Design of Experiments Using Response Surface Methods to Optimize Simulated Reentry Trajectories

Due to the costly nature of performing flight tests of hypersonic vehicles, maximizing resource allocation is an extremely important part of system development. While Modelling and Simulation activities may help to reduce the number of actual flights that must be performed, computational costs can also be prohibitive. The test planner requires methods to reduce the number of simulation runs, while maximizing useful data output. Using modern Design of Experiments methods a test plan can be developed which minimizes simulation runs and enables determination of optimum initial flight conditions in order to satisfy desired flight parameters. The Common Aero Vehicle (CAV), a generic hypersonic aircraft, is an excellent case for the current design study. Reentry trajectories are simulated using the U.S. Air Force Flight Test Center’s PCSIM6D tool, software that implements the six degree of freedom equations of motion for a given control. Initial conditions for these trajectories were used as independent variables, or factors, in the experiment design, with maximum heating and maximum normal force as the resulting responses, or measures of performance. A 2 factorial design was implemented, then augmented with a face-centered central composite design. The data were then used to perform a regression and identify a response surface model to determine the optimal (minimal) stagnation heat flux. An additional constraint was added to maintain normal forces within the vehicle safety limits. With the response surface, it was then possible to estimate optimal initial conditions for the CAV trajectory, based on the observed heating encountered during the initial pull-up maneuver. It was discovered that heating was minimized when initializing with a relatively low velocity at an altitude of approximately 150,000 feet.