Uncertainty Analysis and Robust Design for a Hybrid Rocket Upper Stage

An uncertainty analysis is performed for a hybrid rocket engine, and a robust design method is proposed and applied to a liquid-oxygen/paraffin–based fuel hybrid rocket engine that powers the third stage of a Vega-like launcher. An indirect method is used to optimize a mission-specific objective function, which takes into account both the payload mass and the ability of the rocket to reach the required final orbit despite uncertainties. First, a screening of uncertain model parameters is performed using the Morris method. The screening shows that three groups can be distinguished: parameters with negligible or no effect on model outputs, parameters with small linear effect on model outputs, and parameters with large nonlinear effect on model outputs. The robust optimization design process is then carried out by a particle swarm optimization algorithm considering only the uncertainties of the latter group, which includes six parameters. A fractional factorial design of experiment techniques is considered to characterize the robust performance index. Average launcher performance is considered and the best solution is found by means of Box–Behnken’s array. Finally, the identified robust solution is checked against the second group of parameters uncertainties previously neglected in the robust optimization procedure. The scattering of the robust solution is small, and the robustness of the selected optimal solution is confirmed.