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Sven Eckart a,*, Rene Prieler b, Christoph Hochenauer b, Hartmut Krause a
Experimental Dataset –Training and Validation Data for the NN
Fig.1 Relationship between number of data
points and year of publication
The laminar burning velocity is a fundamental property of a reactive fuel-oxidizer mixture, varying with composition, pressure and initial temperature. These values are important for
validation of reaction mechanisms and the specific design of industrial burners in general, and, with the main aim of this study, for the usage of different hydrogen and methane
mixtures. However, there is a lack of a fast and accurate method for forecasting data for the combustion of hydrogen and methane in different mixing ratios. Commonly, the laminar
burning velocities and other thermo-chemical processes (e.g. in CFD simulations) within a main reaction zone of a flame are predicted solving the detailed or skeletal reaction
mechanisms, which are represented by a set of differential equations. However, the time is a crucial issue when used in control systems or even CFD simulations. This would
significantly simplify the control and adjustment of rapidly changing gas compositions and make the combustion processes even more efficient. Methods of machine learning could
be applied for this purpose. These can derive a control state from already existing large data sets of fundamental flame parameters.
Rationales & Objectives
Conclusions & Outlook
Numerical Method
38TH International Symposium on Combustion, Adelaide, Australia, 24.1. –29.1.2021
a Institute of Thermal Engineering, TU Bergakademie Freiberg, Freiberg, Germany
b Institute of Thermal Engineering, Graz University of Technology, Graz, Austria
USING MACHINE LEARNING TECHNIQUES TO CALCULATE THE LAMINAR
BURNING VELOCITY OF HYDROGEN-METHANE MIXTURES
Comparison of the predictability of all four methods used with the experimental results
* contact:
M.Sc. Sven Eckart
TU Bergakademie Freiberg | Institute of Thermal Engineering
sven.eckart@iwtt.tu-freiberg.de | www.gwa.tu-freiberg.de
* contact:
Ass.Prof. Dr.techn. Rene Prieler
Institute of Thermal Engineering| Graz University of Technology
rene.prieler@tugraz.at | www.iwt.tugraz.at
Fig.3:
Above:
results of the linear regression
below:
results of the SVM method
Methane/Hydrogen/Air experimental conditions
Pressure 1.0 –10.0 bar
Temperature 268.0 –574.0 K
LBV 3.7 –532.41 cm/s
Equivalence ratio 0.3 –3.2
No.of exp. points ~1376+own data
No of papers >33 (2005-2020)
Methods R Square value RMSE
Linear regression 0.402 47.741
SVM 0.743 31.311
Random forest 0.938 15.411
ANN 0.951 14.310
Fig.4:
Above:
results of the random forest
below:
results of the ANN method
1. Generalized linear regression models (GLM)
GLM has the lowest prediction accuracy
oLBVs are under-predicted by the GLM when the H2 content is
increasing
oSignificant errors at higher LBVs occur
oLBVs at a lower level are mainly over-predicted
The GLM fails to predict the LBV for high and low H2
concentrations in the fuel mixture
2. Support Vector Machines (SVM)
The SVMs showed a better prediction performance than
the GLM
oAt higher LBVs the predicted values are still too low
(compare to GLM)
oFor low LBV large dispersion
Fig.5: Results of the calculations for linear
regression, SVM, random forecast and
neuronal network
Fig.3 Relationship between hydrogen
ratio and the temperature in the data sets
Data set on laminar burning rate created from literature from
2005 onwards
one partial data set (basket) each for pre-heating temperature
(T>308 K), pressure (p>1 bar), and remaining data
Equivalence ratio from 0.3 to 3.2 and mixtures from 0-100% H2
admixture in methane
hydrogen content is crucial for the LBV
1. Generalized linear regression models (GLM)
GLM employs the linear function to describe the relationship, considering parallelly the error
distribution. This is the simplest comparison model.
2. Support vector machines (SVM)
Support vector machine (SVM) is a supervised learning model with associated learning
algorithms that analyze data used for classification and regression analysis. Therefore,
computing the (soft-margin) SVM classifier amounts is necessary. SVM defines the
acceptable area in the model to fit the data in a better way. The input is mapped through a
nonlinear function (so called kernel function). To predict the dependent variable, a linear
regression function is computed in a high dimensional feature space.
Main advantage of developed models are the much shorter computational
time, compared to detailed reaction mechanisms
Random forest and ANN showing good predictability over a wide range of
conditions
R² : ANN>RF>SVM>MLM RMSE: ANN<RF<SVM<MLM
Future work: qualitative comparison with detailed reaction mechanisms
and extension to other fuel mixtures, like ammonia-methane-hydrogen
mixtures
All methods show deviations at higher LBV, and thus higher H2
concentrations. In this range even more experimental data is necessary to
train the ANN.
3. Random forest (RF)
The RFs showed a better prediction performance than
the SVM
oRF showed a very good prediction accuracy for the
experimental data
oSingle under-estimation and over-prediction for high LBV
oFor low LBV small dispersion
4. Artificial neural network (ANN)
ANN best prediction accuracy of tested methods
oIndividual data underestimation
oFor low LBV hardly any dispersion
oFor higher LBV/H2 ratios more data
is needed
Instead of calcualting the LBV using a detailed reaction kinetic 4 alternative approaches were used based on machine learning techniques:
3. Random forest (RF)
A RF is a classification and regression method consisting of several uncorrelated decision “trees”. All decision
trees have grown under a certain type of randomization during the learning process. For a classification, each
tree in this forest is allowed to make a decision and the class with the most votes decides the final
classification. A RF can score with many advantages over other classification methods like SVM.
4. Artificial neural network (ANN)
The structure of ANNs, is a multi-layered Feed-Forward Neural Network (MFNN), which consists of three
layers (input, hidden and output layer). Depending on the activation layer of the neurons, the network signal
is transmitted using the activation function. After the activation process, the signal is forwarded to the output
layer. For simplicity, it is assumed that only one neuron is contained in the output layer. The output value of
the neuron in this case is the predicted LBV. Fig.2 Relationship between hydrogen ratio
and the laminar burning velocity
