Uncertainty quantification in the motion of a water-exit vehicle and analysis of the robustness enhancement characteristics of pressure-equalizing exhaust

In the presence of complex wave and current interactions, the carrying platform for a water-exit vehicle frequently exhibits random motions across all six degrees of freedom (6-DOF). The quantification of the robustness of the vehicle's motion under the perturbations induced by the platform's stochastic movements is of paramount importance. Additionally, it is crucial to conduct research into methods that may enhance the robustness of the vehicle's trajectory against such disturbances. In this study, we employ the non-intrusive polynomial chaos expansion for the uncertainty quantification analysis. We construct a sample space and utilize the least angle regression algorithm within the framework of compressed sensing to determine the polynomial chaos expansion coefficients. The research focuses on analyzing the uncertainties in the motion and attitude of a water-exit vehicle influenced by the random 6-DOF motions of the carrying platform. It also examines the mechanism by which pressure-equalizing exhaust contributes to the enhancement of robustness in multi-degree-of-freedom motions. The study performs a sensitivity analysis using the Sobol index to evaluate how the 6-DOF motions of the carrying platform affect the water-exit vehicle's attitude and the pressure inside the exhaust bubble. The study's results demonstrate that the water-exit vehicle undergoes pitch, yaw, and roll deviations attributed to the random 6-DOF motions of the platform. Importantly, the platform's pitch, heave, and forward velocity significantly influence the uncertainty bandwidth regarding the vehicle's pitch attitude. Upon water exit, the vehicle's pitch motion shows heightened sensitivity to the platform's forward velocity, whereas its sensitivity to the platform's heave and pitch motions declines. The roll, sway, and yaw motions of the carrying platform predominantly influence the radial dimension and shape of the exhaust bubble, explaining a significant portion of the variance in bubble pressure. The pressure-equalizing exhaust, which forms a gas film over the vehicle's surface, creates an “equal pressure and robustness” effect. This results in an ‘adaptive’ righting moment and enhances robustness against 6-DOF disturbances.