Nonparametric Importance Sampling Techniques for Sensitivity Analysis and Reliability Assessment of a Launcher Stage Fallout

Abstract

Space launcher complexity arises, on the one hand, from the coupling between several subsystems such as stages or boosters and other embedded systems, and on the other hand, from the physical phenomena endured during the flight. Optimal trajectory assessment is a key discipline since it is one of the cornerstones of the mission success. However, during the real flight, uncertainties can affect the different flight phases at different levels and be combined to lead to a failure state of the space vehicle trajectory. After their propelled phase, the different stages reach successively their separation altitudes and may fall back into the ocean. Such a dynamic phase is of major importance in terms of launcher safety since the consequence of a mistake in the prediction of the fallout zone can be dramatic in terms of human security and environmental impact. For that reason, the handling of uncertainties play a crucial role in the comprehension and prediction of the global system behavior. Consequently, it is of major concern to take them into account during the reliability analysis. In this book chapter, two new sensitivity analysis techniques are considered to characterize the system uncertainties and optimize its reliability.

Global Reliability‐oriented Sensitivity Analysis under Distribution Parameter Uncertainty

“…During the flight, uncertainties can affect several variables in multiple disciplines (e.g., on the perturbation during trajectory or propellant combustion). For instance, focusing on the optimal trajectory assessment leads to consider the separation point as a key point in terms of uncertainty analysis (see, e.g., [35] for an illustration). In practice, separation altitudes may be lower than the Kármán line (which denotes the boundary between the Earth's atmosphere and outer space at around 100 km high).…”

Estimation of high-order moment-independent importance measures for Shapley value analysis

“…M consists of a simplified trajectory simulation code of the dynamic fallout phase of a generic launcher first stage. It has also been used in [74] for an extensive sensitivity analysis study. The simulation code needs to be given flight parameters describing the system state at the instant when the first-stage rocket boosters are ejected.…”

“…The latter is computed from measured data forwarded by embedded systems. The input probabilistic model is presented in Table 9 and it has already been deemed appropriate in previous works, see Table 1 from [74]. All variables are assumed to be independent and normally distributed.…”

Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures

“…We consider in this section a simplified trajectory simulation code of the dynamic fallout phase of a generic launcher first stage [17] which takes six input parameters into account. The input vector X contains the following Table 7 Input probabilistic model of the launcher phase fallout model.…”

“…Multiple fallout trajectories are drawn (red dotted lines), leading to the safe zone (yellow circular surface). Due to uncertainties, one fallout trajectory may lead to a failure impact point (red star) [cf [17]…”