Application of Adaptive Neuro-Fuzzy Inference System for Prediction of Neutron Yield of IR-IECF Facility in High Voltages A. Adineh-Vand, M. Torabi, G. H. Roshani, M. Taghipour, S. A. H. Feghhi, M. Rezaei & S. M. Sadati Journal of Fusion Energy ISSN 0164-0313 J Fusion Energ DOI 10.1007/s10894-013-9631-z
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Author's personal copy J Fusion Energ DOI 10.1007/s10894-013-9631-z
ORIGINAL RESEARCH
Application of Adaptive Neuro-Fuzzy Inference System for Prediction of Neutron Yield of IR-IECF Facility in High Voltages A. Adineh-Vand • M. Torabi • G. H. Roshani M. Taghipour • S. A. H. Feghhi • M. Rezaei • S. M. Sadati
•
Ó Springer Science+Business Media New York 2013
Abstract This paper presents a soft computing based artificial intelligent technique, adaptive neuro-fuzzy inference system (ANFIS) to predict the neutron production rate (NPR) of IR-IECF device in wide discharge current and voltage ranges. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS model. The performance of the proposed ANFIS model is tested using the experimental data using four performance measures: correlation coefficient, mean absolute error, mean relative error percentage (MRE%) and root mean square error. The obtained results show that the proposed ANFIS model has achieved good agreement with the experimental results. In comparison to the experimental data the proposed ANFIS model has MRE% \1.53 and 2.85 % for training and testing data respectively. Therefore, this model can be used as an efficient tool to predict the NPR in the IR-IECF device. Keywords ANFIS Prediction NPR Inertial electrostatic confinement fusion IR-IECF device
A. Adineh-Vand Computer Department, Engineering Faculty, Islamic Azad University, Kermanshah, Iran M. Torabi G. H. Roshani S. A. H. Feghhi M. Rezaei S. M. Sadati Shahid Beheshti University, Tehran, Iran G. H. Roshani (&) Energy Faculty, Kermanshah University of Technology, Kermanshah, Iran e-mail:
[email protected] M. Taghipour Department of Biomedical Engineering, Faculty of Medicine, Kermanshah University of Medical Sciences, Kermanshah, Iran
Introduction Inertial electrostatic confinement (IEC) devices are compact neutron/proton generators that can confine highenergy ions in an electrostatic potential well. Spherical configuration is the most common one that consists of two-concentrate electrodes inside a vacuum chamber. Usually the gridded central electrode connects to a negative high voltage and the outer one grounded. Ions produced by a glow discharge in the inter electrode space gain energy from the applied eclectic field and accelerated to the center inside the hollow cathode and therefore give raise a relatively hot and dense plasma inside the cathode. Because of spherically converging ions, a potential well forms in the plasma core within the cathode, which plays an important role in fusion production [1, 2]. The ions which do not loss (colliding to the grid is the most important loss agent) have a chance to recalculate in the potential well and fuse together. In this case, depending on the working condition beam–beam interaction and beam to target are most dominant process in fusion reaction [3, 4]. As shown in Eqs. (1)–(3), if the IECF device runs by deuterium gas a high flux of neutron and proton can achieve. D þ D ! He3 ð0:82 MeVÞ þ nð2:45 MeVÞ
ð1Þ
D þ D ! Tð1:01 MeVÞ þ pð3:03 MeVÞ
ð2Þ
D þ He3 ! að3:52 MeVÞ þ Pð14:7 MeVÞ
ð3Þ
Depending on the fusion reaction rate and operation mode (continues or pulse mode) IECF device could have variety of application from teaching and material process [5, 6] to high flux neutron sources. Among all of these applications, compact neutron/proton source are most required for cancer detection, cancer treatment boron
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neutron capture therapy (BNCT) [7–9] and personal landmine identifications [10, 11]. Research and development on IECF devices, as a neutron/proton source, have been done extendedly and significant results have been obtained [4, 12, 13]. From economical and research point of view, simulation and theoretical method that can predict neutron production rate (NPR) could be very useful for optimized design and performance of this facility. In this study, we predict the NPR of IR-IECF device [14] by ANFIS at high voltage and discharge current.
Fig. 1 Schematic diagram of IR-IECF device
Fig. 2 IR-IEC device with electrodes in the right [14]
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Experimental Set Up The IR-IECF is a glow discharge based device with a spherical configuration [14, 15]. As shown schematically in the Fig. 1, it consists of a cylindrical vacuum chamber with 60 cm height, 13.5 cm diameter stainless still cathode and 41 cm diameter anode. Figure 2 shows a whole device with electrodes in the right. In the experiments; the device has been adjusted in a given deuterium gas pressure then by raising the cathode voltage, desired plasma has obtained. Finally, for different values of fixed cathode voltage from
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20 to 70 kV the mutual discharge current from 20 to 100 mA has been fixed by controlling the gas pressure. For measuring the NPR a calibrated neutron probe LB6411 has been used.
[18, 19]. ANFIS is based on the first-order Sugeno fuzzy model. An ANFIS consisting of a set of TSK-type fuzzy IF–THEN rules is used to map the system inputs to outputs. To understand the working of ANFIS in simple meaning, for a first order Sugeno fuzzy model, two fuzzy if–then rules are considered:
Modeling Based on ANFIS Rule 1 : If x is A1 and y is B1 ;
then
f1 ¼ p1 x þ q1 y þ r1
ANFIS Architecture
Rule 2 : If x is A2 and y is B2 ;
then
f2 ¼ p2 x þ q2 y þ r2
The adaptive neuro-fuzzy inference system (ANFIS), is one of the examples of neuro-fuzzy systems in which a fuzzy inference system (FIS) is implemented in the framework of adaptive networks. ANFIS is a FIS trained by an artificial neural network (ANN)-learning algorithm [16, 17]. The most important reason for combining FISs with ANNs is to use the learning capability of ANNs
where x and y are the inputs, fi are the outputs, Ai and Bi are the fuzzy sets and pi, qi and ri are the design parameters (i = 1, 2). Figure 3 illustrates the inference method for this Sugeno model. Figure 4 shows a typical ANFIS structure [20, 21]. In this figure, there are two adaptive layers (layers 1 and 4). Layer 1 has modifiable parameters related to the input
Fig. 3 The inference method of the sugeno model
Fig. 4 ANFIS structure
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membership function. The parameters in this layer are called premise parameters. The node functions of this layer are given by Jang [18, 19] and Jang et al. [19]: Ai ðxÞ ¼ lAi ðxÞ;
i ¼ 1; 2
ð4Þ
Bi ðyÞ ¼ lBi ðyÞ;
i ¼ 1; 2
ð5Þ
where x and y are the inputs of the model and lAi(x) and lBi(y) are the fuzzy membership functions. A typical membership function is Dsigmf (built-in membership function composed of difference between two sigmoidal membership functions) with four parameters a1, b1, a2 and b2 given by the following equation: Dsigmf ðxÞ ¼
1 1 þ expða1 ðx b1 ÞÞ 1 1 þ expða2 ðx b2 ÞÞ
ð6Þ
Every node in layer 2 represents the firing strength of the each rule. The fixed node in layer 3 calculates the ratio of the ith rule’s firing strengths to the sum of all rule’s firing strengths. The output of layer 3 is called normalized firing strengths. The output of layer 2 and layer 3 are given by Eqs. (7) and (8), respectively [20, 21]. Wi ¼ Ai ðxÞ Bi ðyÞ; i ¼ 1; 2 wi wi ¼ ; i ¼ 1; 2 w1 þ w2
method and least squares method to update parameters. This algorithm consists of two stages: forward pass and backward pass. In the forward pass, the least-squares method is used to identify consequent linear parameters (the parameters in the layer 4) and in the backward pass, the gradient descent method is employed to tune premise nonlinear parameter (the parameters in the layer 1). Detailed information of ANFIS can be found in Jang [18]. Proposed ANFIS Model The purpose of this paper is to investigate the accuracy of an ANFIS model to predict the NPR of IR-IECF device in wide discharge current and voltage ranges. In the developed ANFIS, two variables consisting of voltage and discharge current are selected as input variables to predict the NPR, which is the target variable. Figure 5 shows a simplified overview of the proposed ANFIS model. ANFIS modeling process starts by obtaining a data set (input– output data pairs) and dividing it into training (to find the
ð7Þ ð8Þ
The outputs of the adaptive nodes in layer 4 are given by: O4;i ¼ wi fi ¼ wi ðpi x þ qi y þ ri Þ;
i ¼ 1; 2
ð9Þ
where pi, qi and ri are called consequent parameters. Layer 5 computes the weighted average of the output signals of the layer 4 by the following equation: O5;1 ¼
w 1 f1 þ w 2 f2 w1 þ w2
ð10Þ
Fig. 6 Comparison of the experimental and predicted results for the training data
The training of the ANFIS model is to tune all the modifiable parameters to make the ANFIS output match the training data. ANFIS applies a hybrid-learning algorithm [19, 22], and combines the gradient descent
Fig. 5 The proposed ANFIS model
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Fig. 7 Comparison of the experimental and predicted results for the testing data
Author's personal copy J Fusion Energ Table 1 The obtained NPR for training data using the proposed ANFIS model in comparison with the experimental Voltage (-kV)
Discharge current (mA)
NPR (n/s) (9106) Experimental
ANFIS
Table 2 The obtained NPR for testing data using the proposed ANFIS model in comparison with the experimental Voltage (-kV)
NPR (n/s) (9106)
Discharge current (mA)
Experimental
ANFIS
30
20
0.055164
0.058982895
50
20
1.130852
1.126840829
40
20
0.364079
0.346367534
30
30
0.052957
0.053360385
60 70
20 20
2.846438 4.468245
2.886784383 4.46734229
70 40
30 40
4.964717 0.34753
5.069799452 0.332687046
40
30
0.358563
0.367689799
70
40
5.681843
5.618292704
50
30
1.152918
1.131691919
60
50
3.166386
3.122481544
60
30
3.033994
2.984878986
40
50
0.342014
0.318160515
30
40
0.052405
0.049922121
30
60
0.035856
0.034549608
50
40
1.130852
1.150745065
60
60
3.210517
3.153693021
60
40
3.072608
3.085758073
40
70
0.28685
0.287435393
30
50
0.042476
0.043210529
70
70
7.060931
7.524078956
50
50
1.125336
1.149567037
50
80
0.915714
0.964636975
70
50
5.95766
5.950154471
30
90
0.014894
0.015490663
40
60
0.292367
0.295518196
70
90
7.060931
6.981909746
50
60
1.10327
1.04687175
50
100
0.904682
0.877110299
70
60
6.729949
6.737933147
30
70
0.027582
0.026099747
50 60
70 70
0.926747 3.199484
0.957147715 3.19684675
Table 3 The obtained errors for the proposed ANFIS model
30
80
0.017652
0.017609357
Error
40
80
0.248236
0.250854839
60
80
3.089157
3.097387806
70
80
7.060931
7.059458937
40
90
0.24272
0.236276293
50
90
0.910198
0.908886184
60
90
3.056059
3.041974107
30
100
0.012136
0.011904104
40
100
0.171007
0.175240295
60
100
2.923667
2.930299327
70
100
6.840276
6.840539717
75
50
7.99871
77
96
11.80499
11.80512942
77
55
11.25336
11.24778307
81 82
26 75
7.722893 13.51506
7.7227766 13.51536227
82
48
14.61833
14.61929399
8.003800703
initial premise parameters for membership functions) and testing data (to validate the trained ANFIS structure) sets. In this study, training and testing data has been obtained by use of IR-IECF experimental data. Total data divided into two sets: 36 samples (about 70 %) are used for training and 15 samples (about 30 %) are used for testing the trained ANFIS model. Testing and training data must be different and are selected randomly from the original data set. MATLAB 7.0.4 software is used for training the ANFIS
Data Train
Test
MAE
0.0102
0.0622
RMSE
0.0172
0.1277
MRE%
1.522
2.845
model. We have tested many different ANFIS architecture with different type of membership functions, number of membership functions and number of epochs to obtain the best ANFIS configuration.
Results and Discussion The optimized ANFIS structure was selected based on the minimal residual error and maximum number of 150 epochs. The proposed ANFIS model being used in this study utilizes Sugeno type FISs. It has 3 Dsigmf membership functions for each input and 9 linear membership functions for the output. The number of MFs assigned to each input variable is chosen by trial and error. It employs 36 linear parameters, 24 nonlinear parameters, and 9 fuzzy rules to predict the output. Figures 6 and 7, Tables 1 and 2 show the comparisons between experimental and predicted results using the proposed ANFIS model, where the correlation coefficient (CC) is calculated by:
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"P CC ¼ 1
N i¼1
ðXi ðExpÞ Xi ðPredÞÞ2 PN 2 i¼1 ðXi ðExpÞÞ
# ð11Þ
Table 3 shows the obtained errors for the proposed ANFIS model, where the mean relative error percentage (MRE%), the mean absolute error (MAE), and the root mean square error (RMSE) are calculated by: MRE% ¼ 100
MAE ¼
N 1X Xi ðExpÞ Xi ðPredÞ N i¼1 Xi ðExpÞ
Z 1X jXi ðExpÞ Xi ðPredÞj N i¼1
"P RMSE ¼
N i¼1
ðXi ðExpÞ Xi ðPredÞÞ2 N
Fig. 8 The obtained NPR using the proposed ANFIS model (in the range of the training and testing data)
Fig. 9 The obtained NPR using the proposed ANFIS model (outside the range of the training and testing data)
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ð12Þ
ð13Þ #0:5 ð14Þ
In Eqs. (11)–(14), N is the number of data and ‘X(Exp)’ and ‘X(Pred)’ stand for experimental and predicted (ANFIS) values respectively. According to the Figs. 6 and 7, Tables 1, 2 and 3, it is clear that the predicted NPR using the proposed ANFIS model is close to the experimental. These results show the applicability of ANFIS as an accurate and reliable model for the prediction of NPR of IR-IECF device according to the discharge current and voltage. The obtained NPR using the proposed ANFIS model versus voltage and discharge current in the range of the training and testing data is shown Fig. 8. In this range, the maximum NPR was happened in current = 69.5 mA and voltage = -82 kV. In this situation IECF can produce 20.161 9 106 neutrons/s. Also the minimum NPR was happened in current = 100 mA and voltage = -30 kV. In this situation IECF can produce 0.0119 9 106 neutrons/s. The obtained NPR using the proposed ANFIS model versus voltage and
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discharge current outside the range of the training and testing data is shown Fig. 9. In this range, the maximum NPR was happened in current = 68 mA and voltage = -130 kV. In this situation IECF can produce 43.01 9 106 neutrons/s.
Conclusion In this paper, an ANFIS model is used for prediction of the neutron yield in IECF devices. For developing of the model, the input parameters are voltage and discharge current and the output is NPR. The comparison between the experimental and predicted results using the proposed ANFIS model shows that there is a good agreement between them with MRE% \1.53 and 2.85 % for training and testing data respectively. Therefore, the proposed ANFIS model can be used as an efficient tool to predict the NPR in the IECF device.
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