Advances in Artificial Intelligence

Research Article

Development of Artificial Neural-Network-Based Models for the Simulation of Spring Discharge

Table 1

Selection of the best model from the batch backpropagation algorithm.


Model inputs	No. of inputs	Algorithm	Architecture	No. of hidden layer	Training		Testing		Validation
Model inputs	No. of inputs	Algorithm	Architecture	No. of hidden layer	R	DC	R	DC	R	DC

R_t, E_t, T_t	3		[3-4-1]	One	0.671	−0.235	0.600	−0.133	0.594	−0.883
Q_t−1, R_t, R_t−1, E_t, E_t ₋₁, T_t, T_t ₋₁	7		[7-2-1]	One	0.979	0.956	0.979	0.941	0.986	0.961
Q_t−1, Q_t−2, R_t, R_t−1, R_t−2, E_t, E_t−1, E_t−2, T_t, T_t−1, T_t−2	11		[11-28-1]	One	0.959	0.907	0.921	0.809	0.953	0.893
Q_t−1, Q_t−2, Q_t-3, R_t, R_t−1, R_t−2, R_t−3, E_t, E_t−1, E_t−2, E_t−3, T_t, T_t−1, T_t−2, T_t−3	15		[15-21-1]	One	0.943	0.851	0.945	0.865	0.967	0.928
Q_t−1, Q_t−2, Q_t−3, Q_t−4, R_t, R_t−1, R_t−2, R_t−3, R_t−4, E_t, E_t−1, E_t−2, E_t−3, E_t−4, T_t, T_t−1, T_t−2, T_t−3, T_t−4	19	Batch backpropagation	[ 19-10-1]	One
R_t, E_t, T_t	3	Batch backpropagation	[3-2-2-1]	Two	0.623	−0.575	0.623	−1.378	0.554	−1.322
Q_t−1, R_t, R_t−1, E_t, E_t−1, T_t, T_t−1	7		[7-6-5-1]	Two	0.982	0.960	0.970	0.935	0.975	0.944
Q_t−1, Q_t−2, R_t, R_t−1, R_t−2, E_t, E_t−1, E_t−2, T_t, T_t−1, T_t−2	11		[11-4-3-1]	Two	0.988	0.975	0.981	0.960	0.967	0.907
Q_t−1, Q_t−2, Q_t−3, R_t, R_t−1, R_t−2, R_t−3, E_t, E_t−1, E_t−2, E_t−3, T_t, T_t−1, T_t−2, T_t−3	15		[15-7-3-1]	Two	0.980	0.958	0.960	0.901	0.985	0.963
Q_t−1, Q_t−2, Q_t−3, Q_t−4, R_t, R_t−1, R_t−2, R_t−3, R_t−4, E_t, E_t−1, E_t−2, E_t−3, E_t−4, T_t, T_t−1, T_t−2, T_t−3, T_t−4	19		[ 19-9-4-1]	Two