Stochastic re-entry trajectory analysis with uncertain initial conditions for safety assessment

In order to assess casualty risks of re-entry, it is necessary to analyze re-entry trajectories and evaluate physical phenomena related to safety such as ground impact area and kinetic energy of reentering objects. However, conventional trajectory analyses, which are conducted in a deterministic manner, may lack reality and reliability. In this paper, a stochastic re-entry trajectory analysis is conducted for an Apollo-type capsule with many uncertain initial conditions at break-up. The present interest is the uncertainty quantification (UQ) of falling range and ground reaching velocity. As a UQ method, Monte Carlo (MC) is the simplest and most classical, but it needs enormous number of sample points. Instead Kriging can approximate response of simulation output with a moderate number of samples and work for efficient UQ, but it does not perform well in a high-dimensional and strong non-linear UQ problem such as the present re-entry trajectory analysis. Hence this paper combines self-organizing maps (SOMs) for dimensionality reduction with the Kriging-based UQ method. The Kriging+SOM-based UQ method can gain the result which is not inferior to MC with less sample points, and significant physical factors to the uncertainties in falling range and ground reaching velocity are identified.