Predictive Analysis, Uncertainty Modelling of Hall Thruster Propulsion, Learning of Parametric Dynamical Systems

Abstract

The goal of this project is to identify dynamical system models from electric propulsion data. This is a system identification task with the purpose of determining the parameters of a delayed dynamical system. The process for identifying these unknowns uses Bayesian Inference. We employ a variation of Markov Chain Monte Carlo (MCMC), the Adaptive Metropolis Hastings Method, to characterize the posterior of the parameters that govern the dynamics. We first describe the probabilistic model to represent the posterior, which we sample via MCMC. This model characterizes data generated from multiple trajectories corresponding to different input conditions and model settings. The MCMC algorithm then begins with an initial sample that represents a preliminary guess of the unknown parameters. Samples are then proposed via an adaptive procedure and accepted based on the Metropolis Hastings accept-reject criterion. After several sampling iterations, the distribution can be analyzed to generate predictions for other settings with uncertainty due to the unknown parameters.