Investigation Of Machine Learning Based Optical Diagnostics Methods For Hall Thrusters

In our digital era,smart computing and “artificial intelligence” algorithms are becoming more and more affordable as well as easy to implement.The democratization of such computing techniques has reached all of the fields of study from health research to space cartography.It is time for researchers to question themselves about the possible usages of new technologies.This master thesis details the application of deep neural networks – a kind of machine learning algorithms – to plasma optical diagnostics,more specifically to diagnostics upon Hall thrusters,using optical emission spectroscopy.The complexity of plasma optical diagnostics results in difficulties when trying to automatize the process in industry.Indeed,the chosen process depends widely on the considered kind of plasma,and even then,usual methods tend to be painful to apply.This is why we had the idea of developing a computing process involving machine learning instead of standard model-based algorithmics.The analysis algorithm developed in the present thesis outputs a set of plasma parameters when given as input said plasma's emission spectrograph.We developed the algorithm until a point where it is highly efficient and complete.More specifically,our work aims at working around the main difficulties that come with optical diagnostics of plasma such as the estimation of scaling factors for one part while improving the time-reliability ratio of the diagnostics method.If not for new processes such as the one developed in our research,a fast,standardized and reliable estimation of the plasma parameters is virtually impossible.Standardization is indeed the key of our work: once the algorithm is designed and running,it can be adapted for most plasma sources without any structural changes.This is made possible by the use of the adaptive technologies that are machine-learning based algorithmics.In this master thesis report,we present a complete algorithm able to efficiently perform optical diagnostics of plasma produced by Hall thrusters,based solely on a partial emission spectrograph.The processing chain comports several functional subprocesses executing the steps of descaling the given spectral lines,estimating the missing lines and finally estimating the plasma parameters.Several of these subprocesses are based on deep learning algorithms of several forms: linear feedforward neural networks,Restricted Boltzmann Machines,Deep Belief Networks.Demonstrating the efficiency of high-end machine learning algorithms and computing devices when performing research tasks such as plasma diagnostics is a secondary goal of our research,the main objective being to provide laboratories with a fully integrated diagnostics tool.Currently and for purpose of design simplicity,our algorithm only outputs the average electronic temperature Te and electronic density ne.We explain in this document how to expand the capabilities to more plasma parameters.Based on an analogy with broad facial recognition software,our algorithm doesn't try to calculate the plasma parameters from a spectrograph,but rather to retrieve the most similar spectrograph to an input in a precompiled database of labelled spectra.Once the k closest matches are retrieved,an interpolation is achieved on them and its result is delivered.This way allows the software to work – ideally – independently from any plasma model;and it avoids the problem of nonlinearity concerning the equations linking spectrographs to plasma parameters.The heart of the diagnostics engine is the k-Nearest Neighbor(k-NN)search over the database of labelled spectra.We would like the reader to notice that this process is very different from directly calculating the output from the input.Our process allows simpler deduction of the output,but to the cost of applying the errors from the database to the output.On the other hand,our method does not necessitate to fit the highly nonlinear correlation between input and output,and thus guarantees a broader application range.Two algorithms are successively presented.The first one is an implementation of direct abstract feature extraction,meaning that we transform the input spectrum into a vector from a low dimensional parametric space and then perform a neighbor search on a similarly transformed database in order to find the plasma parameters;the second one uses an implementation of Vector-based Multiprobe Locality Sensitive Hashing to find the plasma parameters in a database,after several preprocessing steps.For this algorithm – more advanced than the first one – a control loop is added to increase greatly the efficiency of preprocessing.It uses Collisional-Radiative models in the feedback loop.All of our algorithms are trained on synthetic data – generated by CollisionalRadiative models – to the exception of the Scaling Factor Generator,which is trained on a mixed database of experimental and synthetic data.The use of synthetic data,by which we mean data artificially generated from plasma models instead of acquired from an experimental set,is justified by the cardinalities of our training databases as well as by antecedents in literature review.The experimental data is preferred for validation of the overall algorithm,and by all means required for training the Scaling Factor Decoder.The first algorithm introduced corresponds to our initial design to solve our problem.Confronted to the issue of retrieving the closest element to an input in a very large database(possibly tens of thousands of elements at least,up to a million)in high dimension,we focused on algorithmic complexity reduction.The high dimension of the database comes from the number of plasma parameters considered,between two and a dozen.The high cardinality comes from the precision on each axis of the database.In order to reduce algorithmic complexity,the general idea was to project the elements of the database into a low-dimensional space with specific properties,such as global convexity,while preserving the data locality.Once this is achieved,retrieving an element can be as simple as a gradient descent search.However imprecise this might be,it is extremely fast;once an imprecise neighborhood is reached,a more precise search function can be applied to find the actual closest match.While the first algorithm leads to interesting conclusions regarding the capacities of neural networks for plasma research purposes,its reliability in retrieving plasma parameters from a spectrograph are too limited.This is explained by the shape of the implicit functions from plasma physics that link a spectrograph to is plasma parameters.These functions are highly non-linear,which causes troubles when training neural networks like ours.We will detail more precisely why that is,and how it could be worked around.Mostly,we left this algorithm aside because the implementation of the preprocessing steps – for the second algorithm – diminished the necessity of employing high dimension and high cardinal databases,allowing us to move on to a more conventional search engine,such as the vector-based multiprobe locality sensitive hashing.The second algorithm we designed presents with great accuracy and reliability for this task.The parameters are retrieved with error around a percent,and the effective range extends to the whole training range.Such performance is achieved mainly thanks to the addition of the control loop and the preprocessing steps,conditioning the inputs almost ideally.Implementing the control loop between the output of the algorithm and the last preprocessing step,the Spectrum Generator,was the key to improving our algorithm's capacities.Thanks to the feedback,we can eliminate the errors coming from the artificial generation of spectral lines and ensure that the generated spectrum corresponds indeed to the real partial spectrum.Furthermore,we have confirmation that the match found in the database corresponds indeed to the partial input spectrum instead of a cornered divergence of the search process.This reliability factor is extremely important when diagnosticating a plasma source.However,forcing the generative model that is the Spectrum Generator to accept a feedback input is not an easy task;a solution has been proposed and implemented,but the issue could deserve a more specific neural network.The preprocessing steps are of primary importance not only as part of the algorithm,but also as separate tools for a research laboratory.The subprocess responsible for descaling and completing the spectra can be used separately to suit other purposes of Optical Emission Spectroscopy(OES).They are based on generative models,trained on either synthetic or experimental data.The descaling subprocess estimates the scaling factors of every spectral lines on the input;such result can be highly valued for optical emission spectroscopy.Estimating the scaling factors is a major issue in OES,and this specific subprocess should be given dedicated attention for further improvement in reliability and accuracy.Our second algorithm is highly efficient and presents with very low error rates.It constitutes an asset for optical diagnostics of plasma from Hall thrusters,because of its simplicity in usage and reliability of design.However,we will keep on improving its ability and generalize to different plasma sources,as well as broadening its spectrum of output plasma parameters.In the last section of the present master's thesis report,we will present the reader with a real use-case example.A plasma source recreating similar physical conditions to those of a hall thruster in a space chamber will be diagnosed using two different methods.The first method will use a Langmuir probe inserted inside of the plasma while the second method will be using our algorithm coupled with a spectrometer.This test is in fact a series of five experiments,each comporting eleven diagnostics.We will compare the resulting diagnostics from both methods as an illustration of our process' capabilities.The plasma parameters calculated from these two methods are very close,indicating that the real use-case test is successful.If one series of tests cannot be statistically significant,these fifty-five diagnostics are a decent indicator that our algorithm is performing as expected.In a word,the goal of this research project is to provide laboratories with a tool for optical diagnostics based on machine learning.Our work also aims at demonstrating the efficiency of such high-end algorithmic techniques for plasma research and we wish to motivate the readers to investigate in turn similar deep learning based solutions to solve well-known applied plasma physics issues.The specific issues dealt with in this report will stay under investigation for further master thesis,until the tool is finally complete and ready to be distributed;in particular,it will be tested exhaustively on experimental data in order to ensure its reliability.This report is divided into four parts.Firstly,we will introduce the background and motivations for this research.After introducing the subject in exhaustive details,we will briefly deliver some basic elements to the understanding of both optical plasma diagnostics and machine learning.Our second section will be dedicated to the first version of the algorithm: a neural network based search engine,using abstract feature extraction to find the closest matches.Going through the design steps will help bring to a clearer understanding of the key issues regarding our problem.Additionally,this section will prepare the coming of the third section: our final algorithm.In this part,we will detail the functioning principle of every technical subprocess one by one,as well as the whole algorithm.This algorithm received most of our attention during the course of this project and should therefore be considered as the greatest result of this master thesis.We will conclude the document with an analysis of our results and a discussion concerning their conclusions.