Hall Effect Thruster Forecasting using a Topological Approach for Data Assimilation

TL;DR

The paper addresses forecasting spatiotemporal plume fields in Hall Effect Thrusters under non-Gaussian noise. It introduces a generalized Topological Approach for Data Assimilation (TADA) that can incorporate diverse forecast functions, demonstrated with an LSTM network. The method uses assimilation windows to form measurement and prediction point clouds, comparing their persistence diagrams via the Wasserstein distance to update model weights. Applied to high-fidelity AFRL HET simulation data, the approach yields substantially improved forecasts for electron temperature $T_e$ and, after smoothing to mitigate outliers, electric potential $\phi$, supporting robust, noise-model-free estimation of complex thruster plumes.

Abstract

Hall Effect Thrusters (HETs) are electric thrusters that eject heavy ionized gas particles from the spacecraft to generate thrust. Although traditionally they were used for station keeping, recently They have been used for interplanetary space missions due to their high delta-V potential and their operational longevity in contrast to other thrusters, e.g., chemical. However, the operation of HETs involves complex processes such as ionization of gases, strong magnetic fields, and complicated solar panel power supply interactions. Therefore, their operation is extremely difficult to model thus necessitating Data Assimilation (DA) approaches for estimating and predicting their operational states. Because HET's operating environment is often noisy with non-Gaussian sources, this significantly limits applicable DA tools. We describe a topological approach for data assimilation that bypasses these limitations that does not depend on the noise model, and utilize it to forecast spatiotemporal plume field states of HETs. Our approach is a generalization of the Topological Approach for Data Assimilation (TADA) method that allows including different forecast functions. We show how TADA can be combined with the Long Short-Term Memory network for accurate forecasting. We then apply our approach to high-fidelity Hall Effect Thruster (HET) simulation data from the Air Force Research Laboratory (AFRL) rocket propulsion division where we demonstrate the forecast resiliency of TADA on noise contaminated, high-dimensional data.

Figures (13)

• Figure 1: Hall-Effect Thruster (HET).
• Figure 2: Example plots of HET data using a single frame of the electron temperature signals. (a) shows a scatter plot of the spatial locations at one moment in time and (b) shows the corresponding contour plot of the field.
• Figure 3: Electron temperature data matrix for the first 2,500 time points.
• Figure 4: Example of point cloud persistence using the Vietoris-Rips complex. The frames in (a)--(e) show the simplicial complex at various stages of the filtration and values of the connectivity parameter $\epsilon$. The point cloud contains three loops, one of which is prominent ($\ell_1$) and persists relatively far from the diagonal with two smaller loops close to the diagonal ($\ell_2$ and $\ell_3$). These loops are shown in the 1D persistence diagram in (g) as (birth,death) pairs. The 0D persistence pairs (connected components) are also shown as red points along with the infinite persistence pair representing the fully connected component.
• Figure 5: Example minimizing the Wasserstein distance persistence function to reach a point cloud with a target persistence diagram. (a) shows the original point cloud and (b) shows the original persistence diagram and target persistence diagram. (c) shows the optimized point cloud and (d) shows the optimized persistence diagram with the loss plot in (e).