Advances in Artificial Intelligence

Research Article

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

Selection of the best model from the Levenberg-Marquardt 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		[3-8-1]	One	0.606	−0.957	0.491	−1.892	0.623	−1.449
Q_t−1, R_t, R_t−1, E_t, E_t−1, T_t, T_t−1	7		[7-3-1]	One	0.995	0.990	0.966	0.932	0.961	0.909
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		[ 11-10-1]	One
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		[15-10-1]	One	0.983	0.960	0.950	0.894	0.971	0.940
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	Levenberg-Marquardt	[19-13-1]	One	0.982	0.956	0.989	0.969	0.975	0.928
R_t, E_t, T_t	3	Levenberg-Marquardt	[3-2-2-1]	Two	0.528	−210441.73	0.521	−168494.734	0.392	−214100.83
Q_t-1, R_t, R_t-1, E_t, E_t-1, T_t, T_t-1	7		[7-3-2-1]	Two	0.985	0.967	0.970	0.935	0.168	0.934
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		[11-3-2-1]	Two	0.986	0.972	0.983	0.961	0.957	0.914
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		[15-3-3-1]	Two	0.982	0.941	0.93	0.89	0.986	0.91
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		[ 19-4 -3-1]	Two