## Thesis etd-08212023-132243 |

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Thesis type

Tesi di laurea magistrale

Author

MARIANACCI, ALFREDO

URN

etd-08212023-132243

Thesis title

Scaling laws for Hall thrusters: statistical versus machine learning-based approach

Department

INGEGNERIA CIVILE E INDUSTRIALE

Course of study

INGEGNERIA AEROSPAZIALE

Supervisors

**relatore**Prof. Paganucci, Fabrizio

**tutor**Prof. Mazouffre, Stephane

Keywords

- electric propulsion
- gradient boosting
- hall thruster
- machine learning
- propulsion
- regression
- scaling laws
- space

Graduation session start date

26/09/2023

Availability

None

Summary

In recent years, Hall Thrusters are used in most of missions involving putting satellites into orbits around Earth. The advantages of using this type of propulsion technology must be found in the longer lifetime that ensures longer mission duration, in the high thrust-to-power ratio and the better efficiency. In addition, the versatility of these thrusters allows them to be used in a wide range of power levels, from microsatellites to larger space probes.

Despite the many studies carried out on the inner workings of the thruster, some physical processes that influence thruster performance still need explanation. This means that building a thruster from scratch is very complex and some methodologies were developed during the years to help the engineers in this purpose.

The methodologies used so far are all based on finding some physical relation between the parameters involved in the thrust processes. Thanks to these ones, it’s possible to find some proportional scaling laws that give an idea of how one parameter varies with respect to the other and allows to determine the characteristics that a new thruster must have if it has to satisfy some requirement in terms of thrust, power and specific impulse.

This dissertation initially validates a scaling methodology with the help of a well-constructed database, based on tests data of 59 thrusters, showing how to determine the characteristics (in particular the diameter, the height and the length of the channel) using the various laws that relate the parameters.

After, an innovative approach has been studied based on the use of supervised Machine Learning tools.

This approach starts with the use of basic machine learning as linear regression to predict the thrust having as inputs the parameters of the thruster.

After, more advanced supervised ML models were analysed, looking for the best one to use on the database. In this section also the specific impulse was added as parameter to be predicted together with the thrust and a differentiation in terms of several propellants used (Xenon, Kripton, Argon) was made.

The performances of the models were analysed according to the mean absolute error between the actual values and the values predicted by the model. As a final result, the Gradient Boosting Regressor was indicated as the best model.

Once the best model for the specific database was found, the problem of determine the inputs knowing the values of the outputs (thrust and specific impulse) was addressed. Two different approaches are presented:

the first one, graphical, is based on the construction of graphs with the help of the database and the ML model used (GBR). This method allows to visualize on graphs, differentiated by the type of propellant used, all the parameters involved in the thrust process and used to train the model in the prediction of the two outputs. In this way, choosing a point on the graph, it’s possible to determine in a first approximation the characteristics that a new thruster should have in terms of mass flow rate, voltage discharge, geometrical features and magnetic field.

The second approach, analytical, is based on an algorithm of optimization: the desired outputs in terms of thrust and specific impulse are indicated. The Gradient Boosting model predicts the two outputs as usual and the optimization algorithm moves the inputs in such a way that the two outputs predicted by the model are as close as possible to the desired outputs, minimizing the error.

The two approaches can therefore used in synchrony to have an estimation of the characteristics of the new thruster.

Despite the many studies carried out on the inner workings of the thruster, some physical processes that influence thruster performance still need explanation. This means that building a thruster from scratch is very complex and some methodologies were developed during the years to help the engineers in this purpose.

The methodologies used so far are all based on finding some physical relation between the parameters involved in the thrust processes. Thanks to these ones, it’s possible to find some proportional scaling laws that give an idea of how one parameter varies with respect to the other and allows to determine the characteristics that a new thruster must have if it has to satisfy some requirement in terms of thrust, power and specific impulse.

This dissertation initially validates a scaling methodology with the help of a well-constructed database, based on tests data of 59 thrusters, showing how to determine the characteristics (in particular the diameter, the height and the length of the channel) using the various laws that relate the parameters.

After, an innovative approach has been studied based on the use of supervised Machine Learning tools.

This approach starts with the use of basic machine learning as linear regression to predict the thrust having as inputs the parameters of the thruster.

After, more advanced supervised ML models were analysed, looking for the best one to use on the database. In this section also the specific impulse was added as parameter to be predicted together with the thrust and a differentiation in terms of several propellants used (Xenon, Kripton, Argon) was made.

The performances of the models were analysed according to the mean absolute error between the actual values and the values predicted by the model. As a final result, the Gradient Boosting Regressor was indicated as the best model.

Once the best model for the specific database was found, the problem of determine the inputs knowing the values of the outputs (thrust and specific impulse) was addressed. Two different approaches are presented:

the first one, graphical, is based on the construction of graphs with the help of the database and the ML model used (GBR). This method allows to visualize on graphs, differentiated by the type of propellant used, all the parameters involved in the thrust process and used to train the model in the prediction of the two outputs. In this way, choosing a point on the graph, it’s possible to determine in a first approximation the characteristics that a new thruster should have in terms of mass flow rate, voltage discharge, geometrical features and magnetic field.

The second approach, analytical, is based on an algorithm of optimization: the desired outputs in terms of thrust and specific impulse are indicated. The Gradient Boosting model predicts the two outputs as usual and the optimization algorithm moves the inputs in such a way that the two outputs predicted by the model are as close as possible to the desired outputs, minimizing the error.

The two approaches can therefore used in synchrony to have an estimation of the characteristics of the new thruster.

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