, have not undergone this type of advancement, where much of the work is still done with little to no digital technology. Detail oriented tools require a significant amount of time and training to use effectively. This investment is considered worthwhile when high fidelity models are needed. However, conceptual design has no need for this level of detail. Instead, rapid concept generation and evaluation are the primary goals. Considering the lack of adequate tools to suit these needs, new software was created. This thesis discusses the development of that conceptual design application.

Traditional design tools rely on a two dimensional mouse to perform three dimensional actions. While many designers have become familiar with this approach, it is not intuitive to an inexperienced user. In order to enhance the usability of the developed application, a new interaction method was applied. Augmented reality (AR) is a developing research area that combines virtual elements with the real world. This capability was used to create a three dimensional interface for the engineering design application. Using specially tracked interface objects, the user's hands become the primary method of interaction. Within this AR environment, users are able perform many of the basic actions available within a CAD system such as object manipulation, editing, and assembly. The same design environment also provides real time assessment data. Calculations for center of gravity and wheel loading can be done with the click of a few buttons. Results are displayed to the user in the AR scene.

In order to support the quantitative analysis tools necessary for conceptual design, additional research was done in the area of metamodeling. Metamodels are capable of providing approximations for more complex analyses. In the case of the wheel loading calculation, the approximation takes the place of a time consuming FEA simulation. Two different metamodeling techniques were studied in this thesis: polynomial response surface (PRS) and polynomial chaos expansion (PCE). While only the wheel loading case study was included in the developed application, an additional design problem was analyzed to assess the capabilities of both methods for conceptual design. In the second study, the maximum stresses and displacements within the support frame of a bucket truck were modeled. The source data for building the approximations was generated via an FEA simulation of digital mockups, since no legacy data was available. With this information, experimental models were constructed by varying several factors, including: the distribution of source and test data, the number of input trials, the inclusion of interaction effects, and the addition of third order terms. Comparisons were also drawn between the two metamodeling techniques.

For the wheel loading models, third order models with interaction effects provided a good fit of the data (root mean square error of less than 10%) with as few as thirty input data points. With minimal source data, however, second order models and those without interaction effects outperformed third order counterparts. The PRS and PCE methods performed almost equivalently with sufficient source data. Difference began to appear at the twenty trial case. PRS was more suited to wider distributions of data. The PCE technique better handled smaller distributions and extrapolation to larger test data. The support frame problem represented a more difficult analysis with non-linear responses. While initial third order results from the PCE models were better than those for PRS, both had significantly higher error than in the previous case study. However, with simpler second order models and sufficient input data (more than thirty trials) adequate approximation results were achieved. The less complex responses had error around 10%, and the model predictions for the non-linear response were reduced to around 20%. These results demonstrate that useful approximations can be constructed from minimal data. Such models, despite the uncertainty involved, will be able to provide designers with helpful information at the conceptual stage of a design process.