Adaptation of the Morris method to multi-dimensional factors for air-launch-to-orbit separation

This work is part of a technical study of the French space agency CNES (Centre National d'Etudes Spatiales) and the French aerospace laboratory Onera for the development of an air-launch-to-orbit system. This system, based on a dedicated aircraft and a space rocket, aims at offering more flexible dates and trajectories to micro-satellite launching missions. The separation phase between the carrier and the launcher requires deeper insight as it involves various dynamics and brutal changes of the system's parameters. The risk of collision is studied via the evolution of the minimum distance between the aircraft and the launcher after the release. A complete 3D simulation is developed with the system's data to reproduce various problems faced in the history of store separation such as aerodynamic interactions, mechanical malfunction, mass repartition, wind turbulence, improper ejection forces, or design uncertainties. The geometric constraints of the aircraft and rocket are set with limited planes and solids of revolution to allow effective calculations and representative results. The result of the collision study depends on a large number of uncertainty factors representing the variability of the launcher's and carrier's characteristics. In order to evaluate the relative influence of these uncertainties, a sensitivity analysis is performed. Because of the large number of factors, the classic Sobol's method cannot be directly used as it would require too much calculation. The Morris method can efficiently reduce the number of factors by factors fixing but it is normally limited to scalar factors and the separation simulation includes a multi-dimensional factor for the wind turbulences. Different studies, especially in Geographic Information System, showed the interest and the difficulty to use the Morris method with multi-dimensional factors but the problems raised have never been identified. One of the problems highlighted in this work is the variability of the Morris method's results due to the arbitrary choice of the samples used for the multi-dimensional factors. A separation simulation shows that the results are not only variable for the multi-dimensional factor for the wind, but also for classic scalar factors interacting with it, in particular in aerodynamics. Because of the lack of repetitiveness, 20% of the applications of the Morris method on a separation simulation do not provide correct factors influences, an aspect never discussed. The adaptation presented in this paper reduces the variability of the results by averaging the calculations and checking both the histogram and the correlation of the samples. The adapted Morris method followed by the Sobol's method efficiently identify the main factors affecting the variability of the collision results. It is shown that the main factors of the separation are the interaction on the launcher and aircraft, the wind turbulence, the release mechanism, and the relative position of the launcher and aircraft. Finally, two new methods dedicated to multi-dimensional factors representing time or space variations such as the factor for the wind are developed, one to include the amplitude uncertainty, and one to easily estimate the most important part of the time or space variation. It is shown that the influence of the beginning of the wind on the collision results is low, in spite of its effect on the aircraft's trajectory, but that the influence of its end is high because of its effect on the launcher.