Dimensionality Reduction Approach for Response Surface Approximations: Application to Thermal Design

Abstract

of the maximum bottom face temperature is needed. The finite element model used to evaluate the maximum temperature depended on 15 parameters of interest for the design. A small number of assumptions simplified the thermal equations, allowing easy nondimensionalization, which together with a global sensitivity analysis showed that the maximum temperature mainly depends on only two nondimensional parameters. These were selected to be the variables of the response surface approximation for maximum temperature, which was constructed using simulations from the original nonsimplified finite element model. The major error in the two-dimensional response surface approximation was found to be due to the fact that the two nondimensional variables account for only part (albeit the major part) of the dependence on the original 15 variables. This error was checked and reasonable agreement was found. The two-dimensional nature of the response surface approximations allowed graphical representation, which we used for material selection from among hundreds of possible materials for the design optimization of an integrated thermal protection system panel.

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