Abstract:
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Response surface methodology aims to obtain the optimal inputs which reach the optimal responses. Response surface methodology consists of experimental design, model building, and optimization. Dimensional analysis is a widely used methodology in physics and engineering studies. One benefit of utilizing dimensional analysis is to reduce the number of input variables without collecting data. Dimensional analysis can also extract dimensionless variables from original variables while maintaining the essential information. The dimensionless variables, thus, are used to construct models. Since the number of dimensionless variables is less than the number of original variables, the reduction in the number of variables can help in experimental design and model building. A methodology is proposed for response surface methodology via dimensional analysis. We show that the model's goodness of fit based on dimensionless variables can be maintained under some regularity conditions. Airfoil data are used as an illustrative example.
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