Flow Calculation Model for Trapezoidal Gate Based on Artificial Neural Network

doi:10.11988/ckyyb.20230491

Abstract

Abstract:

This study introduces an approach for calculating the free flow and submerged flow through flat-trapezoidal gate. The flow calculation model was established based on BP (Back Propagation) neural network and RBF (Radial Basis Function) neural network, with multiple variables and combinations as well as single output. The input variables for the model included slope coefficient, gate opening, total head in front of the gate, hydraulic radius, contraction depth behind the gate, and downstream channel water depth. The output variable was measured flow rate. The model was trained and tested using experimental data, and extensive validation confirmed that both BP and RBF artificial neural network models demonstrated strong predictive performance. These models exhibited excellent adaptability and high accuracy in predicting flow rates for trapezoidal gates in canal systems in irrigation areas, thereby enabling precise flow control.

Key words: trapezoidal gate, free discharge, submerged discharge, BP neural network, RBF neural network, flow prediction

CLC Number:

TV131水力理论、计算、实验

Cite this article

MENG Wan-shang, ZHAO Shuai-jie, LI Lin. Flow Calculation Model for Trapezoidal Gate Based on Artificial Neural Network[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(9): 86-92.

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URL: http://ckyyb.crsri.cn/EN/10.11988/ckyyb.20230491

http://ckyyb.crsri.cn/EN/Y2024/V41/I9/86

Figures/Tables 8

Fig.1 Trapezoidal gate diagram

Table 1 Input variable combinations for neural network

工况	2个变量	3个变量	4个变量	5个变量
自由出流	1-2,1-3,1-4, 2-3,2-4,3-4	1-2-3,1-2-4, 1-3-4,2-3-4	1-2-3-4
淹没出流	1-2,1-3,1-5, 1-6,2-3,2-5, 2-6,3-5,3-6, 5-6	1-2-3,1-2-5, 1-2-6,1-3-5, 1-3-6,1-5-6, 2-3-5,2-3-6, 2-5-6,3-5-6	1-2-3-5, 1-2-3-6, 1-2-5-6, 1-3-5-6, 2-3-5-6	1-2-3-5-6

Table 1 Input variable combinations for neural network

工况	2个变量	3个变量	4个变量	5个变量
自由出流	1-2,1-3,1-4, 2-3,2-4,3-4	1-2-3,1-2-4, 1-3-4,2-3-4	1-2-3-4
淹没出流	1-2,1-3,1-5, 1-6,2-3,2-5, 2-6,3-5,3-6, 5-6	1-2-3,1-2-5, 1-2-6,1-3-5, 1-3-6,1-5-6, 2-3-5,2-3-6, 2-5-6,3-5-6	1-2-3-5, 1-2-3-6, 1-2-5-6, 1-3-5-6, 2-3-5-6	1-2-3-5-6

Table 2 Predicted results for different combinations of variables in free flow state

神经网络模型	组合方式	组合数据	训练集误差/%	测试集误差/%
BP神经网络	2个变量组合	1-2	27.64	28.58
		1-3	30.66	39.34
		1-4	23.57	25.35
		2-3	7.28	8.06
		2-4	24.34	20.88
		3-4	3.35	3.68
	3个变量组合	1-2-3	4.71	5.68
		1-2-4	8.06	12.85
		1-3-4	2.21	2.34
		2-3-4	2.14	2.28
RBF神经网络	2个变量组合	1-2	27.16	28.14
		1-3	52.93	36.52
		1-4	23.64	25.48
		2-3	6.87	8.09
		2-4	24.14	20.95
		3-4	2.78	4.34
	3个变量组合	1-2-3	2.00	4.02
		1-2-4	10.85	12.91
		1-3-4	2.47	4.25
		2-3-4	2.10	3.18

Table 2 Predicted results for different combinations of variables in free flow state

神经网络模型	组合方式	组合数据	训练集误差/%	测试集误差/%
BP神经网络	2个变量组合	1-2	27.64	28.58
		1-3	30.66	39.34
		1-4	23.57	25.35
		2-3	7.28	8.06
		2-4	24.34	20.88
		3-4	3.35	3.68
	3个变量组合	1-2-3	4.71	5.68
		1-2-4	8.06	12.85
		1-3-4	2.21	2.34
		2-3-4	2.14	2.28
RBF神经网络	2个变量组合	1-2	27.16	28.14
		1-3	52.93	36.52
		1-4	23.64	25.48
		2-3	6.87	8.09
		2-4	24.14	20.95
		3-4	2.78	4.34
	3个变量组合	1-2-3	2.00	4.02
		1-2-4	10.85	12.91
		1-3-4	2.47	4.25
		2-3-4	2.10	3.18

Fig.2 Comparison between optimal predicted and measured free flow rates for different combinations of variables

Table 3 Predicted results for different combinationsof variables in submerged flow condition

神经网络模型	组合方式	组合数据	训练集误差/%	测试集误差/%
BP神经网络	2个变量组合	1-2	14.15	15.28
		1-3	26.44	23.28
		1-5	27.49	23.61
		1-6	23.90	22.25
		2-3	9.70	12.52
		2-5	14.25	16.10
		2-6	10.59	14.20
		3-5	22.33	20.54
		3-6	22.81	21.25
		5-6	21.86	19.56
	3个变量组合	1-2-3	9.82	20.46
		1-2-5	14.78	16.26
		1-2-6	10.48	13.59
		1-3-5	21.27	22.82
		1-3-6	22.66	33.88
		1-5-6	21.22	18.59
		2-3-5	4.58	5.30
		2-3-6	7.86	8.56
		2-5-6	2.89	3.93
		3-5-6	17.69	17.49
	4个变量组合	1-2-3-5	2.28	2.26
		1-2-3-6	7.59	25.50
		1-2-5-6	3.59	4.14
		1-3-5-6	20.05	31.33
		2-3-5-6	1.71	2.04
RBF神经网络	2个变量组合	1-2	14.10	15.60
		1-3	35.60	24.12
		1-5	27.72	22.12
		1-6	29.33	21.40
		2-3	10.65	11.19
		2-5	14.07	16.12
		2-6	10.89	13.47
		3-5	23.11	23.53
		3-6	38.61	21.19
		5-6	27.61	20.48
	3个变量组合	1-2-3	10.37	11.85
		1-2-5	13.78	16.20
		1-2-6	10.76	13.44
		1-3-5	22.47	25.49
		1-3-6	29.90	26.33
		1-5-6	29.84	20.28
		2-3-5	5.41	6.68
		2-3-6	8.46	8.89
		2-5-6	3.94	4.49
		3-5-6	33.51	21.37
	4个变量组合	1-2-3-5	2.35	3.38
		1-2-3-6	7.52	8.51
		1-2-5-6	3.83	4.77
		1-3-5-6	22.04	46.55
		2-3-5-6	1.56	2.06

Table 3 Predicted results for different combinationsof variables in submerged flow condition

神经网络模型	组合方式	组合数据	训练集误差/%	测试集误差/%
BP神经网络	2个变量组合	1-2	14.15	15.28
		1-3	26.44	23.28
		1-5	27.49	23.61
		1-6	23.90	22.25
		2-3	9.70	12.52
		2-5	14.25	16.10
		2-6	10.59	14.20
		3-5	22.33	20.54
		3-6	22.81	21.25
		5-6	21.86	19.56
	3个变量组合	1-2-3	9.82	20.46
		1-2-5	14.78	16.26
		1-2-6	10.48	13.59
		1-3-5	21.27	22.82
		1-3-6	22.66	33.88
		1-5-6	21.22	18.59
		2-3-5	4.58	5.30
		2-3-6	7.86	8.56
		2-5-6	2.89	3.93
		3-5-6	17.69	17.49
	4个变量组合	1-2-3-5	2.28	2.26
		1-2-3-6	7.59	25.50
		1-2-5-6	3.59	4.14
		1-3-5-6	20.05	31.33
		2-3-5-6	1.71	2.04
RBF神经网络	2个变量组合	1-2	14.10	15.60
		1-3	35.60	24.12
		1-5	27.72	22.12
		1-6	29.33	21.40
		2-3	10.65	11.19
		2-5	14.07	16.12
		2-6	10.89	13.47
		3-5	23.11	23.53
		3-6	38.61	21.19
		5-6	27.61	20.48
	3个变量组合	1-2-3	10.37	11.85
		1-2-5	13.78	16.20
		1-2-6	10.76	13.44
		1-3-5	22.47	25.49
		1-3-6	29.90	26.33
		1-5-6	29.84	20.28
		2-3-5	5.41	6.68
		2-3-6	8.46	8.89
		2-5-6	3.94	4.49
		3-5-6	33.51	21.37
	4个变量组合	1-2-3-5	2.35	3.38
		1-2-3-6	7.52	8.51
		1-2-5-6	3.83	4.77
		1-3-5-6	22.04	46.55
		2-3-5-6	1.56	2.06

Fig.3 Comparison between optimal predicted and measured submerged flow rates for different combinations of variables

Table 4 Calculated results for each evaluation indicator

出流方式	神经网络模型	R	RMSE/(m³·s^-1)	MAPE/%
自由出流	BP	0.999 1	1.60×10^-4	1.76
自由出流	RBF	0.998 6	2.03×10^-4	3.23
淹没出流	BP	0.996 1	2.43×10^-4	2.15
淹没出流	RBF	0.994 7	2.83×10^-4	2.19

Table 4 Calculated results for each evaluation indicator

出流方式	神经网络模型	R	RMSE/(m³·s^-1)	MAPE/%
自由出流	BP	0.999 1	1.60×10^-4	1.76
自由出流	RBF	0.998 6	2.03×10^-4	3.23
淹没出流	BP	0.996 1	2.43×10^-4	2.15
淹没出流	RBF	0.994 7	2.83×10^-4	2.19

Fig.4 Comparison of trapezoidal gate flow rate between prediction and measurement

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