Artificial neural networks for explainable thrust prediction in applied-field magnetoplasmadynamic thrusters

Abstract Electric propulsion devices are promising propulsion candidates for future sustainable orbital and deep-space missions. Applied-field magnetoplasmadynamic thrusters have gained particular interest among others, due to their ability to achieve high specific impulse, and their high thrust to exhaust plume area ratio. However, traditional models for thrust prediction (empirical/analytical formulas), which are crucial for thruster design stage, have faced various challenges over the years due to the complex coupling interactions between controllable and structural parameters. As a result, machine learning (ML) techniques have recently been implemented as an effective alternative to thrust prediction. This paper expands on that work by introducing neural networks (NNs) as an alternative ML technique to address the limitations of traditional models. Specifically, feedforward neural network (FFNN) and cascade-forward neural network (CFNN) are developed and compared in this paper. Additionally, this work provides an aspect of explainability into the black-box nature of the ML models by incorporating a SHapley Additive exPlanations (SHAP) analysis. Results show that with adequate training and hyperparameter tuning, both FFNN and CFNN outperform previous traditional models, with CFNN producing the highest $$\text {R}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>R</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:math> (99.83%), lowest RMSE (0.4136) and lowest MAE (0.1534).