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Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks

Neven Kanchev

Neven Kanchev

Department of Electrical Measurements, Technical University of SofiaBulgaria
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Kanchev, Neven
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Nikolay Stoyanov

Nikolay Stoyanov

Department of Electrical Measurements, Technical University of SofiaBulgaria
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Stoyanov, Nikolay
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Georgi Milushev

Georgi Milushev

Department of Electrical Measurements, Technical University of SofiaBulgaria
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Milushev, Georgi
  
24. Feb. 2025
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Online veröffentlicht: 24. Feb. 2025
Seitenbereich: 1 - 9
Eingereicht: 18. Juli 2024
Akzeptiert: 08. Jan. 2025
DOI: https://doi.org/10.2478/msr-2025-0001
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© 2025 Neven Kanchev et al., published by Sciendo
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Fig. 1.

Ultrasonic flow measurement principle.
Ultrasonic flow measurement principle.

Fig. 2.

Schematic diagram of the MLP-ANN.
Schematic diagram of the MLP-ANN.

Fig. 3.

Schematic diagram of the RBF-ANN.
Schematic diagram of the RBF-ANN.

Fig. 4.

Effect of the number of hidden neurons of the MLP-ANN for the LM algorithm.
Effect of the number of hidden neurons of the MLP-ANN for the LM algorithm.

Fig. 5.

Effect of the number of hidden neurons of the MLP-ANN for the SCGD algorithm.
Effect of the number of hidden neurons of the MLP-ANN for the SCGD algorithm.

Fig. 6.

Scatter plot of predicted values versus observed values for MLP-ANN.
Scatter plot of predicted values versus observed values for MLP-ANN.

Fig. 7.

Plot of predicted values versus observed values for MLP-ANN.
Plot of predicted values versus observed values for MLP-ANN.

Fig. 8.

Scatter plot of predicted values versus observed values for RBF-ANN.
Scatter plot of predicted values versus observed values for RBF-ANN.

Fig. 9.

Plot of predicted values versus observed values for RBF-ANN.
Plot of predicted values versus observed values for RBF-ANN.

Fig. 10.

Comparison of relative errors of the MLP-ANN and the RBF-ANN model.
Comparison of relative errors of the MLP-ANN and the RBF-ANN model.

Comparative analysis of LM and SCGD algorithms_

Algorithm R2 MSNE RMSE MAE
LM 0.99032 0.0581 0.1206 0.087
SCGD 0.94229 0.0953 0.1543 0.1144

Comparison between MLP and RBF models_

Type ANN R2 MSNE RMSE MAE
MLP-ANN 0.99032 0.0581 0.1206 0.087
RBF-ANN 0.99899 0.000729 0.0135 0.0075

Tested combination of activation functions of MLP-ANN_

Activation function hidden layer Activation function output layer R2 MSNE RMSE MAE
tansig tansig 0.99032 0.0581 0.1206 0.087
tansig purelin 0.99219 0.3866 0.3109 0.2363
logsig tansig 0.94438 0.1034 0.1607 0.1072
logsig purelin 0.98062 0.6353 0.3985 0.3117
purelin tansig 0.82875 0.1136 0.1685 0.1184
logsig logsig 0.83831 0.2505 0.2502 0.1884
tansig logsig 0.85305 0.2536 0.2518 0.195
purelin logsig 0.68672 0.2955 0.2718 0.2067

Influence of hidden neurons of RBF-ANN_

Spread value Neurons MSE MSNE RMSE MAE
0.1 140 0.99899 0.00073 0.0135 0.0075
0.3 140 0.99742 0.0019 0.0215 0.0108
0.5 140 0.99477 0.0038 0.0306 0.014
0.1 130 0.9973 0.0019 0.022 0.0141
0.3 130 0.99257 0.0053 0.0365 0.0181
0.5 130 0.99272 0.0052 0.0361 0.0177
0.1 120 0.9936 0.0046 0.0339 0.02
0.3 120 0.98875 0.0081 0.0449 0.0268
0.5 120 0.98833 0.0084 0.0457 0.0266
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