Prediction of interfacial area concentration based on interpretable neural network

Yuhao ZHOU; Wangtao XU; Li LIU; Longxiang ZHU; Luteng ZHANG; Liangming PAN

doi:10.11889/j.0253-3219.2024.hjs.47.080502

NUCLEAR TECHNIQUES, Volume. 47, Issue 8, 080502(2024)

Prediction of interfacial area concentration based on interpretable neural network

Yuhao ZHOU^1,3, Wangtao XU^1,3, Li LIU^1,3, Longxiang ZHU^1,2,3、*, Luteng ZHANG^1,3, and Liangming PAN^1,3

¹Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400044, China

²Postdoctoral Station of Power Engineering and Engineering Thermophysics at Chongqing University, Chongqing 400044, China

³Department of Nuclear Engineering and Technology, Chongqing University, Chongqing 400044, China

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Figures & Tables(10)

Fig. 1. Diagram of double hidden layer neural network

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Fig. 2. Comparison between predicted and experimental values for 5 different input features(a) Input features are j_f and j_g, (b) Input features are j_f and α, (c) Input features are j_f/j_g and α, (d) Input features are j_f, j_g and α, (e) Input features are lg(j_f), lg(j_g) and lg(α)

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Fig. 3. Relationship between value and flow pattern division (color online)

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Fig. 4. First layer calculation results of three input features

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Table 1. The parameter range of training data

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Table 1. The parameter range of training data

作者Author	年份Year	截面平均数据量Data size	$j_{f}$ / m∙s^-1	$j_{g}$ / m∙s^-1	管道直径Geometry / mm
Worosz et al.^[5]	2015	9	2	0.18~0.29	50.8
Shen et al.^[14]	2012	27	0.051~0.31	0.013~0.373	200
Dang^[15]	2017	15	0.3~1.0	0.2~10	25.4
Schlegel et al.^[16]	2012	16	0.39~1	0.19~3.06	152，203
Wang et al.^[17]	2017	10	1.25~2.14	0.08~11	25.4
Wang et al.^[18]	2020	24	0.5~2	0.092~5.04	25.4
Qiao et al.^[19]	2017	12	4	0.108~0.284	50.8
Smith et al.^[20]	2012	9	0.3	0.15~1	152
Smith et al.^[21]	2012	15	0.05~1.03	0.052~8	102，152

Table 2. Prediction accuracy of different input feature combinations
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Table 2. Prediction accuracy of different input feature combinations
序号Number 输入特征Input features 预测正确率Prediction accuracy / %
1 $j_{f}$ 、 $j_{g}$ 64.23
2 $j_{f}$ 、 $α$ 80.29
3 $j_{f} / j_{g}$ 、 $α$ 63.50
4 $j_{f}$ 、 $j_{g}$ 、 $α$ 90.51
5 $l g (j_{f})$ 、 $l g (j_{g})$ 、 $l g (α)$ 95.62

Table 3. Coefficient index of existing interfacial area correlation

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Table 3. Coefficient index of existing interfacial area correlation

作者Author	$σ / ρ_{f}$ 指数 $σ / ρ_{f}$ index	$α$ 指数 $α$ index	$ε, j_{f}$ 或 $j_{g}$ 指数 $ε, j_{f}$ , $j_{g}$ index
Hibiki, Ishii^[23]	-0.5	0.847	0.070 7 $(ε)$
Millies et al.^[24]	-0.6	0.83	0.4 $(ε)$
Kocamustafaogullariet al.^[25]	-0.33	0.78	0.22 $(ε)$
Tabei et al.^[26]	―	0.847	0 $(ε)$
Calderbank^[27]	-0.33	0.775	0.125 $(j_{g})$
Serizawa, Kataoka^[28]	―	0.87	0.2 $(j_{f})$
Viswanathan^[29]	-0.6	1	-0.085 $(j_{g})$
Akita, Yoshida^[30]	-0.5	1	0.12 $(j_{g})$

Table 4. Comparison of mean and variance before and after logarithmic transformation
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Table 4. Comparison of mean and variance before and after logarithmic transformation
$j_{g}$ $j_{f}$ $l g (j_{g})$ $l g (j_{f})$
平均值Average 1.222 1.121 -0.408 -0.176
方差Variance 5.748 1.203 0.409 0.240

Table 5. Size of neural network training process matrix

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Table 5. Size of neural network training process matrix

	输入矩阵Input matrix	权重矩阵Weight matrix	输出矩阵Output matrix
第一次参数计算First parameter calculation	1×3	3×32	1×32
第一次参数计算Second parameter calculation	1×32	32×32	1×32
第一次参数计算Third parameter calculation	1×32	32×1	1×1

Table 6. Calculated and biased b₃ values before each layer

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Table 6. Calculated and biased b₃ values before each layer

隐藏层1前Before hidden layer 1

\sum_{i = 1}^{32} W_{1} X

隐藏层2前Before hidden layer 2

\sum_{i = 1}^{32} W_{2} X

输出层前Before output layer

$W_{3} X$

偏置Bias

b_{3}

对数变换Logarithmic transformation

88.319

252.909

0.947

0.154

未对数变换Non-logarithmic transformation

-0.008

8.494

-0.292

0.639

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Yuhao ZHOU, Wangtao XU, Li LIU, Longxiang ZHU, Luteng ZHANG, Liangming PAN. Prediction of interfacial area concentration based on interpretable neural network[J]. NUCLEAR TECHNIQUES, 2024, 47(8): 080502

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