detection and identification of instability and blow-off
TRANSCRIPT
KTH Industrial Engineeringend Management
Detection and Identification ofInstability and
Blow-off/Flashback Precursors inAeronautical Engines using Deep
Learning techniques
Antony CELLIEREmail: [email protected] / [email protected]
MASTER of SCIENCE THESISKTH School of Industrial Engineering and Management
Energy Technology EGI-TRITA-ITM 2020:66DIVISION of HEAT and POWER TECHNOLOGY
SE-100 44 STOCKHOLM, SWEDEN
Master of Science Thesis EGI-TRITA-ITM-EX 2020:66
Detection and Identification of Instability and Blow-off/Flashback Precursors
in Aeronautical Engines using Deep Learning techniques
Antony CELLIER
Approved Examiner Supervisor
2020/03/11 Björn LAUMERT Nenad GLODIC
Commissioner Contact Person
Thierry POINSOT
Abstract
The evolution of injection processes toward more fuel efficient and less polluting combus-tion systems tend to make them more prone to critical events such as Thermo-Acoustic In-stabilities, Blow-Off and Flash-Back. Moreover, the addition of Di-Hydrogen as a secondaryor as the main fuel is in discussion by aeronautical engines manufacturers. It drasticallymodifies the stability of the system and thus raise several interrogations concerning the mul-tiplicity of its use. Being able to predict critical phenomena becomes a necessity in orderto efficiently operate a system without having to pre-test every configuration and withoutsacrificing the safety of the user. Based on Deep Learning techniques and more specificallySpeech Recognition, the following study presents the steps to develop a tool able to success-fully detect and translate precursors of instability of an aeronautical grade swirled injectorconfined in a tubular combustion chamber. The promising results obtained lead to proposalsfor future transpositions to real-size systems.
Keywords: Thermo-Acoustic Instabilities, precursors, Deep Learning, Speech Recogni-tion.
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Sammanfattning
Utvecklingen av injektionsprocesser mot mer bränsleeffektiva och mindre förorenande för-bränningssystem, tenderar att göra dem mer benägna att utsättas för kritiska händelser somThermo-Acoustic Instabilities, Blow-Off och Flash-Back. Dessutom diskuterar flygmotorkon-struktörer möjligheten att använda Dihydrogen som sekundärt eller som huvudbränsle. Detmodifierar drastiskt systemets stabilitet och det väcker frågan hur man kan använda det effek-tivt. Att kunna förutsäga kritiska fenomen blir en nödvändighet för att använda ett system utanatt behöva att på förhand testa varje konfiguration och utan att reducera användarens säkerhet.Baserat på Deep-Learning-tekniker och Speech-Recognition-tekniker, presenterar följande studiestegen för att utveckla ett verktyg som kan upptäcka och översätta föregångare till instabilitethos en swirled flygmotorerinsprutningspump som är innesluten i en förbränningskammare. Delovande resultaten leder till idéer om hur man kan anpassa det här verktyg till ett system i verkligstorlek.
2
Contents
1 Introduction 9
2 Presentation of the structures involved 102.1 CERFACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 IMFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 ISAE-Supaero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 European Research Council . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.3 Safran Aircraft Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Presentation of SCIROCCO 113.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 The Master-Thesis project within SCIROCCO . . . . . . . . . . . . . . . . . . . 11
4 Experimental setup 12
5 Combustion theory 145.1 Combustion instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1.1 Interactions between acoustics and flames . . . . . . . . . . . . . . . . . . 145.1.2 Simple energy criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.1.3 Limits of simple criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.1.4 Toward precursors of instability . . . . . . . . . . . . . . . . . . . . . . . . 17
5.2 Blow-off event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.3 Flash-back event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6 Preliminary Data Analysis: Combustion Instabilities 196.1 Conducted experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196.2 Stability map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.2.1 RMS Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.2.2 Crest factor Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.3 Precursors of instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236.3.1 Burst detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236.3.2 Burst detection and usual stability analysis . . . . . . . . . . . . . . . . . 256.3.3 Updated stability maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7 Deep Learning theory 287.1 Introduction to Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7.1.1 Definition of Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . 287.1.2 Toward Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.2 Tasks definition for the current problem . . . . . . . . . . . . . . . . . . . . . . . 317.2.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317.2.2 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.3 Applying Deep Learning to combustion instabilities . . . . . . . . . . . . . . . . . 327.3.1 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327.3.2 Basis of the implemented models . . . . . . . . . . . . . . . . . . . . . . . 33
7.4 Building blocks of a SR Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.4.1 Learning local features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337.4.2 Learning global features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.4.3 Interpreting the learnt features . . . . . . . . . . . . . . . . . . . . . . . . 34
7.5 Classical limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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7.5.1 Introduction to generalization defects . . . . . . . . . . . . . . . . . . . . . 357.5.2 Addressing generalization defects . . . . . . . . . . . . . . . . . . . . . . . 357.5.3 Conclusion on generalization . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.6 Conclusion : Building a state-of-the-art Speech Recognition Network . . . . . . . 37
8 Apply Deep Learning to the experimental results 388.1 First Step : Classifying signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.1.1 Preparation of the Deep Learning study . . . . . . . . . . . . . . . . . . . 388.1.2 Summary of the Learning task . . . . . . . . . . . . . . . . . . . . . . . . 418.1.3 Define a learning architecture . . . . . . . . . . . . . . . . . . . . . . . . . 428.1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
8.2 Second Step : Generalization of the results . . . . . . . . . . . . . . . . . . . . . . 458.2.1 Preparation of the Deep Learning study . . . . . . . . . . . . . . . . . . . 458.2.2 Summary of the Learning task . . . . . . . . . . . . . . . . . . . . . . . . 468.2.3 Define a learning architecture . . . . . . . . . . . . . . . . . . . . . . . . . 478.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
8.3 Third Step : Toward an operable detection system . . . . . . . . . . . . . . . . . 498.3.1 Preparation of the Deep Learning study . . . . . . . . . . . . . . . . . . . 498.3.2 Summary of the Learning tasks . . . . . . . . . . . . . . . . . . . . . . . . 528.3.3 Define learning architectures . . . . . . . . . . . . . . . . . . . . . . . . . 528.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
9 Discussion 599.1 Machine Learning and the concept of "Black Box" . . . . . . . . . . . . . . . . . 599.2 Validation of the use of CNN with LSTM . . . . . . . . . . . . . . . . . . . . . . 599.3 Robustness to modifications of the experimental conditions and setup . . . . . . . 61
10 Conclusion 63
11 Appendices 6611.1 APPENDIX 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6611.2 APPENDIX 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6811.3 APPENDIX 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6911.4 APPENDIX 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7011.5 APPENDIX 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7211.6 APPENDIX 9.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4
List of Figures
1 Schematic of MIRADAS the experimental setup on which the analysis is per-formed [27] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Detail of the injector for the MIRADAS experiment [27] . . . . . . . . . . . . . . 133 Destruction of a US rocket engine part due to combustion instabilities [30]. . . . 144 Combustion instability growth: linear and non-linear zones [32], [31]. . . . . . . . 175 Experimental grid of the operating points acquired during the experimental study 196 Schematic representation of the injection configurations [27] . . . . . . . . . . . . 207 Mapping of the RMS of the pressure from M1 in case Ref with acoustic dB. . . . 228 Mapping of the ratio between the crest factor for the pressure from M1 in case Ref 229 M1 microphone signal for the case Ref at Usw = 30m.s−1 and φ = 0.8 . . . . . . 2310 Product of HW hot-wire and M1 microphone signals for the case Ref at Usw =
30m.s−1 and φ = 0.8 normalized by its RMS . . . . . . . . . . . . . . . . . . . . . 2411 Burst detection applied on the product of the M1 microphone and HW hot-wire for
the case Ref at Usw = 30m.s−1 and φ = 0.8, (a) Burst detection power spectralamplitude, (b) product of the M1 microphone and HW hot-wire normalized by itsRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
12 Estimation of the Rayleigh criterion on the case Ref at Usw = 30m.s−1 andφ = 0.8, (a) Burst detection power spectral amplitude, (b) Measure of the delaybetween pressure and heat release, (c) M1 microphone output normalized by itsRMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
13 Mapping of the number of bursts detected during the acquisition time in case Ref 2614 Mapping of the average energy of the bursts in case Ref with logarithmic scaling
(E0 = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2615 Schematic representation of the concept of supervised Machine Learning [5] . . . 2816 Schematic representation of the learning process in supervised Machine Learning
[5], [21] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917 Schematic representation of the learning process in Deep Learning for a multi-layer
architecture [5], [14] ch. 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3118 Schematic representation of a typical convolution block to build a CNN . . . . . 3319 Schematic representation of a SR network, variations are used in § 8 [47] . . . . . 3720 Example of selection of samples in a bursting signal for the First Approach. (M1)
Normalized pressure from M1, (M1.HW) Normalized product of the pressure M1and the velocity HW, (PM) Normalized heat release from PM . . . . . . . . . . . 39
21 Scores extracted from the signals for the case Ref and RMS mapping of M1microphone signal as a font . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
22 Examples signal shapes generally found for each class for the case Ref (RMSmapping of M1 microphone signal as a font) . . . . . . . . . . . . . . . . . . . . . 40
23 Schematic representation of the network used in § 8.1 and § 8.2 . . . . . . . . . 4224 Training results of the First Approach : (a) Training and validation Accuracy, (b)
Training and validation loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4325 First Approach : Network output on a rolling window for the test case MH1,
Usw = 30m.s−1, φ = 0.8. (a) Network prediction, (b) M1 Microphone pressuresignal. Ground Truth is represented by a continuous red line (Class 2 for thisoperating point). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
26 First Approach : Network output on a rolling window for the test case MH1,Usw = 30m.s−1, φ = 0.8, Focus on a 1s window. (a) Network prediction, (b) M1Microphone pressure signal. Ground Truth is represented by a continuous red line(Class 2 for this operating point). . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
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27 Example of selection of samples in a bursting signal for the Second Approach. (M1)Normalized pressure from M1, (M1.HW) Normalized product of the pressure M1and the velocity HW, (PM) Normalized heat release from PM . . . . . . . . . . . 46
28 Training results of the Second Approach : (a) Training and validation Accuracy,(b) Training and validation loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
29 Second Approach : Network output on a rolling window for the test case MH1,Usw = 30m.s−1, φ = 0.8. (a) Network prediction, (b) M1 Microphone pressuresignal. Ground Truth is represented by a continuous red line (Class 2 for thisoperating point). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
30 Second Approach : Network output on a rolling window for the test case MH1,Usw = 30m.s−1, φ = 0.8, Focus on a 1s window. (a) Network prediction, (b) M1Microphone pressure signal. Ground Truth is represented by a continuous red line(Class 2 for this operating point). . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
31 Architecture of the 3 networks system for precursors of instability detection . . . 5032 Schematic representation of the labels attribution on a truncated map (RMS map-
ping of M1 microphone signal as a font) . . . . . . . . . . . . . . . . . . . . . . . 5133 Management of the boundary conditions in terms of neighbour number evaluation
N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5234 Labels attribution in the Third Approach for the case Ref (RMS mapping of M1
microphone signal as a font) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5235 Training results of L1 : (a) Training and validation Accuracy, (b) Training and
validation loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5436 Training results of L2.1 : (a) Training and validation Accuracy, (b) Training and
validation loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5437 Training results of L2.2 : (a) Training and validation Mean Absolute Error, (b)
Training and validation loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5538 Third Approach : Averaged predictions for the test case MH1 (RMS mapping of
M1 microphone signal as a font) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5639 Third Approach : Reference label attribution for the test case MH1 (RMS map-
ping of M1 microphone signal as a font) . . . . . . . . . . . . . . . . . . . . . . . 5640 Third Approach : Localisation of sources of errors for the test case MH1, (RMS
mapping of M1 microphone signal as a font). . . . . . . . . . . . . . . . . . . . . 5741 Third Approach : Networks outputs on a rolling window for the test case MH1,
Usw = 30m.s−1, φ = 0.8. (a) L1 instability prediction I, (b) L2.1 prediction ofthe number of unstable neighbours N , (c) L2.2 prediction of the RMS amplitudeof the unstable neighbours Y , (d) M1 Microphone pressure signal. Ground Truthsare represented by a continuous red line (I = 0, N = 2, Y = 0.49). . . . . . . . . 58
42 Comparison of the networks outputs on a rolling window for the test case MH1,Usw = 30m.s−1, φ = 0.8. (a) MLP output, (b) CNN output, (c) CNN + LSTMoutput, (d) M1 Microphone pressure signal. Ground Truths are represented as acontinuous red line (2 unstable neighbours for this operating point) . . . . . . . . 60
43 Mapping of the RMS of the pressure from M1 in case Ref2 with acoustic dB forExp 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
44 Representation of the potential use of the system developed in § 8.3 . . . . . . . 6345 Scheme of the weighted average used for neighbour influence determination in
Algorithm 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7046 Schematic representation of the algorithm for label attribution (Algorithm 2) . . 7047 Schematic representation of the network used in § 8.3 to associate the number of
unstable neighbours and their average amplitude to a signal element. . . . . . . . 7248 Reconstruction with 60 modes of a sample from M1 in the case Ref, Usw =
30m.s−1, φ = 0.8, for a window of 15 ms . . . . . . . . . . . . . . . . . . . . . . . 73
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List of Tables
1 Fuel injection configurations used for data acquisition [27] . . . . . . . . . . . . . 212 Summary of the first learning task . . . . . . . . . . . . . . . . . . . . . . . . . . 413 First Approach : Precision of the network . . . . . . . . . . . . . . . . . . . . . . 434 Summary of the first learning task . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Second Approach : Precision of the network . . . . . . . . . . . . . . . . . . . . . 476 Summary of the learning tasks for the three networks system . . . . . . . . . . . 537 Third Approach : Precision of the networks L2.1 and L2.2 . . . . . . . . . . . . 568 Comparison of the precision of the networks . . . . . . . . . . . . . . . . . . . . . 609 Comparison of the experimental setup for the first and second campaign. . . . . . 6110 Comparison of the atmospheric conditions for the first and second campaign. . . 6111 Precision of the networks L2.1 and L2.2 on Exp 2 . . . . . . . . . . . . . . . . . 61
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Nomenclature
¯τ tensor of viscous stresses
ωT heat release rate
mF fuel mass flow rate
mO oxidizer mass flow rate
γ specific heat ratio
λ thermal conductivity
φ equivalence ratio
ρ density
~u velocity vector
c local sound speed
Cp constant pressure heat capacity
e acoustic energy
Fs sampling frequency
g growth ratio
p pressure
r mass ideal gas constant
s stoichiometric mass ratio
Sn swirl number
T temperature
Usw bulk velocity - controlling the mass flow rate of the setup
x∗ complex conjugate of the magnitude x
x0 mean value or steady value of the magnitude x
x1 perturbation or unsteady value of the magnitude x
XmCH4
proportion in mass of CH4
XmH2
proportion in mass of H2
MAE Mean Absolute Error
MSE Mean Square Error
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1 Introduction
The recent discussions on energy production are strongly influenced by the environmentaland climatic context. Heading to resilient sources of power is essential both in terms of pollutionand of fuel production. The aeronautical field is not spared. More efficient systems have tobe developed, with a focus on fuel consumption and pollutant emission, without neglecting theoperating safety.
Lean premixed combustion is currently one effective way of reducing the consumption andensuring generally low pollution levels. However, this type of combustion is subject to criticalevents that can be crippling in terms of safety. Unsteady phenomena such as Thermo-AcousticInstabilities, Blow-Off or Flash-Back are more likely to spontaneously appear, reducing the per-formances of the device in the best cases, increasing the risks of accident in the worst ones [42],[31]. In parallel with lean premixed injection, the use of fuel mixing is under study in order toboth increase the safety and address the initial environmental problem.
In this framework, Di-Hydrogen (H2) is a serious candidate. As it is a carbon-free fuel, itis efficient for the reduction of Carbon-Dioxide emission and has interesting flammability limits.Using H2 as a side fuel has been under study for several years [17], [4], [39], [38]. It is bothinteresting for direct power generation, when it is used as the principal fuel and for stabilizationpurposes [27]. Finally, producing H2 can be done without any fossil resources or as a by-productof common fossil fuel generation, which is essential for the transformation of the energy mix tocome.
Yet, H2 addition poses problems as it does not necessarily mitigate unsteady phenomena andcan even trigger them if it is misused. Also, the cost and time needed to test every configurationpossible with every level of H2 injection would be limiting. Plus, this multiplicity of tests wouldnot ensure a perfect safety. Consequently, techniques to predict and counter oncoming criticalphenomena are to be analysed and developed.
Diverse techniques based on signal analysis were proposed to counter Thermo-Acoustic In-stabilities [32], [26]. However, it is still a complex question to predict such phenomena. Severalgroups have worked on the definition of precursors of unsteady phenomena [12], [19], [25]. Furtherdetecting precursors is also in discussion but reveals difficulties [37], [33], [2].
With the recent improvement of computational power and the evolution of GPUs, DeepLearning techniques applied to physics are now accessible. This study aims at using DeepLearning tools to build an efficient predictor for combustion instability of a confined swirledaeronautical grade injector.
First of all, the frameworks of the study are described, including the experimental setupand the phenomena observed. Later, an introduction to Deep Learning and explanations on theconstruction of the models used in this study are given. The evaluation of the system developedis then performed. Finally, discussions on how to capitalize on the results is proposed in order toapproach a future practical objective: developing an efficient predicting tool for critical eventsin combustion systems and more specifically, aeronautical engines.
9
2 Presentation of the structures involved
2.1 CERFACS
The CERFACS (for Centre Européen de Recherche et de Formation Avancée en Calcul Sci-entifique or European Centre for Research and Advanced Training in Scientific Com-puting) is a french civil society specialised in offering solutions for companies regarding complexphysical and computational problems. Involved in several subjects such as Fluid Dynamics, Com-bustion, Environment or Climate, the CERFACS has been creating partnerships with companiesin order to ease the access to convenient solutions (Safran, Airbus Group, CNES, ONERA, MétéoFrance, EDF, Total). It is also allied to french research groups (CNRS, IRIT, CEA and INRIA)and dispenses education and training for academics and companies. The teams of CERFACSare mainly composed of engineers and researchers from a large variety of fields corresponding tothe missions of the company. Because of its multidisciplinary profile, the thesis was linked toboth Combustion groups and Deep Learning groups. All computations and experimental dataanalysis were conducted at the CERFACS.
2.2 IMFT
The IMFT (for Institut de Mécanique des Fluides de Toulouse or Fluid Dynamics Insti-tute of Toulouse) is a research laboratory joint with CNRS (Centre National de la RechercheScientifique), the Polytechnic Institute of Toulouse and the Paul Sabatier University. Its mis-sions are widely shared between the different aspects of research in fluid dynamics. The teamconcerned with combustion has access to test facilities and experimental setups to perform ad-vanced research for aeronautics, energy production or transportation. It is composed of engineersresearchers and PhD students specialised in the subject. All experimental works have been con-ducted in the laboratories of the IMFT and in collaboration with the entire team and morespecifically Andrea ANIELLO and Titouan MORINIERE who have PhD student positions.
2.3 Supports
2.3.1 ISAE-Supaero
The ISAE-Supaero (for Institut Supérieur de l’Aéronautique et de l’Espace or Aeronauticsand Aerospace superior Institute) is an engineering school and a research laboratory spe-cialised in aeronautics and aerospace problems. It gathers engineering students, PhD studentsand researchers in all the fields concerned by these problems (aerodynamics, propulsion, elec-tronics, computer science, applied mathematics, ...). The institute offered their advice aboutboth combustion and deep learning matters during the master thesis.
2.3.2 European Research Council
The ERC (for European Research Council) is a supporting entity that offers financialand academic help to researchers. They fund, spread and structure projects in order to ease thecompletion of the aim and give resonance to its applications. The SCIROCCO project has beenfunded by an ERC advanced grant for five years. It is an essential partner along the path to theresults proposed in this work.
2.3.3 Safran Aircraft Engines
Safran Aircraft Engines is a french aeronautic engine constructor. It is part of the Safrangroup. Safran Aircraft Engines offered a technical support to the project by providing the injectorand swirlers of the experimental setup. It is of aeronautical category such that it reproduces the
10
behaviour of the injection of a real aircraft engine. The study is thus possibly transferable tofuture industrial applications.
3 Presentation of SCIROCCO
3.1 Context
Under the context of global warming and energetic transition, the SCIROCCO project iscreated to assert the question of Di-Hydrogen in combustion. Changing the energy mix hasbecome a key problem in modern combustion. The use of renewable gases such as Di-Hydrogenwould be game-changing.
However, knowledge on both the storage and the proper utilization of this gas is still lacking.The project is thus dedicated to the study of solutions involving Di-Hydrogen for flame stabiliza-tion and energy production. Enhancing existing systems and developing new combustion devicesis the practical aim of the whole venture.
The project is funded by an ERC advanced grant for the next five years and led by Pr.Thierry POINSOT, research director at IMFT and scientific council at CERFACS. In order toefficiently address both experimental and numerical problems, the IMFT and the CERFACSjoined their expertise.
3.2 Experiments
The experimental setups available to reach the objectives of the project are of three natures:
1. Small laminar flames controlled by H2
2. Turbulent swirled two-phase flames controlled by H2 injection.
3. Flames stabilized on porous burners
The first type of experiments concerns the development of new solutions for both domesticand industrial heaters in order to substitute efficiently current fuels by H2. The second typeof experiments concerns the control of pre-existing systems by adding a restrained quantity ofDi-Hydrogen. Stabilization effects are thus asserted on aeronautical class injectors for a potentialuse in future aircrafts. The third type of experiments is focused on the study of porous mediato control and stabilize H2 for a potential domestic use for stoves, heaters, ...
The diversity of the experiments is thus an asset to tackle, in the widest way, the issuesencountered when substituting usual fuels by H2.
3.3 The Master-Thesis project within SCIROCCO
Changing the fuel mix for aeronautic injectors is a thorny issue as it is accompanied by drasticchanges of the behaviour of the system concerning instabilities. Major changes of its sensibilityto rapid bifurcations from stable to unstable states is often observed. It is therefore of firstimportance to predict the incoming instabilities.
The following work asserts the possibility to use Deep Learning techniques (See § 7) inorder to detect and identify efficiently precursors of instability in a swirled aeronautical-classinjector confined in a cylindrical combustion chamber (See § 4). The fuels studied are Methane(CH4) and Di-Hydrogen. The main aim is therefore to implement a first demonstrator of theDeep Learning study of this laboratory scale experiment to open the field of possibilities to atransposition to, first and foremost, liquid fuels, then annular combustion chambers and finallyreal bench engine configurations. The results obtained during the thesis will be used in the frameof a joint PhD work between the IMFT, the CERFACS and Safran Aircraft Engines under theSCIROCCO project.
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4 Experimental setup
The experimental setup, namedMIRADAS, studied in this document is presented in Figure1. It is an evolution of the system used by Palies et al. [28] and Durox et al. [9].
Photo-Multiplier
Quartz
Microphone M1
Microphone MB
Water Cooling
Piloting FuelInjection Tube
Hot Wire
Honeycomb
Main MixtureInjection
Main MixtureInjection
Telecentric Lens
Ø 65 mm
Ø 22 mm
258
mm
60 m
m96
mm
297
mm
PL
EN
UM
CO
NV
ER
GE
NT
CO
MB
US
TIO
N C
HA
MB
ER
Swirler
Figure 1: Schematic of MIRADAS the experimental setup on which the analysis is performed [27]
12
The instrumented system is composed of a swirled injector in a cylindrical combustion cham-ber. The main mixture is injected in the lower part of the plenum of circular cross-section andhomogenized by a honeycomb panel. Then, the flow passes through a convergent and startsrotating after its injection through the swirler. The flamed is anchored at the base of the com-bustion chamber which is a cylindrical transparent quartz tube. The confinement of the flameallows the appearance of thermo-acoustic instabilities (See § 5) which is the first purpose of thissetup. The swirler, the length and diameter of the chamber and the length of the plenum arechangeable to modify the structure and behaviour of the burner.
A zoomed schematic of the injector is given in Figure 2. The central tube is used to injectpure fuels in order to observe flame piloting. It allows to modify instability triggering and offersa diversity of fuel configurations. In this study, the configurations involve both Methane (CH4)and Di-Hydrogen (H2). The different types of injection are presented in § 6.
Figure 2: Detail of the injector for the MIRADAS experiment [27]
To study instabilities, the system is equipped with a set of 2 microphones for the measurementof unsteady pressures. The microphones are located at the bottom of the plenum (MB) andthe exit section of the convergent (M1). At this location, the microphone M1 is coupled with aconstant temperature hot-wire for velocity measurement (HW).
Thanks to the presence of a transparent combustion chamber, the measurement of unsteadyheat release can be performed by a Photo-Multiplier (PM). When used with a band-pass filtercentered on the emission spectrum of CH∗ radicals, it is possible to retrieve the heat release ratefluctuations.
The system is also equipped with a telecentric lens to obtain photographs of the flame. Thislast equipment has not been used during the thesis.
The MIRADAS experiment is therefore a versatile system capable of using different fuelsunder different injection configurations. Furthermore, its resilience to large amplitude oscilla-tions of the flow parameters makes it efficient to study combustion instability phenomena. Thediagnostics added through sensors offer then the possibility to monitor these phenomena andthe information extracted from the experiments represents the data base useful for the DeepLearning study that follows.
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5 Combustion theory
This project deals with various phenomena that have to be introduced :
• 1) Combustion instabilities (or thermoacoustic instabilities)
• 2) Blow-off
• 3) Flash-back
Those phenomena can be encountered during the usage of a large amount of devices (Gasturbines, furnaces, power plants, ...) and are both detrimental to the safety of the user and theperformances of the system. In addition, the environmental question is now a key parameterfor the further development of combustion systems. The stricter regulations tend to obligemanufacturers to operate at extreme conditions that can trigger those behaviours. Understandingthose phenomena is thus essential to study their occurrence.
In this document, the focus is put on combustion instabilitites as it is the cornerstone of mostworrisome phenomena observed in a common combustion system. However the extension of thiswork to more specific phenomena such as blow-off and flash-back is discussed afterwards.
5.1 Combustion instabilities
5.1.1 Interactions between acoustics and flames
Heat source and acoustics interactions are well known processes already studied for a long time(Rayleigh [34], Rijke [35]). The interactions are mainly based on the coupling between unsteadycombustion and acoustic waves in confined systems (Theoretical and Numerical Combustionch.8 [31]). Regarding combustion, the fact that a flame is capable of high heat releases and thuslarge energy variations explains the critical aspect of combustion instabilities. The oscillationsalimented by the coupling can reach dramatic amplitudes which can potentially lead to thedestruction of the system (see Fig. 3).
Figure 3: Destruction of a US rocket engine part due to combustion instabilities [30].
Apart from this worst case scenario, combustion instabilities are also involved in the decreaseof the performance of the system. Recently, due to the stricter regulations about pollution andconsumption, lean premixed combustion has been promoted. This type of combustion is more
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prone to instabilities and thus to decrease in efficiency. Schmitt et al. [40] have even assessedboth experimentally and numerically that the fluctuations of the magnitudes due to combustioninstabilities inside the combustion chamber of a swirled turbulent high-pressure burner can in-fluence largely the production of nitric oxide, which is in total contradiction to the initial goalaimed with lean combustion.
It is thus of first importance to study this phenomenon in order to design robust systems thatcan avoid this unintended consequences. Huge advances have been made during the past decadeand several solutions have been imagined to model, predict and finally mitigate combustioninstabilities in real systems (Poinsot [30], [32]).
But first, to get a better insight on the underlying mechanisms, a simple model will be derivedin the next section.
5.1.2 Simple energy criteria
Although combustion instabilities are known for more than a century, there are still difficultiesin modelling them. A simple acoustic-flame interaction model can be derived from the linearisedand simplified acoustic energy conservation equation. The unsteady acoustic energy is posed tobe:
e1 =1
2ρ0 ~u1
2 +1
2
p21ρ0c20
(1)
Where the index 1 refers to the unsteady part of a magnitude (perturbations) and the index 0to the steady part of a magnitude (mean value). The first term of the Right Hand Side (RHS) ofEq. (1) accounts for the kinetic energy contribution or the contribution of velocity fluctuationsand the second term accounts for the potential energy contribution or the contribution of pressurefluctuations.
The acoustic energy in presence of a flame follows the linearised and simplified relation:
∂e1∂t
+∇.(p1 ~u1) =γ − 1
γp0p1ωT1 (2)
The steps to derive this equation are addressed in APPENDIX 5.1. The Left Hand Side(LHS) of Eq. (2) is composed of the time fluctuation of the acoustic energy and the spatialvariation of the acoustic flux p1 ~u1. The RHS term is a correlation between the unsteady heatrelease rate ωT1 and the unsteady pressure p1.
To obtain insights on the role of these parameters, it is needed to integrate this equation overthe studied volume which gives (see APPENDIX 5.2):
d
dt
˚Ve1dV +
"Sp1 ~u1. ~dS =
γ − 1
γp0
˚Vp1ωT1dV (3)
A particular case is chosen where the studied magnitudes are assumed to be harmonic oscilla-tions at a pulsation 2πf or a period τ (p1 = P (t)e−2iπft, ~u1 = ~U(t)e−2iπft, ωT1 = W (t)e−2iπft)with P (t), ~U(t) and W (t) as complex functions of time slowly varying in comparison to theacoustic pulsation. After time averaging over a period, the following result is obtained:
d
dtE1 + F1 = R1 (4)
With :
E1 =
˚V
1
τ
ˆ τ
0e1dt dV =
˚V
1
4ρ0c20PP ∗ +
1
4ρ0~U.~U
∗ dV (5)
F1 =
"S
1
τ
ˆ τ
0p1 ~u1dt ~dS =
1
2
"S<(P ~U∗). ~dS (6)
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R1 =γ − 1
γp0
˚V
1
τ
ˆ τ
0p1ωT1dt dV =
γ − 1
γp0
1
2
˚V<(PW ∗) dV (7)
Analysing the stability of the studied magnitudes is possible with the assumption that theirchanges in amplitude are slow compared to the period of oscillation. The posed model for theamplitudes are therefore:
P (t) = AP egt, ~U(t) = ~AUe
gt, W (t) = AW egt (8)
Where g is the growth rate and τ � 1g
Injecting Eq. (5), (6) and (7) into Eq. (4) and then replacing P , ~U and W by the model ofEq (8) gives:
2gE1 + F1 = R1
g =R1 − F1
2E1
(9)
If the growth rate g (9) is positive, the amplitudes of the oscillation grow exponentially. Onthe contrary, if the growth rate is negative, the oscillations are damped.
The extended Rayleigh criterion is therefore built such that:
• R1 > F1 characterizes an unstable system
• R1 < F1 characterizes a stable system
R1 is the correlation between the unsteady heat release and the unsteady pressure: it is thesource term. F1 links pressure and velocity variations at the boundaries of the system and iscalled the acoustic losses term. Reformulating this criterion leads to the idea that an unstableregime is obtained when the sources overcome the losses.
A simpler case is also derived when losses are neglected. This relation is called the classicalRayleigh criterion and is built such that:
• R1 > 0 characterizes an unstable system
• R1 < 0 characterizes a stable system
It adds the following observation: in order to get a positive and maximum R1, the pressureand unsteady heat release must be in phase. Measuring the phase shift between those twoquantities is thus theoretically offering a measure of the instability of a regime.
5.1.3 Limits of simple criteria
The previous paragraph highlighted two simple criteria based on the measure of three quan-tities: the pressure, the unsteady heat release rate and the velocity. Strong hypothesis have beenintroduced to derive those criteria, they are recalled here:
• H1 : The unsteady part of each considered magnitude is a small perturbation around themean value
• H2 : The system behaves linearly around the mean value
• H3 : The unsteady part of each magnitude is assumed to be harmonic oscillations
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• H4 : The amplitudes of the harmonic oscillations are slowly varying in comparison to theperiod of the oscillations
Those hypothesis can be difficult to verify, even for the simplest cases. Poinsot et al. [32] haveused an active control system on a non-premixed turbulent combustor to observe the evolutionof combustion instabilities from the stable regime to the unstable regime (See Fig. 4)
Figure 4: Combustion instability growth: linear and non-linear zones [32], [31].
The experiment reveals that after the time t0 where the Active Control is disconnected, alinear zone is observed where the amplitude of the pressure signal grows exponentially. Howeverafter the time t4, a limit cycle where non-linear effects limit the amplitude is monitored. Thiszone is not suitable for a simple Rayleigh criterion as it does not respect fundamental hypothesis.Thus it remains difficult to characterize simply and robustly the instability of a system.
To complete Rayleigh’s stability study, other criteria have been developed such as the Chucriterion derived from his work on fluctuation energy [6].
However, the limitation to linear cases emphasizes the current narrow range where an insta-bility analysis is expected to offer reliable insights. Furthermore, more information have to befound to eventually detect and analyse precursors of instability.
5.1.4 Toward precursors of instability
Knowing the consequences of sustained instabilities to a combustion system leads to thenecessity of preventing their occurrence. It is thus essential to be able to detect the precursorsof these regimes. Yet no exact definition of a "precursor of instability" has been accepted by thecombustion community.
Several other groups work on the idea of intermittency of the signal such as George, Sujithet al. [12] and Krishnan, Sujith et al. [19] which is a line of thoughts for this project as it is oneof the particularity of the signal observed during the experiments (see § 6.2.2 and Fig 9).
This phenomenon brings the theoretical and experimental frame of subcritical bifurcation inflames explored by Noiray et al. [25] also observed by Vishnu, Sujith et al. [43]. Contrary toclassical approaches, the system is not only either stable (Combustion Noise) or unstable (LimitCycle of Thermoacoustic instability). Interstates exist such as intermittency where bifurcation
17
to instability is only true for a small duration. Intermittency often triggers instability when inletconditions are varied and thus is a candidate for the definition of a precursor of instability as itis observed in the experiments conducted further but also by Sujith’s team [12] [19].
The initial aim of this work is thus to analyse thoroughly the signals of a large panel of ex-periments to be able to detect the mechanisms that trigger instabilities by detecting, recognizingand classifying the interstate defined as intermittency. These mechanisms lead to the derivationof a notion of classification of signals useful for the eventual learning process.
5.2 Blow-off event
The objectives to reduce pollutants emission and fuel consumption have driven the evolutionof the combustion systems toward more extreme operating conditions. These conditions flirtwith inflammability limits of the mixtures where the best compromises could be found regardingpollution and efficiency. These limits are specific to each mixture and depend on experimentalconditions [10].
One limit of extinction is called the blow-off limit. It occurs when the inlet conditions arepushed to a very lean mix and/or when the stream velocity is too high for a proper flamestabilization [44]. The total extinction of the burner is, above all, detrimental to the safety. Asthe flame is extinguished, the unburnt mixture continues to flow and could potentially createpockets of flammable fluids. Concerning aeronautical applications, engine stalling due to blow-offis to be avoided at all costs. Blow-off prediction and control are therefore essential steps towardsafer operations.
Visualizing and predicting blow-off has already been the subject of study of several groups.Dawson et al. offer, for example, a method to observe blow-off and the different steps leading toa total extinction [8]. Besides, a form of data analysis on precursors of blow-off is also performedusing Symbolic Time Series Analysis by Mukhopadhyay et al. which encourages the use of moreefficient data extraction tools [22]. Nair et al. have also worked on the detection of blow-offevents and forms of acoustic precursors [23]. One interesting link that can be found betweeninstability precursor detection and blow-off detection is offered by a continuation of this work bySachan et al. [36] where forms of unstable intermittency were observed at the onset of blow-off.
As interconnections between these phenomena exist, It seems legitimate to first study pre-cursors of instability in order to develop a method that could be extended afterwards to blow-offprediction.
5.3 Flash-back event
Once again, the operating conditions imposed to the most recent combustion systems tendto increase their sensitivity to certain dramatic phenomena. The flash-back is characterized byan inversion of the direction of propagation of the flame toward the mixing region [10]. As theflame flows upstream, it can enter the injector and a risk of damaging the system appears.
Flash-back has several origins which are discussed by Sommerer et al. [41]. One origin isdirectly linked with thermo-acoustic instability. Keller et al. have conducted an experimentalwork which confirmed that strong instabilities can trigger flash-back [18]. These results werebased on observations made by Plee et al., commented by Coats [29] [7].
This connection between instability and flash-back confirms that it is necessary to first as-sert the problem of instability precursors detection in order to build an efficient model for theprediction of flash-back events.
The following document is therefore focused on the identification of precursors of instability.The possible extension of this study to blow-off and flash-back is discussed in the conclusion ofthe document.
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6 Preliminary Data Analysis: Combustion Instabilities
The first step of this study is to analyse the behaviour of the experimental setup under differ-ent operating conditions (mass flow rates or here bulk velocities, noted Usw, and equivalence ratio,noted φ) and configurations (types of fuel and injection processes). From this experimental dataanalysis, potential precursors of instability are identified and selected for the further applications.
The fuels utilised are Methane (CH4) and Di-Hydrogen (H2).In this document, the equivalence ratio is defined as:
φ = smF
mO(10)
where s is the stoichiometric mass ratio (s = 4 for CH4 and s = 8 for H2), mF is the fuelmass flow rate and mO is the oxidiser mass flow rate.
Two injection processes are offered by the system : air premixed swirled injection and pilotinginjection. The latter one is done by a small tube in the center of the injector outlet. It allows toinject pure fuel in a localised manner to act on the stability of the system (see §4).
From this data analysis, examples of precursors of instability are highlighted so that it ispossible to detect and predict their occurrence.
6.1 Conducted experiments
In order to ensure both repeatability, for the cases that have similar stability behaviours, anddiversity, for comparison during the learning process, different fuel injection configurations havebeen tested. For every fuel injection configuration, the bulk velocity Usw is varied from 14m.s−1
to 40m.s−1 with a 2m.s−1 step and the equivalence ratio φ is varied from 0.70 to 0.85 with a0.05 step. It represents a maximum of 56 points per fuel configuration. However, several pointswere difficult to reach as instabilities were too strong and threatened the integrity of the setup(generally at high Usw and high φ). These points were extrapolated as the most unstable pointalready acquired to complete the grid. Similarly, some points were difficult to reach at low Uswbecause the mass flow controller could not regulate and reach a stable value of mass flow. Thosepoints were also extrapolated as the least unstable (generally located in low Usw, low φ regions).The test grid is sketched in Fig. 5. The results of the experiments will be plotted on the formof maps on this grid.
Figure 5: Experimental grid of the operating points acquired during the experimental study
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The main fuel injected is always methane. Di-hydrogen is used as a stabiliser in a smallproportion to evaluate its efficiency to modify the behaviour of the entire system [27].
The mass flow proportion of H2 (resp. CH4) injected is written as :
XmH2
=mH2
mH2 + mCH42
(11)
The proportion in power of H2 injected PH2 is used to control the H2 injection. It is either1% or 2% for the present experiments. PH2 is then defined as:
PH2 =XmH2.LH2
XmH2.LH2 +Xm
CH4.LCH4
(12)
where LH2 (resp. LCH4) is the mass lower heating value of H2 (resp. CH4). It is thenpossible to recover the injected proportions XH2 which are 0.41% for PH2 = 1% and 0.83% forPH2 = 2%.
There are 7 different fuel injection configurations such that:
• Ref : premixed CH4
• PH1 : premixed CH4 + pilot H2 (1% in power)
• PH2 : premixed CH4 + pilot H2 (2% in power)
• PC1 : premixed CH4 + pilot CH4 (1% in power)
• PC2 : premixed CH4 + pilot CH4 (2% in power)
• MH1 : premixed CH4 + H2 (1% in power)
• MH2 : premixed CH4 + H2 (2% in power)
The fuel injection configurations are eventually gathered in Table 1 and schematically repre-sented in Fig. 6
Mai
n
Pil
ot
Mai
n
CH4+Air
CH4
Mai
n
Mai
n
CH4+Air
PC1 - 1%PC2 - 2%
Mai
n
Pil
ot
Mai
n
CH4+Air
H2
PH1 - 1%PH2 - 2%
CH4+H2+Air
Mai
n
Mai
n
MH1 - 1%MH2 - 2%Ref
Figure 6: Schematic representation of the injection configurations [27]
For each fuel injection configuration, and then for each point on the test grid, signals of the4 sensors (microphone MB, microphone M1, hot-wire HW, global heat release (photo-multiplier)PM, see § 4) are acquired simultaneously at a sampling frequency of 10kHz during 10.3 seconds.
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Table 1: Fuel injection configurations used for data acquisition [27]
Case name Premixed flow Pilot flow P%premixed P%
pilot P%H2
XmH2
(%) XmCH4
(%) XmH2
(%) XmCH4
(%)
Ref 0.0 100.0 0.0 0.0 100.0 0.0 0.0
PC1 0.0 99.0 0.0 1.0 99.0 1.0 0.0
PC2 0.0 98.0 0.0 2.0 98.0 2.0 0.0
PH1 0.0 99.59 0.41 0.0 99.0 1.0 1.0
PH2 0.0 99.17 0.83 0.0 99.0 2.0 2.0
MH1 0.41 99.59 0.0 0.0 100.0 0.0 1.0
MH2 0.83 99.17 0.0 0.0 100.0 0.0 2.0
Therefore, the complete dataset is structured as:
1. 7 fuel injection configurations
2. 56 operating points (defined by Usw and φ)
3. 4 sensors
4. 10.3 seconds of acquisition
5. Sampling frequency Fs = 10 kHz
6.2 Stability map
6.2.1 RMS Map
The initial step toward the extensive analysis of the stability of the system is to explorethe graphs of the RMS (Root Mean Square) of the pressure recorded by the microphone M1.Such an average amplitude of the signal gives direct insight on the state of the system. A largeRMS pressure represents strong oscillations of the flow parameters, characteristic of combustioninstabilities. For the reference case Ref, Fig. 7 is obtained.
The darker zones delimit operating points where sustained combustion instabilities occurred.An empirical threshold of 250 Pa (or 20.log10(
pRMSp0
) = 141.9 dB with p0 = 2.0 .10−5 Pa) is setto be the limit of combustion instabilities. It is important to notice that the map is not simplyseparated into two distinct zones, one unstable and the other one stable. Several points can befound stable but are surrounded by unstable states (φ = 0.80 and Usw ∈ [24, 30] for example inthis case). This first raw result motivates further investigations on the determination of moreprecise tools to highlight precursors of instability in apparently stable regions that are actuallyclose to unstable regions.
6.2.2 Crest factor Map
In the last paragraph, seemingly stable operating points surrounded by unstable operatingpoints have been highlighted. A higher level of analysis is introduced here with the notion ofintermittency. For most apparently stable points, the signal presents short periods of large am-plitude oscillations surrounded by quieter long periods of combustion noise making the whole
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Figure 7: Mapping of the RMS of the pressure from M1 in case Ref with acoustic dB.
signal appear stable. It is thus important to exhibit this behaviour. A first indicator of inter-mittency can be highlighted by detecting and saving the highest amplitude in the signal anddividing it by its RMS to construct the crest factor map (See Fig. 8). Again, the area φ = 0.80and Usw ∈ [24, 30] shows high amplitudes in comparison to its relatively low RMS. The pressureis thus encountering at least one strong short-time increase in amplitude (called a burst for thefollowing study).
Figure 8: Mapping of the ratio between the crest factor for the pressure from M1 in case Ref
To better understand what a burst is, the plot of the M1 microphone pressure at Usw =30m.s−1 and φ = 0.8 is given in Fig. 9. It is clear that a number of bursts are visible onthe signal where amplitude encounters sudden growth. The burst is characterized by its largeamplitudes and short duration.
A few studies have already identified these peculiarities of the signal in certain conditions tobe precursors of thermoacoustic instabilities (George et al. [12], Krishnan et al. [19]). This workaims at completing these researches by the classification of these bursts.
This leads to the following open questions which are the core problems of this thesis:
1. Are bursts effectively signaling incoming instabilities ?
2. How close to instability is a system which encounters bursts ?
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Figure 9: M1 microphone signal for the case Ref at Usw = 30m.s−1 and φ = 0.8
The first milestones on the way to the answers to these questions are then:
1. Is there information in the shape, amplitude, number, ... of these bursts ?
2. Is it possible to differentiate and recognize bursts ?
3. Is a learning system able to differentiate and recognize bursts ?
4. And finally, is the signal in-between burst also carrying information ?
6.3 Precursors of instability
This section focuses on the study of bursts as precursors to instabilities. The determinationof a burst’s specificity is the base of the construction of the further learning models.
First and foremost, bursts have to be detected and inventoried.
6.3.1 Burst detection
Automating burst detection on every signal experimentally obtained is a key step. Thefollowing solution has been developed in order to efficiently detect the bursts of interest in anoisy signal.
First a signal on which the detection can be done is chosen. Ideally this signal should havea high "signal to noise" ratio in a majority of the experimental configurations and operatingpoints in order to properly see the bursts (the signal of interest is the burst and the noise is thecombustion noise). The product of the unsteady velocity and the unsteady pressure (SensorsHW and M1) is thus chosen. It depicts the acoustic flux at the exit of the plenum. The productof these two magnitudes offers a better correlation of the signals thus reducing the noise andamplifying the elements of interest (See Fig. 10 where bursts appear clearer in comparison toFig. 9).
In order to systematically detect and classify the bursts, a routine based on the spectral studyof the signal has been developed. A brief summary of the corresponding algorithm is given inAlgorithm 1 in APPENDIX 6.1 .
An example of signal on which burst detection is done is plotted in parallel with the outputof the product of the hot-wire HW signal with the M1 microphone signal in Fig. 11.
The y-axis of the frame (a) in Fig. 11 is labeled as "Power Spectral Amplitude". For a pureharmonic signal of constant amplitude, the frame (a) would show a constant value of 1 over theentire duration. Thus, a burst appears as a high peak due to the fact that it overwhelms the lowRMS of the signal during a short period and this signal is systematically normalised by its RMSbefore the detection.
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Figure 10: Product of HW hot-wire and M1 microphone signals for the case Ref at Usw = 30m.s−1
and φ = 0.8 normalized by its RMS
Figure 11: Burst detection applied on the product of the M1 microphone and HW hot-wire for the caseRef at Usw = 30m.s−1 and φ = 0.8, (a) Burst detection power spectral amplitude, (b) product of theM1 microphone and HW hot-wire normalized by its RMS
The threshold applied during the detection can be tuned in order to select the bursts whichsufficiently surpass the combustion noise or which are of interest in terms of amplitude. Fur-thermore selecting Spectrogram signal around the frequency of the carrier signal is chosen. Theburst spectra are usually narrow around this frequency, a maximum of information can thus beextracted.
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6.3.2 Burst detection and usual stability analysis
In order to understand what a standard stability analysis would render on an intermittentsignal, the real-time classical Rayleigh criterion introduced in § 5.1.2 is developed in parallelto the burst detection. The delay between the unsteady pressure and the unsteady heat release(measured by the Photomultiplier PM) is computed. A null time delay means that both signalsare in phase and, assuming that the system respects the assumptions and hypothesis recalled in §5.1.3, the system’s stability is compromised. However, it is important to keep in mind that suchcriteria are limited by the assumptions made before and the further results are only displayedto make the link between classical instability detection and the method developed during thethesis.
The Figure 12 renders the comparison between the burst detection system and the Rayleighcriterion application.
Figure 12: Estimation of the Rayleigh criterion on the case Ref at Usw = 30m.s−1 and φ = 0.8, (a)Burst detection power spectral amplitude, (b) Measure of the delay between pressure and heat release,(c) M1 microphone output normalized by its RMS
During bursts, the unsteady pressure and the unsteady heat release are seen in phase (orlocked) which validates the fact that for a short duration, the system is detected as unstableby the approximate Rayleigh criterion under the restrictive assumptions made before. Theintermittent unstable behaviour of the signal underscored by this side observation enhances theinterest to study more thoroughly the phenomenon. It motivates the further map analysis onburst occurrence to develop a more complete instability/intermittency analysis.
25
6.3.3 Updated stability maps
From the previous paragraphs, data is extracted on bursts for every signal on the test grid.New metrics that take into account the occurrence of bursts in the signal and their simplestspecificity can be defined, thus giving further information on the nature of the operating points.
The output of the burst detection algorithm is a list of three important parameters : thepositions of the bursts, the duration of the bursts and a measure of the power of the burst.
The first metric computed from this output is the number of bursts that occurred duringthe 10.3 seconds of acquisition for all configurations and operating points. Figure 13 gives thecorresponding map for the Ref case.
Figure 13: Mapping of the number of bursts detected during the acquisition time in case Ref
The second metric is the average of the energy of the bursts for each signal. The energy of aburst is defined as the product of the duration of the burst and the measure of its power. It isgiven by the product of the height of the peak detected multiplied by its width (See Algorithm1 in APPENDIX 2.1).
Figure 14 maps this metric.
Figure 14: Mapping of the average energy of the bursts in case Ref with logarithmic scaling (E0 = 1)
26
Coupling both maps (Fig 13 and Fig 14) with Fig. 7 gives more insight in the apparentbehaviour of the system concerning bursts:
• Areas close to unstable zones tend to encounter strong bursting.
• Unstable regions have no bursts (E. g. Usw = 32m.s−1 and φ = 0.85)
• Two main bursting behaviour tend to appear:
1. An operating point can encounter a few bursts that are of high energy (E. g. Usw =30m.s−1 and φ = 0.8)
2. An operating point can encounter a large amount of bursts that are of low energy (E.g. Usw = 38m.s−1 and φ = 0.8)
• Stable regions are subjected to low energy bursting (E. g. Usw = 14m.s−1 and φ = 0.7)
These observations lead to the idea of classifying the signals depending on the RMS map(Fig. 7), the map of the number of bursts encountered (Fig. 13) and the map rendering theaverage energy of the bursts (Fig. 14) by finding acceptable criteria that define precursors ofinstability and by training a Deep Learning model to retrieve these criteria in small elements ofsignal.
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7 Deep Learning theory
This section aims at defining the essential keys to perform an analysis using Deep Learningtechniques. However, this field of research is vast and reveals thorny theoretical aspects. There-fore, the following descriptions will mainly emphasize user-centered questions in order to betterunderstand the results obtained in further sections. More detailed theoretical demonstrationsare available in Machine Learning written by T. M. Mitchell [21] and in Deep Learning writtenby I. Goodfellow [14]. The computational framework for this study is Keras under TensorFlow[1] [5].
Explanations on how the models used afterwards are built are given in the following para-graphs.
7.1 Introduction to Deep Learning
7.1.1 Definition of Machine Learning
Machine Learning is built around a fundamental paradigm : If a system is able to increaseits performance when doing a dedicated task by practicing through training experience, thesystem is learning [21].
More specifically in this work, only supervised Machine Learning is explored and it is basedon a rather simple intuition : it is possible to program a computer in order for it to learn howto associate a given input to an output by defining its own set of rules (See Fig. 15). Definingthe task, the experience (set of inputs and corresponding outputs here) and a way to measurethe performance is the practical challenge of Machine Learning.
Figure 15: Schematic representation of the concept of supervised Machine Learning [5]
A simple example is the handwritten figures recognition [20]:
• Task: Associate pictures of handwritten figures (inputs) to numerical figures (outputs)
• Performance: Proportion of figures correctly associated
• Experience: database of pictures of handwritten figures together with their correct nu-merical equivalent
To solve this optimization problem, one common solution is to rely on the concept of back-propagation. A variety of other branches exist but are not investigated in this study. Theback-propagation can be explained as follows.
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Once the problem is posed, a model is chosen to associate the given input to the correctoutput. The model has free parameters called weights initially set randomly. For example, alinear model is shaped such that:
y = F (X) = w0 +n∑i=1
wixi (13)
Where (wi)i∈J0,nK is the set of weights of the model, X = (xi)i∈J1,nK is the input vector andy = F (x) is the output of the model corresponding to the input x. n accounts for the lengthof the input if the input is a vector. The input shape is generalized to the notion of tensor andthus can be multi-dimensional.
The learning process is eventually unrolled such that experience is used to optimize the freeweights of the model to realise the task under acceptable performance criteria:
1. The learning process begins with the input X0 = (x0i )i∈J1,nK given to the model. The modelrenders an output y which can be compared to the original output y.
2. The measure of the error made by the model (or its performance, measured by the lossfunction) is then back-propagated toward the model in order to adjust the weights in asuitable direction.
3. The updated model is then fed again by the input X1 and the loop starts again until themeasured error is sufficiently low according to the specifications of the user.
One cycle of optimization where every input Xk has been passed through the model once iscalled an epoch. Several epochs are then successively achieved until the precision specificationsare fulfilled.
The last model is called trained and ready for further use, namely, predicting the output frominputs where the user has not been able to collect an output. A schematic view of the learningprocess is sketched in Fig. 16.
Model
Loss FunctionOptimizer
Free Weights
Inputs X Outputs y
Predictions ŷ
Loss ε
Figure 16: Schematic representation of the learning process in supervised Machine Learning [5], [21]
The optimizer is a crucial element of the process. It translates the knowledge of the lossto an optimization of the free weights of the model in order to minimize the loss after the nextstep. The optimization process follows generally well-known concepts such as stochastic gradientdescent [14] ch. 5, [21].
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Finally, the steps to build and train a supervised learning system are:
1. Gather inputs and corresponding outputs to constitute an experience set.
2. Define the task to perform with these inputs and outputs.
3. Define a measure of the performance through loss to assert if the task is well done.
4. Choose a suitable model for the problem.
5. Implement the measure of the performance into a loss function.
6. Define an optimization routine to back-propagate the knowledge of the loss to the weightsof the model through an optimizer.
7. Train the model by running a number of epochs until the loss satisfies the requirements ofprecision.
8. Save the trained model and its weights for further use.
For simplicity, and as only supervised training is performed in this document, supervisedlearning will be presented as Machine/Deep Learning.
7.1.2 Toward Deep Learning
As a recent branch of Machine Learning, Deep Learning involves its theoretical background.
When the complexity of the data set increases, the size of the model has to rise. It isthus possible to connect several models to each other usually by stacking them and feeding thesuccessive models with the output of the preceding one. Each model is a layer and the feedingprocess which can be tuned by the user is called connection. After each layer, a new, moreabstract representation of the input data is obtained.The last layer provides the output.
With the recent improvement of computational power, especially concerning GPUs’ technol-ogy, the layers can be more numerous and more complex. The word "deep" is then a referenceto the idea of this large succession of layers where the final depth of the network is the numberof layers composing the model [14] ch. 6, [5]. A typical simple Deep Learning architecture isrepresented in Fig. 17.
Each layer is built around series of operations done on the input data. These operationsinvolve the weights in a specific manner proper to the type of layer studied. Finding the appro-priate class of layer to solve a problem is one of the key questions to answer in order to developan efficient architecture for the problem.
This multi-layer architecture, especially when convolution layers are involved (See § 7.4.1),reveals good performances for inputs with a high dimension and large quantities of data (suchas sound samples, images and films) with its ability to find meaningful features where classicalMachine Learning experienced drastic limitations. Furthermore, the choice of the model inmachine learning is always guided by strong assumptions on how outputs have to be mappedwith inputs. These assumptions are more and more difficult to make as the dimensions of theinput increase [14] ch. 5.
The data set analyzed in § 6 presents a high sample rate and the dynamics of the structuresto study are observed in windows of at least 0.3 seconds which makes the inputs improper forclassical Machine Learning. Moreover, the complexity of these structures asks for more expressivemethods where fine features can be extracted. These findings tend to motivate the use of DeepLearning.
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Layer 1
Loss FunctionOptimizer
Free Weights
Inputs X Outputs y
Predictions ŷ
Loss ε
Free Weights
Free WeightsFree Weights
Free WeightsFree Weights
Free WeightsFree Weights
Layer 2
Layer n
Output Layer
...
1st representation
nth representation
Figure 17: Schematic representation of the learning process in Deep Learning for a multi-layer archi-tecture [5], [14] ch. 6
7.2 Tasks definition for the current problem
The data analysis conducted in § 6 suggests that characteristic events happening duringacquisition such as bursting could be precursory to instability. Therefore a leading idea forthe following study is that the signal treated as the input can be attributed a score reflectingits proximity to instability. The objective of the Deep Learning system is to build an efficientmapping of this attribution based on the analysis of features of the signal. This objective isreached through two types of tasks defined as classification and regression.
7.2.1 Classification
In classification, the system must predict a specific class for the input, among a finite numberof distinct classes. The program thus builds a function that maps the input X to an outputy ∈ J1, kK where k is the number of classes. An example of classification has already been givenin § 7.1.1 with the objective to recognize handwritten figures as numerical figures. The numericalfigures are actually part of 10 classes, the task is thus to specify to which class a handwrittenpicture belongs [20].
Regarding the problem asserted in this work, a classification task could be to attribute aninteger "score of instability" to an element of signal (See § 8.1, § 8.2 and § 8.3).
Determining if a classification is correctly done is based on the level of accuracy of the model:the proportion of inputs falsely classified. A usual way to monitor the loss of a model performinga classification is to use cross-entropy:
CE = −C∑j=1
δX,j log(pX,j) (14)
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where C is the number of categories in the classification, δX,j is 0 if the class of the input Xobserved is not j and 1 if it is j (ground-truth). pX,j is the probability given by the model thatthe input X observed is part of the class j (prediction). For a perfectly classified input, CE = 0and for a totally misclassified input, CE = +∞. The average of the cross-entropy computedfor every experience composing the data set is then an efficient monitor of the evolution of theprecision of the network through the epochs of training.
7.2.2 Regression
In the regression task, a floating-point value is predicted for the input. In comparison witha classification problem, this value is not an integer anymore, it is taken in an interval.
An example of regression problem is the prediction of house pricing based on comfort andlocalisation criteria. Prices are predicted inside an interval based on former transactions ofcomparable goods [5].
Concerning the problem treated in this document, a regression task could be defined if the"instability score" were not an integer but a real number taken inside an interval (See § 8.3).
A regression problem does not fundamentally change the system, the implementation is how-ever impacted as the loss function and the optimization routine have to be adapted to this formof continuous output. The precision of the model is not anymore based on Boolean evaluations.Measures such as Mean Squared Error (MSE) or Mean Absolute Error (MAE) are thus oftenused as loss functions:
MAE =1
N
N∑i=1
|yi − yi| (15)
MSE =1
N
N∑i=1
(yi − yi)2 (16)
where (yi)i∈J1,NK is the vector of predictions and (yi)i∈J1,NK is the vector of reference outputsand N is the number of experience in the data set.
7.3 Applying Deep Learning to combustion instabilities
7.3.1 Literature survey
The use of Deep Learning applied to problems in physics is recent. The development of themethods and the fast increase of the computational power available motivate the cross-study ofcombustion and Deep Learning. However, only a few practical methods have been implementedin ready-to-use systems.
Sarkar et al. [37], [33] relied on Symbolic Time Series Analysis coupled with Deep Learning(Deep Belief Network) performed on images of a swirled flame. The trained network is directlywired to the experiment and can predict the incoming instability. This first result opens thepath for the study that this document is interested in, as one of the objectives is to provethat instability detection is possible through the analysis of the signals gathered during theexperiment. One first challenge is to counter the fact that sensors extract an essentially differentinformation, difficult to compare to Sarkar’s high-speed camera imaging, but easier to link toreal-world applications.
Regarding the detection of precursors of instability, Steinberg et al. [2] have observed that aphenomenon called Critical Slowing Down can be detected in the onset of instability on unsteadypressure signals. It is an encouraging result, as it proves that specific artefacts are contained inthe signal and Deep Learning techniques for signal processing learn to identify complex patternsthat are not detectable by simple filtering techniques.
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7.3.2 Basis of the implemented models
In order to perform the assigned tasks further described in § 8, it is necessary to buildnetworks able to extract representative and useful features in the signal. The nature of thesignal observed suggests a recurrent theme in Deep Learning : Speech Recognition (SR). It is awell documented sub-field of research where the usual inputs are voice samples, or to translate,pressure signals from microphones. A parallel can then be drawn between the signals obtained(see § 6) and human voice recording.
Furthermore, Speech Recognition is initially based on filtering technologies which is the mostcommon way to handle signals from experiments. The real advance offered by DL for SR is thepossibility to systematically fit a complex filter answering the needs of the user when the user isnot able to formulate the exact shape of a conventional filter. In the present case, the complexityof the tracked phenomena indicates that the analysis could benefit from the SR / DL approach.
Based on the studies already conducted on SR problems, it is necessary to find the propercomponents of the networks susceptible to perform well for the problem tackled further. Thework of Nassif et al. [24] gathers the most common technologies adapted for SR. The followingparagraph aims at describing the different elements needed to build a network and the logicbehind its construction for this project.
7.4 Building blocks of a SR Network
The structure of a network is based on several blocks stacked in order to benefit from theirspecificity. The blocks are composed of layers that are built to perform operations on the inputdata. The operations involve fixed parameters imposed by the user and trainable parametersthat are free weights to optimize during the training. The constituting layers of the networksused further are introduced in the next sections.
7.4.1 Learning local features
A classical approach when the input is a 1-Dimensional signal is to use a Convolutional NeuralNetwork (CNN). Contrary to hand-designed filtering approaches, a CNN learns an optimal setof filters in the form of convolutional kernels. A typical CNN block is represented in Fig. 18.
Figure 18: Schematic representation of a typical convolution block to build a CNN
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a) 1D Convolution layer
A convolution layer is built around the discrete convolution operation:
z(n) = (x ∗ w)(n) =+∞∑
m=−∞x(m).w(n−m) (17)
where x is the input of the layer and w is the vector of weights of the layer. w is called akernel. As the convolution has to be computed on a finite domain, the length of the vector ofweights, or kernel size, limits the infinite sum to a finite sum, the kernel is compact. Each layerhas two key parameters which are the kernel size and the number of filters applied. Each layeris thus made of different filters which are all optimized together during training [14] § 9, [24].
The output of each layer is passed through a unit called the activation function. The purposeof this unit is to introduce non-linearity in the network. One function generally used for that isthe rectified linear unit based on z → max(0, z) which selects positive values as activating values.It is important to observe that this function is fundamentally non-linear. Using non-linearity innetworks is useful to guarantee that the system learns to map the inputs and the outputs withmore complex functions than only linear relations [16].
b) Max Pooling layer
After one or more convolution(s) it is often admitted that the most representative values ofthe output should be selected [14] § 9. The max pooling layer is given a slice of the output ofthe precedent layer and selects the maximum value of this slice. The dimension of the slice iscontrolled by a kernel size l. For example for l = 4 in 1D, the output vector of the precedentlayer will be sliced in elements of four values and the maximum of the four value will be selectedby the max pooling layer. It is a common technique for CNN networks [47], [24] [14] § 9. The useof max pooling is a usual way to enhance the performance of a network and avoid generalizationerrors (introduced in § 7.5.1).
7.4.2 Learning global features
The study of the state of the art in Speech Recognition reveals that CNN is one of the mostcommon architectures to use for time-series analysis. The CNN is a technology able to focus onlocal features where the majority of the information is. However, in some cases such as emotiondetection classification in speech [47], the local feature is not sufficient to precisely classify asignal as the influence of the longer time dependencies has also to be taken in account. To addthis consideration, Recurrent Neural Networks (RNN) can be used with the underlying idea thatthe learning network is able to consider both the current input and a representation of the inputalready analysed. The Long Short Term Memory (LSTM) layer is one specific type of recurrentlayer that has both the possibility to store the dependency of the current state to older statesand the possibility to forget the states that seem not useful anymore.
Coupling CNN and LSTM is a currently well documented technique to study signals especiallyin Speech Recognition [11], [47], [45] and § 8.3.
7.4.3 Interpreting the learnt features
Once features are learnt, it is necessary to interpret them. Fully Connected Layers (or DenseLayers) are therefore put at the end of the network. The layer connects each output with all theinputs. Each connection is weighted such that the features can be mapped to an output. Thus,the dense layers are effectively performing the task initially specified to the network by using thefeatures extracted through the first layers (convolution layer, LSTM layer, ...).
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7.5 Classical limitation
7.5.1 Introduction to generalization defects
As introduced before, a Machine Learning algorithm often aims at performing well on thetraining set. A minimum error during training guarantees that the model succeeded to learn away to link the inputs to the outputs. However, this minimum of error during training doesn’tnecessary imply that the model is actually efficient for inputs it has never studied. Generalizingfor a learning system is thus its ability to perform its dedicated task both for training data andtesting data, not seen during training [5], [14] § 5. It is eventually crucial to address generalizationerrors.
Generalization errors often occur when the capacity of the network is not exactly suited forthe problem. The capacity of the network is a measure of the complexity of the function it cancreate. It is often loosely associated to the number of parameters of the network which is a goodfirst approximation to picture it. When the capacity is too low, the network is not able to learnenough features to properly map the inputs to the outputs. The system is underfitting. Onthe contrary, too much capacity can be detrimental as the model starts to learn "by heart" thetraining data and thus performs badly on new incoming inputs, the system is overfitting. Thebalance between those limits is complex to find in practice and it is often necessary to selecta model with overcapacity and manage overfitting with other methods presented in the nextparagraph.
Another essential parameter when searching for generalization is the amount of data availablefor training. An undersized training data set is reducing the ability of the model to generalize.When data are insufficient because of the nature of the acquisition, it is possible to artificiallyenhance the data set through data augmentation. This is discussed in the next section.
7.5.2 Addressing generalization defects
Reducing the generalization error without impinging on the training performances is a generalfield in Deep Learning : it involves regularization methods. The methods used in this projectare briefly underscored in the next paragraphs. Mathematical demonstrations are not reproducedhere but can be found in Deep Learning [14] § 7.
a) L1 and L2 Regularization
One first approach concerning regularization is the parameter norm penalty. It consists inadding a penalty term to the loss function based on the parameters of the model. As the model’smain objective is to minimize the loss, the penalty constrains the evolution of its parametersin order to respect a criteria set prior to the training. L1 and L2 parameter regularization arereferring to a norm penalty. L2 (resp. L1) regularization involves the use a of the L2 (18) norm(resp. L1 (19) norm) of the weights of the model as penalty.
Loss = Loss+α
2wT .w (18)
Loss = Loss+ α∑i
|wi| (19)
where α is a parameter to set, which controls the contribution of the penalty.These methods aim to avoid a too wide dispersion of the weights and thus smooth the training.
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b) Dropout
The Dropout is one effective way to prevent the algorithm from overfitting by randomlysetting to zero a portion of the weights of a layer. This action shuts down several connectionsat each step of the training. This artificial obstacle to the result is interpreted as an obligationfor the network to learn more robustly. It can’t rely on a certain proportion of what it learnt asit is dropped randomly. The concept may be counter-intuitive but has been proven to work wellon fully connected layers [5], [14] § 7.
c) Data Augmentation
Generalization is possible when the data set is of sufficient size. When it is not the case, acommonly admitted solution is to create artificial data. Several techniques exist to enrich thetraining data [14] . It is also a way to increase the robustness of the model when the artificial dataare only slight modifications of the original data [46]. Concerning Speech Recognition severalother methods were tried [11].
In this project, the retained idea is to perform a linear combination of two signals in orderto create a third one which resembles both of them. It is implemented in § 8.1 and § 8.2 tomitigate the under-representation of certain classes.
d) Batch Normalization
Batch normalization was not initially designed to improve generalization but its implemen-tation has been confirmed to help the convergence of the calculations and creates a sound en-vironment for the learning network. It is originally added to reduce the inhomogeneity of thedifferent layers composing the model [14] § 8. The output of the layer is segmented in batchesBi. Each batch Bi is then transformed such that:
B′i =Bi − µiσi
(20)
where µi is the mean and σi the standard deviation of Bi.Using batch normalization optimizes the learning process, especially concerning CNNs, and
is thus widely used in this type of network [47].
7.5.3 Conclusion on generalization
For this project, several of these techniques have been combined in order to ease the learningprocess. It is actually complex to define which method will give the best results as there is amultitude of possibilities. It is always a work-in-progress to optimize the network and offer thebest performances.
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7.6 Conclusion : Building a state-of-the-art Speech Recognition Network
As explanations about the logic behind the construction of Deep Learning networks havebeen given, it is necessary to practically build a network and prepare it for training (See § 8).Figure 19 displays the structure of a model built for SR inspired from the works of Zhao et al.[47], Etienne et al. [11] and Nassif et al. [24]. Versions of this example of network are used inthe next section (§ 8) to perform the detection and analysis of precursors of instability using thesignal acquired in § 6.
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Batch Normalization
Batch Normalization
Batch Normalization
Input of the network
Batch Normalization
LSTM Layer
Dense Layer
Dropout Layer
Output Dense Layer
Output of the network
Dropout Layer
Dense Layer
L2 Regularization
L2 Regularization
L2 Regularization
L2 Regularization
L2 Regularization
ReLU
ReLU
ReLU
ReLU
L2 RegularizationActivation : adapt to the task
L2 RegularizationActivation : ReLU
L2 RegularizationActivation : ReLU
LOCAL
FEATURE
LEARNER
GLOBAL FEATURE
LEARNER
INTERPRETER
OUTPUT
Figure 19: Schematic representation of a SR network, variations are used in § 8 [47]
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8 Apply Deep Learning to the experimental results
The following study aims at proving that the transition from a stable state (combustionnoise) to an unstable state (thermo-acoustic instability) can be predicted. The different steps togo through in order to develop an operable system are thus:
• First Step : Prove that a classification of characteristic elements of signal (noise, burstsand instability) by order of instability is possible through Deep Learning
• Second Step : Verify that the classification can be extended to elements of signal chosenrandomly, thus not characteristic a priori.
• Third Step : Build an operable system which performs a finer analysis of the instabilityof the system, based on the Second Step achievement.
8.1 First Step : Classifying signals
The objective of this paragraph is to demonstrate that classifying characteristic elements ofsignal is possible.
As introduced in § 7, an operating learning process needs well posed inputs and correspond-ing targets to reach.
8.1.1 Preparation of the Deep Learning study
The first approach is a classification problem. The objective is to empirically label thedifferent signals to create 4 distinct classes. Each class represents a different state of the systemand is defined with experimental considerations and using the results gathered during the signalanalysis carried out in the chapter § 6.
1. Class 0: Combustion Noise (Stable)
2. Class 1: Bursting (Close to stability)
3. Class 2: Bursting (Close to instability)
4. Class 3: Thermo-acoustic instability (Unstable)
a) Choice of Inputs
The conducted analysis implies that the inputs should be elements of the signals that seemcharacteristic of the state of the system and could be differentiated from a state to another.
It has been decided to truncate the signals of the sensors in segments of 0.3s. The aim isto capture bursts such that at least every burst is in the center of a segment. Segments arealso taken in signals that are not subject to bursting in order to also be able to differentiatebetween combustion instability and combustion noise. Figure 20 displays the process of selectionof characteristic events in a bursting signal.
More explicitly, the input data base is built with N samples such that a sample is made of :
• Duration : 0.3 s
• 3 Channels :
1. Microphone M1
2. Product of the microphone M1 and the hot-wire HW
3. Photomultiplier PM
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Figure 20: Example of selection of samples in a bursting signal for the First Approach. (M1) Normal-ized pressure from M1, (M1.HW) Normalized product of the pressure M1 and the velocity HW, (PM)Normalized heat release from PM
• Normalization : every channel is randomly normalized in order to make the model focuson signal "shapes" and not amplitudes. For a learning system, it is observed that settingrandomly a parameter (here the normalization) makes it preclude the parameter as it isnot possible to find features in it.
The samples are taken from the signals of 5 of the 7 fuel injection configurations recalled in§ 6.1 : Ref, PC1, PC2, MH2, PH2.
The configurations MH1 and PH1 are saved to perform the diagnostics of the model afterthe training.
b) Choice of Targets
For this problem, the targets are defined as the digit of the class considered. Each input isattributed a label corresponding to this target. The thorniest action is then to perform this at-tribution such that it matches the classification. Algorithm 2 in Appendix has been developedto translate in a reproducible manner the considerations taken in account for label attribution.A schematic representation of this Algorithm is also depicted in APPENDIX 7.1 (See Fig 46).
The magnitudes used for the class determination are:
• The RMS of the M1 microphone pressure (Fig. 7)
• The number of bursts occurring in the whole signal (Fig. 13)
• The average energy of the bursts (Fig. 14)
• The weighted average of the closest neighbours’ RMS of the M1 pressure signal (Fig. 45in APPENDIX 7.1)
The label attribution performed on the Ref case is rendered in Fig. 21.
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Figure 21: Scores extracted from the signals for the case Ref and RMS mapping of M1 microphonesignal as a font
The general shape of the signals for each class is given by Fig. 22. It is interesting toobserve that strong bursts appear in category 2 operating points classified as such because oftheir proximity to unstable operating points.
Figure 22: Examples signal shapes generally found for each class for the case Ref (RMS mapping ofM1 microphone signal as a font)
c) Objective of this study
It is important to emphasize the limits of such labelling. It is performed with empiricalthresholds determined in order to create a distinction between the classes. These parameters aretuned by the user to fit experimental considerations and beliefs. In fact, the current state of theart in burst detection does not present a commonly admitted classification of bursts. The essenceof this study is not to create this classification but rather to demonstrate that a classification is
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possible and that a Deep Learning network is able to perform this classification when trained.Furthermore, such score attribution introduces the notion of neighbourhood consideration
which is a first step toward a notion of precursor. A positive result for this study would meanthat an apparently stable operating point located in a dangerous area due to the instability ofthe points positioned nearby would warn the user of this worrying location. The four magnitudestaken in account are computed on a whole map known beforehand. Indeed, to compute the firstthree values, the entire signal of the operating point is needed (10.3 s of acquisition). For thelast value, the knowledge of the operating points located nearby is necessary. The aim of thefollowing study is thus to address this fundamental question:
Is it possible to find enough information in a short period signal (0.3s, see 8.1.1.a) withoutany knowledge of the map, to attribute the global instability score defined knowing the map ?
Finally, the attribution of the targets to the samples is done such that :
• Operating point labelled 0 : The samples are extracted randomly in the whole signaland each sample is labelled 0.
• Operating point labelled 1 : The bursts are detected and then extracted. The samplesare therefore always containing a burst. Each sample is labelled 1.
• Operating point labelled 2 : The bursts are detected and then extracted. The samplesare therefore always containing a burst. Each sample is labelled 2.
• Operating point labelled 3 : The samples are extracted randomly in the whole signaland each sample is labelled 3.
8.1.2 Summary of the Learning task
A brief summary of the first learning task is given in Table 2
Table 2: Summary of the first learning task
Input
• 3 channels
• 0.3 s
• random normalization
• only characteristic events (bursts for bursting sig-nals, combustion noise and thermo-acoustic instabili-ties for non-bursting signals)
• Train on fuel configurations Ref, PC1, PC2, MH2,PH2
→ 3181 samples
• Test on fuel configurations MH1, PH1
→ 1269 samples
Target Instability score x ∈ {0, 1, 2, 3}
Expected OutcomeThe classification of characteristic elements of signalunder a simple tuned instability score is possible usingDeep Learning techniques
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8.1.3 Define a learning architecture
To perform the task exposed in the last paragraphs, a simple architecture that aims forcharacteristic features without involving a recurrent layer is built (See Fig. 23). L2 regularizationand Batch Normalization are used.
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Batch Normalization
Batch Normalization
Batch Normalization
Input of the network
Batch Normalization
Flatten Layer
Dense Layer
Output Dense Layer
Output of the network
Dense Layer
L2 Regularization
L2 Regularization
L2 Regularization
L2 Regularization
ReLU
ReLU
ReLU
ReLU
Activation : Softmax
Activation : ReLU
LOCAL
FEATURE
LEARNER
FLATTEN THE
OUTPUT FOR THE
INTERPRETER
INTERPRETER
OUTPUT
Activation : ReLU
L2 Regularization
L2 Regularization
- Filters : 8- Kernel Size : 13
- Filters : 16- Kernel Size : 11
- Filters : 32- Kernel Size : 9
- Filters : 64- Kernel Size : 7
- Pooling Size : 3
- Pooling Size : 3
- Pooling Size : 3
- Pooling Size : 3
- Units : 256
- Units : 128
- Units : 4
Figure 23: Schematic representation of the network used in § 8.1 and § 8.2
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The task defined earlier is a classification into 4 distinct categories. The output layer is thusdedicated to compute a vector of 4 values taken in [0, 1], 1 value per category. Each value refersto the probability that the observed signal is part of the corresponding category. Thus, the 4values sum up to 1. This is made possible through the use of a "softmax" activation function.
The results of the training are presented in the next section.
8.1.4 Results
To assert the precision and efficiency of the network, two diagnoses are performed: theverification of the accuracy of the network after training and the test in usage conditions.
a) Training results
For a multi-class classification problem, the usual performance criterion is the accuracy. Itcomputes the proportion of labels correctly attributed to the samples. In order to monitor theevolution of the training, the training data base is split into two sets. The first one is used forthe optimization, the second one is isolated and used as a validation set. The network is notoptimized on the validation data set. The measure of the precision on this second set is thus away to verify that the network is correctly learning features and not simply learning by heartthe training set.
Figure 24: Training results of the First Approach : (a) Training and validation Accuracy, (b) Trainingand validation loss.
The Fig. 24 depicts the training and validation performance over the epochs. The loss of thenetwork is first decreasing as the model learns features but eventually increases again becauseof overfitting. The network reaches a good compromise between accuracy and loss at 20 epochswhere the training just starts to worsen. The precision of the 20 epochs model on the test cases(MH1, PH1) and validation sets is exposed in Table 3
Table 3: First Approach : Precision of the network
Global Class 0 Class 1 Class 2 Class 3
Test Accuracy MH1 88 % 96 % 76 % 98 % 95 %
PH1 89 % 90 % 84 % X 98 %
Validation Accuracy 92 %
Despite some difficulties to correctly classify the category 1 samples, the global precisionreaches 88 % and 89 % on test samples, which confirms the fact that the training is successful.
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When a ’X’ appears in the table, it means that for the considered injection configuration(here PH1), no operating point of class 2 were detected. Thus, no samples of class 2 are foundin the test dataset.
b) Utilization of the network
From a Machine Learning point of view, the results presented in the last paragraph seempositive. However, the usefulness of such a network is questionable. To simulate a potentialuse of the network, the prediction of the model is evaluated on a rolling window. As the signalstreams to the network, the prediction is recorded which gives the Fig. 25. The model seessnapshots of 0.3 seconds of signal and renders its prediction. In the example given in Fig 26,it can be observed that the model predicts non-zero values intermittently, when it encountersbursts. This is due to the fact that only characteristic events were used during training. Thus,the long periods of combustion noise in-between bursts are predicted as class 0 signals.
Figure 25: First Approach : Network output on a rolling window for the test case MH1, Usw =30m.s−1, φ = 0.8. (a) Network prediction, (b) M1 Microphone pressure signal. Ground Truth is repre-sented by a continuous red line (Class 2 for this operating point).
c) Outcomes and limits
In view of the results it appears that the classification of characteristic elements of signal ispossible using the CNN technology. This successful first implementation demonstrates a highvalidation and testing accuracy which implies that a form of generalization is made possible.
Yet, an essential limitation emerges. As only characteristic events are classified and as theseevents are subjected to intermittency, the detection of precursors is only intermittent. It makesthe network practically unusable (See Fig. 25). This conclusion drives the extension asserted inthe next section.
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Figure 26: First Approach : Network output on a rolling window for the test case MH1, Usw =30m.s−1, φ = 0.8, Focus on a 1s window. (a) Network prediction, (b) M1 Microphone pressure signal.Ground Truth is represented by a continuous red line (Class 2 for this operating point).
8.2 Second Step : Generalization of the results
The limitations of the first trained network motivate the extension of the classification. Thefirst network is only fed by characteristic elements of signal (noise, bursts, instability). It is basedon the assumption that only characteristic events in the signal can be recognized. But, does thenoise between these characteristic events also carry sufficient information to be classified? Or torephrase it, the following section asserts the idea that non-characteristic elements of signal arealso effectively signaling the incoming instability.
8.2.1 Preparation of the Deep Learning study
This second approach is strongly based on the study previously conducted. The 4 distinctclasses introduced in § 8.1.1 are reused:
1. Class 0: Combustion Noise (Stable)
2. Class 1: Bursting (Close to stability)
3. Class 2: Bursting (Close to instability)
4. Class 3: Thermo-acoustic instability (Unstable)
a) Choice of Inputs
The choice of input is the main difference with the precedent section. Instead of selectingonly characteristic elements of signal in the experimental data base, new elements are takenrandomly for every operating point in every fuel configuration. Thus, signal elements are nolonger snapshots of special events and are much more difficult to differentiate for a user. Figure20 displays the process of random selection in a bursting signal (compared to the selection donein the First Approach, See Fig. 20).
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Figure 27: Example of selection of samples in a bursting signal for the Second Approach. (M1) Nor-malized pressure from M1, (M1.HW) Normalized product of the pressure M1 and the velocity HW, (PM)Normalized heat release from PM
b) Choice of Targets
The targets are identical to the targets developed in § 8.1.1.b. The attribution of thetarget to the samples is performed such that every segment of signal randomly extracted froman operating point labelled i is attributed the label i.
8.2.2 Summary of the Learning task
A brief summary of the first learning task is given in Table 4
Table 4: Summary of the first learning task
Input
• 3 channels
• 0.3 s
• random normalization
• random choice of samples for every operating pointin every fuel configuration.
• Train on fuel configurations Ref, PC1, PC2, MH2,PH2
• Test on fuel configurations MH1, PH1
Target Instability score x ∈ {0, 1, 2, 3}
Expected OutcomeThe classification of non necessarily characteristic el-ements of signal under a simple tuned instability scoreis possible using Deep Learning techniques
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8.2.3 Define a learning architecture
The learning architecture is taken exactly identical to the one used before and representedin Fig. 23 (8.1.3). This choice is motivated by the fact that the task is not truly different froman optimization point of view, even if it seems harder.
8.2.4 Results
Thanks to the strong similarities between the First and Second approaches, it is possible touse the same criteria to assert the performance of the network. Thus, training precision andutilization efficiency are both explored.
a) Training results
The training and validation precision measures are represented in Fig. 28. At 30 epochs, agood precision is reached. The test and validation accuracy are gathered in Table 5.
Figure 28: Training results of the Second Approach : (a) Training and validation Accuracy, (b) Trainingand validation loss.
Table 5: Second Approach : Precision of the network
Global Class 0 Class 1 Class 2 Class 3
Test Accuracy MH1 81 % 79 % 71 % 85 % 85 %
PH1 82 % 75 % 73 % X 95 %
Validation Accuracy 90 %
The global accuracy of the network is lower than the accuracy reached in the First Approach(See Table 3). It is certainly due to the increase in complexity of the task. The samples classifiedare no longer of characteristic shape and the features previously easily observable by the user arenow hidden. Notwithstanding these findings, the accuracy obtained remains sufficient enoughwith less than 20 % of failed classification.
b) Utilization of the network
The behaviour of the model simulated on a rolling window is depicted in Fig. 29. The networknow predicts a nearly constant value of 2. Thanks to the choice of extension of the training tonon-characteristic events, the system is more robust to intermittency. Figure 30 confirms the
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fact that the network is now also classifying periods of combustion noise as non-zero categorysamples.
Figure 29: Second Approach : Network output on a rolling window for the test case MH1,Usw = 30m.s−1, φ = 0.8. (a) Network prediction, (b) M1 Microphone pressure signal. Ground Truth isrepresented by a continuous red line (Class 2 for this operating point).
Figure 30: Second Approach : Network output on a rolling window for the test case MH1, Usw =30m.s−1, φ = 0.8, Focus on a 1s window. (a) Network prediction, (b) M1 Microphone pressure signal.Ground Truth is represented by a continuous red line (Class 2 for this operating point).
c) Outcomes and limits
The results gathered in this section are of first importance for the detection of precursors ofinstability. It empirically proves that a Deep Learning network is able to learn usable featuresfrom combustion noise. These features seem to be associated to the proximity of instability as
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elevated scores are observed close to instability regions on the map of the operating points (See21). The potential of such a method could be revealed in a simple scenario. A user is changingthe operating conditions to move on the operating map. As an unstable region gets closer, thepredicted score of the signal increases, warning the user about potential incoming instabilities.Thanks to the results obtained in this section, the warning would be constant as it is maintainedduring periods of a priori harmless combustion noise.
Yet, is it possible to perform such an analysis with more complete criteria than an empiricaldiscrete score ? The following section aims at addressing this problem by proposing operablecriteria and a method to link them to signal samples on the basis of the results obtained in thelast sections.
8.3 Third Step : Toward an operable detection system
On the strength of the two results obtained through the first and second approaches, itis possible to build an architecture which outputs usable criteria from the analysis of signalsamples. This architecture is based on the collaborative work of 3 networks. Each of thempredicts a specific score out of the sample analysis.
8.3.1 Preparation of the Deep Learning study
The three networks output three different scores that offer more insight in the proximity ofan unstable operating point on a 2D map. The map is built on the experimental grid alreadypresented in § 6.1 (Fig. 5).
The three scores are:
• Line L1 : Probability I ∈ [0, 1] that the system is unstable (1 is unstable, 0 is stable).
• Line L2.1 : Real number N ∈ J0, 4K where N is the number of unstable operating pointsnearby.
• Line L2.2 : Real number Y ∈ [0, 1] where Y is the normalized average amplitude of theunstable operating points nearby.
Thus, the combination of the three scores answer these three questions:
• 1/ Line L1 : Is the sample part of an unstable operating point ?
• 2/ If the answer is negative:
– 2.1/ Line L2.1 : How many unstable operating point are there nearby the operatingpoint currently studied?
– 2.2/ Line L2.2 : How elevated is the amplitude of the unstable operating pointsnearby?
Answering the three questions gives an insight on the local shape of the map around astudied operating point. High scores predicted by the lines L2.1 and L2.2 are thus signaling theproximity of strongly unstable operating points on the experimental map.
From a Deep Learning point of view the tasks performed by the three networks are:
• 1/ Line L1 : a Binary classification task
• 2.1/ Line L2.1 : a Multiple-class classification task
• 2.2/ Line L2.2 : a Regression task
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Figure 31: Architecture of the 3 networks system for precursors of instability detection
The total architecture is schematically represented in Fig. 31.
a) Choice of Inputs
In order to capitalize on the results of § 8.2 the same input is taken. It is thus a threechannels (M1, M1*HW, PM) and 0.3 s normalized sample. The sample is taken randomly in thewhole signal for every operating point in every fuel configuration. The sole difference is that thenetwork L1 is trained on stable and unstable samples and both the network L2.1 and L2.2 aretrained on stable samples exclusively.
b) Choice of Targets
The target attribution is based on the RMS analysis of the M1 microphone conducted in8.2.1 (See Fig. 7). Each operating point has potentially three labels to be attributed, one foreach network.
For every operating point, the first task is to assert its general stability.On the one hand, if the RMS of the M1 microphone exceeds the empirical threshold of 250Pa,
the operating point’s first label I is set to 1. In this case the second and third labels are of nouse.
On the other hand, if the RMS of the M1 microphone does not exceed the threshold, thefirst label I of the operating point is set to 0. The second label N is set to the number ofunstable points nearby (from 0 to 4 according to the four possible directions: left, right, up anddown). The third label Y is set to the average of the RMS pressure of the detected unstableoperating points nearby. This average is normalized by the highest RMS ever recorded for allthe experiments : 2000Pa or 160dB.
For example, if 2 unstable operating points were detected in the neighbourhood with 400 and800Pa of RMS, the second label would be 2 and the third label would be 400+800
21
2000 = 0.30.A schematic representation of the label attribution is given in Fig. 32.
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Figure 32: Schematic representation of the labels attribution on a truncated map (RMS mapping ofM1 microphone signal as a font)
The management of the boundaries of the map and the presence of failed acquisitions due todifficult operating conditions is represented in Fig. 33. The treatment is such that:
1. The lower equivalence ratio φ boundary is treated as stable neighbours.
2. The lower bulk velocity Usw boundary is treated as stable neighbours.
3. The higher equivalence ratio φ boundary is treated as unstable neighbours.
4. The higher bulk velocity Usw boundary is treated as unstable neighbours.
5. The failed acquisitions at low equivalence ratio and low bulk velocity are treated as stableneighbours
6. The failed acquisitions at high equivalence ratio and high bulk velocity are treated asunstable neighbours
For the case Ref, the label attribution is depicted in Fig. 34.
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Figure 33: Management of the boundary conditions in terms of neighbour number evaluation N
Figure 34: Labels attribution in the Third Approach for the case Ref (RMS mapping of M1 microphonesignal as a font)
8.3.2 Summary of the Learning tasks
A brief summary of the learning tasks is given in the Table 6
8.3.3 Define learning architectures
Three learning networks have to be defined in order to build the whole architecture. Thethree networks are trained and tested separately. they are eventually used together in § 8.3.4.bin order to evaluate the potential of such a method in a simple usage scenario.
a) Line L1
The first line L1 is dedicated to the determination of the stability state of the system throughthe analysis of a sample. As the task is close to the task proposed in § 8.2, the same network
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Table 6: Summary of the learning tasks for the three networks system
L1 L2.1 L2.2
Input
• 3 channels
• 0.3 s
• random normal-ization
• random choiceof samples forevery operatingpoint in every fuelconfiguration.
• Train on fuelconfigurationsRef, PC1, PC2,MH2, PH2
• Test on fuel con-figurations MH1,PH1
• 3 channels
• 0.3 s
• random normalization
• random choice of samples for everystable operating point in every fuel con-figuration.
• Train on fuel configurations Ref, PC1,PC2, MH2, PH2
• Test on fuel configurations MH1, PH1
Target Instability Probabil-ity x ∈ [0, 1]
Number of unsta-ble neighbours N ∈{0, 1, 2, 3, 4}
Normalized AverageRMS of unstableneighbours Y ∈ [0, 1]
ExpectedOutcome
The user is able to obtain local information on unstable operatingpoints located nearby the studied operating point by the analysis ofa short sample of signal
architecture has been chosen (See Fig. 23). However, the last layer is transformed to output theright score. The activation function is a "sigmoïd" which outputs a value in the range [0,1] andis thus adapted for binary classification.
b) Line L2.1
The network L2.1 is attributed the task to classify samples into 5 different categories. Thepositive contribution of a global feature learner after the CNN blocks has been asserted. Thenetwork architecture is depicted in Fig. 47 in APPENDIX 8.1. The last layer has an activationfunction of type "softmax" (see § 8.2.3) to output a vector of 5 values P ∈ [0, 1]5 assimilatedto probabilities. The number of unstable operating points nearby the current point is thusapproximated by N =
∑4i=0 i.Pi.
c) Line L2.2
The network L2.2 is assigned to determine a score through regression. The network archi-tecture is copied from L2.1 and is represented in Fig. 47 in APPENDIX 8.1. A common way tohandle a regression is to take off the activation function of the last layer such that the networkoutputs one floating point number without any constraint.
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8.3.4 Results
The three models used to build the architecture have their own method to monitor theirprecision. The next sections are dedicated to the diagnosis of the different networks.
a) Training results
L1 model:
A good trade-off between a high accuracy and a low loss is obtained after 80 epochs of train-ing. This simple binary classification is achieved with a validation accuracy of 99 % and a testaccuracy for MH1 (resp. PH1) of 97 % (resp. 94 %). It confirms that recognizing instability isa task nearly perfectly feasible by a CNN network (see Fig. 35).
Figure 35: Training results of L1 : (a) Training and validation Accuracy, (b) Training and validationloss.
L2.1 model:
The L2.1 model reaches its best precision at 42 epochs with a validation accuracy of 90 %(See Fig. 36). Further insights on the efficiency and accuracy of the model are given in the nextparagraph § 8.3.4.b.
Figure 36: Training results of L2.1 : (a) Training and validation Accuracy, (b) Training and validationloss.
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L2.2 model:
As the task of this model is a regression, the notion of accuracy would make no sense.Therefore, the precision of the network is verified by computing the Mean Absolute Error (MAE).The MAE is computed as such:
MAE =1
N
N−1∑i=0
|pi − li| (21)
where (pi)i∈J0,N−1K is the vector of predictions and (li)i∈J0,N−1K is the vector of referencelabels and N is the number of experience in the data set.
The optimum is then obtained at 95 epochs with a validation MAE of 0.075 (see Fig. 37).
Figure 37: Training results of L2.2 : (a) Training and validation Mean Absolute Error, (b) Trainingand validation loss.
b) Utilization of the network
Rebuild the map of label using predictions
In order to better assert the precision of the whole method, the map of averaged predictionson rolling windows is computed for each test case (MH1 and PH1). The example of MH1 isgiven in Fig. 38. This map has to be compared to the map of the reference labelling initiallycomputed to build the target of the training displayed in Fig. 39.
As the comparison value by value remains tedious, the root mean square error and the meanabsolute error are computed for each test case. Once normalized to lie in [0, 1], these twomeasures approximate the error of both L2.1 and L2.2 models. These two errors measurementwill be referred to as "mapping RMSE" and "mapping MAE".
For example a mean absolute error of 0.1 means that, on average for every operating point,the mean prediction is off by 10 % of the total range. For L2.1, the total range is 4 (maximumnumber of unstable neighbours) and for L2.2, the total range is 1 (due to prior normalization).
These results are gathered in Table 7:Both measures imply that the predictions are, on average close to the reference labelling.
Yet, these are only global criteria. It is possible to observe where most prediction errors are bycomputing the magnitude E:
E =√E2L2.1 + E2
L2.2 (22)
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Table 7: Third Approach : Precision of the networks L2.1 and L2.2
L2.1 MH1 PH1
mapping RMSE 0.104 0.216
mapping MAE 0.072 0.184
L2.2 MH1 PH1
mapping RMSE 0.150 0.159
mapping MAE 0.106 0.119
where EL2.1 (resp. EL2.2) is the error made by L2.1 (resp. L2.2) normalized by the maximumrange R (R = 4 for L2.1 and R = 1 for L2.2). Figure 40 represents the localisation of errors.The diameter of the circles is proportional to the magnitude E.
It can be observed that errors seem to be localised in the upper right corner of the domainwhich means that for most operating points, the precision achieved is high.
Figure 38: Third Approach : Averaged predictions for the test case MH1 (RMS mapping of M1microphone signal as a font)
Figure 39: Third Approach : Reference label attribution for the test case MH1 (RMS mapping of M1microphone signal as a font)
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Figure 40: Third Approach : Localisation of sources of errors for the test case MH1, (RMS mappingof M1 microphone signal as a font).
Using the final system on a rolling window
The use of the architecture is represented in Fig 41 for the case MH1, Usw = 30m.s−1
and φ = 0.8. L1 predicts correctly the stability of the system. L2.1 predicts a steady value of2 which corresponds to the fact there are exactly 2 unstable neighbours on the map (See Fig.39). Finally, L2.2 is more volatile but consistently predicts an average value of 0.41 close to thereference value of 0.49.
c) Outcomes and limits
The construction of the architecture and the different results obtained are promising. Theprediction of proximity criteria on the operating point map is successfully performed. It consol-idates the fact that the fine analysis of features in the signal can be done by a learning model.These features can then be related to unsophisticated criteria which inform the user on the cur-rent state of the system. Moreover, as the samples used are of length 0.3s, the predictions onthe system are nearly a real-time information.
At last, the use of simple positional considerations makes the interpretation of the outputsof the different networks straightforward.
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Figure 41: Third Approach : Networks outputs on a rolling window for the test case MH1, Usw =30m.s−1, φ = 0.8. (a) L1 instability prediction I, (b) L2.1 prediction of the number of unstable neighboursN , (c) L2.2 prediction of the RMS amplitude of the unstable neighbours Y , (d) M1 Microphone pressuresignal. Ground Truths are represented by a continuous red line (I = 0, N = 2, Y = 0.49).
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9 Discussion
This section aims at providing a critical perspective on the approaches presented in this studyand it explores the different possibilities to answer to these criticisms. The ideas underscoredhere are also openings to a better comprehension and usage of these results and the chance toprepare the next steps for the studies beginning after the end of this thesis.
9.1 Machine Learning and the concept of "Black Box"
The promising results obtained in the precedent sections point toward an observation onstability analysis. More than the apparent efficiency of Learning models, it is the opportunity tohave the confirmation that meaningful features are present in the signal at the onset of instability.
However, the use of Deep Learning raises one crucial criticism. Even if the model efficientlyassociates features to empirical scores, it is difficult to find out the exact characteristic of thesefeatures. This is due to the fact that the model is built by an optimization algorithm whichis practically impossible to interpret. Finding which features of the input has led to a specificoutput is a complicated task. This is the concept of "Black Box". It is a problem when thereliability of the tool has to be evaluated. Even if the system is efficient, not knowing how ithappens to be efficient raises one crucial question: is it possible to certify such a system forreal-conditions use ?
In § 7.1.1, the supervised Machine Learning is exposed as the ability to produce internal rep-resentations from the analysis of inputs and their corresponding outputs (See Figure 15). A majorproblem remains generally unsolved: These internal representations can be used for predictionpurposes but can not be explained. Even if several groups have worked on the interpretability ofneural networks [13], [3] these remain case-by-case approaches adapted to very specific tasks. Inthis study, there is no simple intuition to explain certainly what allows convergence based on thecombustion theory. Nevertheless, asserting this problem is a work-in-progress. One possibility isto use synthetic signal. Artificially created signal imply that the user knows exactly which set ofparameters composes the signal (modes, frequency, ...). In APPENDIX 9.1, a potential track fora precise modal reconstruction, named after the mathematician Gaspard de Prony, is exposedand could be an initial idea to explain which parameter of each mode influences the decisions ofthe networks.
9.2 Validation of the use of CNN with LSTM
The choice of CNN + LSTM layers during the construction of the network has been justifiedin the paragraph § 7.4. Nevertheless, it is still necessary to verify that this choice is practicallymore efficient than other simpler approaches concerning the Machine Learning part of this study.
In order to give a first answer to this problem, the comparison between the performance of1- a simple Multi-Layer Perceptron, 2- a network composed of CNN blocks only (Fig. 23) and3- the network composed of both CNN and LSTM blocks (Fig. 47) is conducted. A Multi-LayerPerceptron (MLP) is one of the simplest types of network. It is only composed of Dense layers(See § 7.4.3). In this case the MLP chosen is composed of 2 Dense layers of same size than theinterpreter used in the more complete networks. It is a good simple way to see the advantagesof using local and global feature learners (CNN and LSTM blocks).
The learning task on which the three networks are trained are the task of the L2.1 layerin the three networks approach (See § 8.3.2): classifying stable samples regarding the numberof neighbours surrounding the current operating point. The precision of the networks based onaveraged predictions on the whole MH1 test map are given in Table 8.
The CNN + LSTM approach thus gives better results than the two other simple methodswhich confirms partially that its use is preferable. However the MLP seems to give better resultsin terms of averaged predictions (See mapping RMSE and MAE in Table 8) than the CNN
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Table 8: Comparison of the precision of the networks
L2.1 MLP CNN CNN + LSTM
Validation Validation Accuracy 56.7 % 86.4 % 90.5 %
Test Test Accuracy (MH1) 68.9 % 70.4 % 71.8 %
mapping RMSE 0.115 0.118 0.104
mapping MAE 0.081 0.088 0.072
network even if the validation accuracy is much lower. To verify that the CNN is in fact moreprecise, the evaluation of the predictions on a rolling window is done in Figure 42.
Figure 42: Comparison of the networks outputs on a rolling window for the test case MH1, Usw =30m.s−1, φ = 0.8. (a) MLP output, (b) CNN output, (c) CNN + LSTM output, (d) M1 Microphonepressure signal. Ground Truths are represented as a continuous red line (2 unstable neighbours for thisoperating point)
It is therefore possible to see that the MLP is actually retrieving perfectly the average of thescore to predict. Yet, the model disperses more than the two other networks that have a moreconstant behaviour. Moreover, it appears that the combined use of a CNN + LSTM networkoffers a more stable behaviour than a sole CNN architecture.
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This last figure thus confirms the fact that:
1. The use of a local feature learner is beneficial (CNN blocks)
2. The use of a global feature learner is beneficial (LSTM layer)
3. A simple MLP is capable of performing the classification but disperses which makes itimprecise in a real usage scenario such as the rolling window prediction.
9.3 Robustness to modifications of the experimental conditions and setup
The training of every network is performed on the dataset presented in § 6. But, is theprediction still possible when the experimental setup and conditions are modified ?
In a second experimental campaign, two aspects of the experimental conditions and setup arechanged. The first aspect concerns the geometry of the combustor as elements are changed. Thesecond concerns the atmospheric conditions. The Tables 9 10 and gathers the differences betweenthe two experiments. This provided an opportunity to test the robustness of the networks tosignificant changes in the setup, as well as different atmospheric conditions.
Table 9: Comparison of the experimental setup for the first and second campaign.
Experimental setup Exp 1 Exp 2
Swirler : swirl angle θs = 15◦ θs = 35◦
Quartz chamber diameter 46 mm 64 mm
Table 10: Comparison of the atmospheric conditions for the first and second campaign.
Operating atmospheric conditions Exp 1 Exp 2
Season Spring 2019 Winter 2019
mean atmospheric Temperature Tatm = 21.2◦C Tatm = 15.8◦C
mean atmospheric Pressure patm = 1.00 bar patm = 0.98 bar
The stability analysis of the reference case Ref2 is performed (only methane in premixedinjection). The map of the RMS of the M1 microphone pressure is displayed in Figure 43.
The behaviour of the system with respect to the parameters Usw and φ is largely changedin comparison to the initial experimental setup (See Figure 7). The use of the three networkssystem developed in § 8.3 on this new set of data is then performed and the errors made by thedifferent networks is summarized in Table 11.
Table 11: Precision of the networks L2.1 and L2.2 on Exp 2
Network L2.1 L2.2
Configuration Exp 1 MH1 Exp 2 Ref Exp 1 MH1 Exp 2 Ref
mapping RMSE 0.104 0.280 0.150 0.240
mapping MAE 0.072 0.240 0.106 0.220
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Figure 43: Mapping of the RMS of the pressure from M1 in case Ref2 with acoustic dB for Exp 2
The errors are more than doubled, in comparison to the typical level of error obtained in§ 8.3.4.b. However, these errors remain low regarding the fact that several important changeshave been done between the two systems. Even if the passage from a combustor to anothermeans that the predictions’ precision will decrease, it is possible to observe that the featureslearnt by the network on the first data set are still useful for convincing predictions on a differentsystem.
These results are a first step toward the transposition of the learning system developed hereto industrial size combustion devices. A deeper understanding of the impact of geometry changesand experimental is to be obtained thanks to the modularity of MIRADAS-type systems. Nextsteps are thus to assert individually the influence of:
• Changes in swirl number
• Changes in fuel proportions (higher H2 proportions for example)
• The switch to liquid fuels (n-Heptane (C7H16) and n-Dodecane (C12H26))
• Repeated experiments at different atmospheric conditions (changes in Hydrometry, Tem-perature and Pressure)
Finally an implementation of this learning system on a multi-injector annular combustionchamber is in discussion, as well as the possibility to transpose this work to a real configurationwith the SAFRAN Aircraft Engines partnership.
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10 Conclusion
This work was focused on the development of a first solution for the detection and predictionof unstable phenomena. The analysis performed on a laboratory scale experiment composed ofan aeronautical grade swirled injector confined in a combustion chamber as revealed promisingresults and the opportunity to open the path to further improvements.
Based on the stability analysis of the combustor, the occurrence of characteristic events -bursting - could be observed and led to the definition of classes for a first approach. The analogybetween the data obtained experimentally and voice samples led to the use of Speech Recognitiontechnologies. Therefore, networks built with Convolutional Neural Network (CNN) blocks andLong Short Term Memory (LSTM) were implemented and trained on the dataset.
The first task was to prove that classifying signal using such a technology was possible forcharacteristic events. Furthermore, the extension to non-a-priori-characteristic events was neces-sary to ensure a constant warning for the user. Eventually, the development of a tool constructedaround three networks could lead to more user-centered criteria for instability prediction (SeeFig 44).
NO
LineL1
LineL2.1
LineL2.2
Probability II > 0.9
N
Y
CurrentO.P.
sampleI
Sensors
M1
M1.HW
PM
- Is the system unstable ?
- Are we close to unstableO.P. ?
- How dangerous is it ?
SYSTEMSIDE
USERSIDE
Figure 44: Representation of the potential use of the system developed in § 8.3
The promising performances of this last system offer several opportunities to develop newtools for instability prediction. To continue this study, it is possible to work on several aspects.
First and foremost, it is important to adapt the results to other combustion events such asblow-off and flash-back. As instability is often a precursor to these events, the transpositionfrom the study of precursors of instability to the prediction of blow-off and flash-back should bepossible. The PhD study that follows this introduction work will have to discover the modalityof this transposition.
Furthermore, having a better insight into the activity of the network is a priority in orderto better understand what are the parameters of interest that are chosen by the model to beanalysed. This may be possible through the artificial creation of signal thanks to the Pronyanalysis (See § 9.1). This tool would offer a way to reconstruct signal from samples and thengives the possibility to play with the parameters of the reconstruction. The artificial signal couldthen be sent to the input of the model in order to see the effects of each parameter on the output.It is one option for a better understanding of the networks’ activity.
An additional need is also to continue searching new models and better structures in the DeepLearning library of tools. More efficient limitations management are to be found to perform evenbetter. Finding the most optimized system for such a task is still awork in progress.
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Finally, an essential challenge is to continue the transposition of the method to other systems.First, the study of modifications of the geometry in parallel with the monitoring of the perfor-mance of the models will be continued (See § 9.3). This is a first key to assert the flexibility ofthe whole method as it is currently a gap to fill in this work. As the main aim is to transposethis methodology to real engine configurations, the next step will be to train and test the modelon liquid injection systems, followed by the adaptation to annular chamber configurations andeventually to real engine bench (thanks to the partnership of SAFRAN Aircraft Engines).
These challenges are milestones on the way of the development of a user-ready prototype ofcritical event predictor built around Deep Learning techniques (instability, aging, destruction,stalling, ...). This work has the opportunity to be a step on this way.
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Acknowledgements
I would like to thank particularly the teams of the CERFACS and the IMFT who helped meand guided me through all the different challenges of this thesis. I especially want to express mygratitude to Dr. Thierry Poinsot for the amazing opportunity to join the SCIROCCO projectwith a very original and interdisciplinary subject that was a chance to be introduced to newscientific researches and to develop new concepts freely. I also thank Nenad Glodic for acceptingto be my supervisor for KTH.
I also thank the MIR / SCIROCCO team from the IMFT for sharing their knowledge andfor their redaction advice : Dr. Thierry Schuller, Dr. Laurent Selle, Dr. Omar Dounia and thePhD students Gorkem Öztarlik, Sylvain Marragou, Titouan Morinière, Andrea Aniello, Pierre-Alexandre Masset, François Muller and Mohamed Zekad.
I would like to express my regards to the Deep Learning / E0 team of the CERFACS whooffered their help and knowledge : Dr. Corentin Lapeyre, Victor Xing, Nicolas Cazard andCamille Besombes.
I finally thank all the people that helped me to achieve this journey to the master thesis.
This project has received funding from the European Research Council under the EuropeanUnion’s Horizon 2020 research and innovation program Grant Agreement 832248, SCIROCCO.
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11 Appendices
11.1 APPENDIX 5.1
Derivation of the acoustic energy equation (2) from the simplified Navier andStokes equations
The starting equations are:
Dρ
Dt+ ρ∇.~u = 0 (23)
ρD~u
Dt= −∇p+∇.¯τ (24)
ρCpDT
Dt= ωT +
Dp
Dt+∇(λ∇T ) + ¯τ : ∇~u (25)
Where
• Eq. (23) is the conservation of mass
• Eq. (24) is the conservation of momentum
• Eq. (25) is the conservation of energy
In Eq. (25), the different terms are such that they account for:
• ρCp DTDt : variation of enthalpy of the system
• ωT : heat rate released by the combustion
• DpDt : work rate released by pressure variation
• ∇(λ∇T ) : heat rate dissipated by conduction
• ¯τ : ∇~u = τij∂ui∂xj
: heat rate dissipated by viscous effects
The validity of Eq. (23), (24) and (25) is limited to mono-specie gases or multi-species gaseswith negligible molecular weight and heat capacity variations from a specie to another (heatlosses due to diffusion of the different species are thus neglected).
For negligible viscous effects and conduction dissipation, the three equations can be rewrittenas:
Dρ
Dt+ ρ∇.~u = 0 (26)
ρD~u
Dt= −∇p (27)
ρCpDT
Dt= ωT +
Dp
Dt(28)
1 Modify the energy equation:
By dividing the Eq. (28) by ρCpT and differentiating the ideal gas law, in the assumption ofnegligible molecular weight variations, the two following relations are derived:
66
1
p
Dp
Dt=
1
ρ
Dρ
Dt+
1
T
DT
Dt(29)
1
T
DT
Dt=
1
ρCpTωT +
1
ρCpT
Dp
Dt(30)
By merging Eq. (29) and (26) to express the term 1TDTDt as 1
pDpDt −∇.~u and further injecting
it in (30), the acoustic wave equation is obtained:
1
p
Dp
Dt(1− 1
ρCpT)−∇.~u =
1
ρCpTωT (31)
Using the ideal gas law and Cp = γrγ−1 , it rewrites as:
1
γp
Dp
Dt−∇.~u =
γ − 1
γpωT (32)
2 Linearise the energy and momentum equations:
Let p, ~u, ωT and ρ be such that:
p = p0 + p1
~u = ~u0 + ~u1
ωT = ωT0 + ωT1
ρ = ρ0 + ρ1
(33)
With p0, ~u0, ωT0 and ρ0 the mean values around which the perturbations p1, ~u1, ωT1 and ρ1evolve (|p1| � p0, |~u1| � |~u0|, |ωT1| � ωT0 and |ρ1| � ρ0).
If the convective derivative (~u.∇~u ≈ ~u0.∇~u1) is neglected in comparison to the time derivative∂~u∂t = ∂~u1
∂t , Eq. (27) is linearised as:
ρ0∂~u1∂t
= −∇p1 (34)
And by assuming that spatial derivatives are negligible in comparison to time derivatives(|~u0.∇p1| � |∂p1∂t |), Eq. (32) is linearised as:
1
γp0
∂p1∂t−∇. ~u1 =
γ − 1
γp0ωT1 (35)
3 Derive the equation for unsteady acoustic energy:
The unsteady acoustic energy is expressed as:
e1 =1
2ρ0 ~u1
2 +1
2
p21ρ0c20
(36)
Taking the scalar product of Eq. (34) by ~u1 and multiplying Eq. (35) by p1 lead to:
∂
∂t(1
2ρ0~u
21) + ~u1.∇p1 = 0 (37)
∂
∂t(1
2
p21γp0
) + p1∇.~u1 =γ − 1
γp0p1ωT1 (38)
Summing Eq. (37) and (38) and using the relation c20 = γp0ρ0
eventually gives the linearisedacoustic energy equation in presence of a flame:
∂e1∂t
+∇.(p1 ~u1) =γ − 1
γp0p1ωT1 (39)
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11.2 APPENDIX 5.2
Integration of the equation (2) over a control volume
Integrating Eq. (2) over the control volume V gives:˚
V
∂
∂te1 +∇.(p1 ~u1) dV =
˚V
γ − 1
γp0p1ωT1 dV (40)
The time derivative can be put out of the integral and as e1 is a function of the position andthe time, its integral over the volume is only depending on the time, thus ∂
∂t is changed for ddt :
d
dt
˚Ve1 dV +
˚V∇.(p1 ~u1) dV =
γ − 1
γp0
˚Vp1ωT1dV (41)
Green-Ostrogradski’s theorem is eventually used to obtain the final form of the integralacoustic energy equation:
d
dt
˚Ve1dV +
"Sp1 ~u1. ~dS =
γ − 1
γp0
˚Vp1ωT1dV (42)
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11.3 APPENDIX 6.1
Simple routine for burst detection and storing
Algorithm 1 Burst detectionX ←M1.HW
1. Find the frequency of the carrier signal
Compute PSD[X](f)fmax = arg(max(PSD[X](f)))
2. Derive a new signal on which peak detection is possible
Compute Spectrogram[X](f)Select a slice of the Spectrogram around fmaxAverage in frequency the selected portion (→ Savg(t))
3. Perform peak detection on the temporal signal obtained
Detect peaks in Savg(t)Return peaks data:→ Peak positions (location of the burst on the time-line)→ Peak heights (power of the burst)→ Peak widths (duration of the burst)
Comments:1. PSD: Power Spectral Density2. Spectrogram: Consists in a short time rolling window PSD of the signal in order toevaluate the temporal evolution of the frequency decomposition of the signal and is thus threedimensional : time, frequency, power amplitude.3. Selecting around the frequency of the carrier ensures a better visibility and detection as itis at this frequency that the system resonates when the burst appears
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11.4 APPENDIX 7.1
Label attribution algorithm for the first approach
Figure 45: Scheme of the weighted average used for neighbour influence determination in Algorithm 2
Figure 46: Schematic representation of the algorithm for label attribution (Algorithm 2)
70
Algorithm 2 First approach: Label attribution routineTuned parameterspthr1RMS # pressure amplitude thresholdpthr2RMS # neighbour average pressure amplitude thresholdN thrb # number of bursts threshold
Ethrb # burst average energy thresholdW1 # weight of the closest neighbours (see Fig. 45)W2 # weight of the further neighbours (see Fig. 45)
Initialised OutputL # grid of labels, each element is set to zero for initialisation
Inputpi,jRMS # RMS of the pressure (M1) of the operating point OP(i, j)N i,jb # Number of bursts detected for the operating point OP(i, j)
Ei,jb # Average energy of the bursts detected for the operating point OP(i, j)
Label attributionfor each column i dofor each row j do
if pi,jRMS = 0 thenLi,j ← ”X” # No data acquired
end if
if pi,jRMS > pthr1RMS thenLi,j ← 3 # Unstable state
end if
if N i,jb > N thr
b thenif Ei,jb > Ethrb then
pi,jRMSneigh← f(W1,W2) # Where f is the weighted averaging function (see Fig. 45)
if pi,jRMSneigh> pthr2RMS then
Li,j ← 2 # Class 2 burst (close to instability)
elseLi,j ← 1 # Class 1 burst (further to instability)
end if
end ifend if
end forend for
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11.5 APPENDIX 8.1
Scheme of the network used in § 8.3
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Convolution Layer
Activation Unit
Max Pooling Layer
Batch Normalization
Batch Normalization
Batch Normalization
Input of the network
Batch Normalization
LSTM Layer
Output Dense Layer
Output of the network
L2 Regularization
L2 Regularization
L2 Regularization
L2 Regularization
L2 Regularization
ReLU
ReLU
ReLU
ReLU
LOCAL
FEATURE
LEARNER
GLOBAL FEATURE
LEARNER
- Filters : 8- Kernel Size : 13
- Pooling Size : 3
- Filters : 16- Kernel Size : 11
- Pooling Size : 3
- Filters : 32- Kernel Size : 9
- Pooling Size : 3
- Filters : 64- Kernel Size : 7
- Pooling Size : 3
Dense Layer
Dense Layer
Activation : To Determine
Activation : ReLU
Activation : ReLU
L2 Regularization
L2 Regularization
INTERPRETER
OUTPUT
- Units : 256
- Units : 128
- Units : 4
- Units : 128
Activation : tanh
Recurrent Activation: sigmoïd
Figure 47: Schematic representation of the network used in § 8.3 to associate the number of unstableneighbours and their average amplitude to a signal element.
72
11.6 APPENDIX 9.1
Prony: the modal reconstruction method
In order to find more clues on what the model is detecting, a possibility is to artificiallyproduce some signal and feed it to the network. A major problem is to find a method preciseenough to artificially build a convincing signal that would contain the information needed by thenetwork. Yet, a simple Fourier analysis and reconstruction would not offer enough precision asonly frequency and amplitudes of each mode are extracted. Thus, the method of Prony wouldbe a better candidate [15]. It is based on a modal decomposition:
x(t) = <{M∑m=0
Amexp(νmt)exp(2πj(fmt+ φm))} (43)
Each mode is thus characterized by its amplitude Am, frequency fm, damping νm and phaseφm. A main difficulty with this method is that the analysis is only valid on a short window as thepresence of either positive or negative dampings makes the decomposition diverge or converge tozero for long windows. An example of reconstruction is done in the Fig. 48 with a sample fromthe M1 Microphone signal in the case Ref.
Figure 48: Reconstruction with 60 modes of a sample from M1 in the case Ref, Usw = 30m.s−1,φ = 0.8, for a window of 15 ms
Even if the signal is complex due to its noisy characteristics, the method is able to reconstructwith a high degree of fidelity the original signal. The error on the energy of the signal calculatedin eq. 44 is of 5 %.
Err =|´ t1t0
[xo(t)]2dt−
´ t1t0
[xr(t)]2dt|´ t1
t0[xo(t)]2dt
(44)
It would thus be a promising tool to produce artificially convincing signals to better under-stand what are the features detected by the networks. The implementation of this approach maybe an important axis of the following PhD study.
73
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