Modeling Martian planetary entry descent and landing using Monte Carlo driven response surface methodology.

摘要

Response surface methodology (RSM) is a statistical method that explores the relationships between several descriptive variables and one or more response variables. For over sixty years, among other areas, it has been utilized in quality engineering, process engineering, aircraft engineering, economics, chemical engineering, automotive engineering and design/technique optimization. In this dissertation, RSM is utilized to produce regression models that represent the planetary entry, descent and landing (EDL) process. A complete understanding of EDL process is an essential component of any planetary exploration. Research in this area is ongoing and confidence in the ability to explore known celestial bodies is growing. The purpose of this research was to develop a unique technique for modeling EDL scenarios based on an understanding of the Martian atmosphere and the Viking Lander. A two degree of freedom trajectory simulation was developed for a Martian EDL. Statistical engineering was applied through formal experiment design to provide an empirical model between sixteen input variables and thirty-eight outputs pertinent to EDL. RSM was used in conjunction with the EDL simulation to develop second order regression models for each response as a function of all of the factors. The challenge comes when reducing the full quaradic model to a reduced model with the minimum amount of variables while remaining statistically sound. In this research full quadratic regression models were reduced using a technique developed during the research process called the Multiple Adjusted R-Squared Reduction (MARR) method. The MARR method is a process of reducing regression models so that their calculated Adjusted R-Squared (ARS) values are as close to a target ARS (chosen here as 0.99 +/- 0.004) as possible. Eighteen of the thirty-eight models developed met the Adjusted R-Squared target and were further used in Monte Carlo experiments to test the models dependence on the input variables and to develop EDL pertinent trade studies based on the reduced models.