A method to predict the orbital lifetimes of free tethers and tethertrailing satellites using artificial neural networks
Abstract
The development of a method to predict the orbital lifetimes of uncontrolled free tethers and tethertrailing satellites originating in lowtomoderate altitude Earth orbits is discussed. The problem is solved by application of the 'empirical method.' Two mathematical models to simulate the orbital evolution of tethered systems are developed. In both models the system is discretized into a series of interconnected point masses, orbiting an oblate Earth and transiting an oblate, rotating, temporally and globally averaged atmosphere. For aerodynamic drag calculations, tether segments are modeled as right circular cylinders, and any endbody is modeled as a sphere. Drag coefficients vary as a function of shape and Knudsen number. In the 'multibody model', connections between masses are elastic, and the system is free to assume any orientation. Newtonian equations of motion are numerically integrated. In the 'orbital element propagation model', connections between masses are inelastic, and the system is constrained to remain aligned along the local vertical. Gauss' form of Lagrange's Planetary Equations, in terms of equinoctial elements, are used to propagate the orbital elements describing the orbit of the system's center of mass. The element propagation model is shown to provide, for initially unstretched systems aligned along the local vertical, accurate results, very quickly, as compared to those obtained using the multibody model. An algorithm to train feedforward artificial neural networks, by minimizing the sum of the squares of percent errors, is derived and shown to be invaluable in training networks to represent widelyspread realvalued data. A hybrid training approach, using the derived algorithm in conjunction with the standard back propagation training algorithm, is described and demonstrated. This approach often reduces network training time, and it is used to train three networks with lifetime data provided by the element propagation model: one to predict the orbital lifetimes of free tethers, one to predict lifetimes of upwarddeployed subsatellites trailing a tether, and one to provide correction factors that account for the effects of initial orbit inclination and argument of latitude. The accuracies of networkpredicted lifetimes, as compared to those obtained using the multibody model, are demonstrated in 90 cases with randomly chosen initial conditions and system physical dimensions. In all cases, the network's results are shown to be accurate to within plus or minus 20 percent of results obtained using the multibody model.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1992
 Bibcode:
 1992PhDT........52W
 Keywords:

 Mathematical Models;
 Neural Nets;
 Orbital Elements;
 Service Life;
 Tethered Satellites;
 Aerodynamic Drag;
 Drag Measurement;
 Earth Orbits;
 Equations Of Motion;
 Knudsen Flow;
 Spacecraft Design, Testing and Performance