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The SPSS simulations are performed for a multilayer perceptron model with one input layer, one hidden layer, and an output layer. The hidden nodes are varied from 1 to 50 in the hidden layer. The network architecture consists of eight input nodes, a few hidden nodes, and an output node. The scaled conjugate gradient principle is mostly used as an optimization algorithm to determine weights. The data have been divided into 70% training and 30% testing datasets. The overall regression coefficients (R2 values), RMSE, MAE, MBE, D, and NSE are given in Table 7. The preliminary SPSS simulations are explored primarily to study the suitability of neural networks for stream water quality modeling problems. The fine tuning of the neural network simulations in model architecture, variety of training algorithms, testing, and validation are explored using MATLAB simulations as explained in the next section.

Table 7

The regression metrics of output parameters using SPSS simulations

S. No.ParameterRMSEOverall R2DMAEMBENSENetwork architecture
1 DO (mg/L) 0.50 0.52 0.71 0.40 0.04 0.51 8-5-1 
2 pH 0.33 0.35 0.21 0.24 0.01 0.21 8-5-1 
3 Electrical conductivity (mS/cm) 133.07 0.79 0.92 91.43 −2.76 0.78 8-5-1 
4 BOD (mg/L) 0.94 0.64 0.82 0.50 −0.02 0.63 8-5-1 
5 COD (mg/L) 6.63 0.83 0.95 5.12 −0.188 0.83 8-8-1 
6 Nitrate 0.87 0.47 0.78 0.60 0.04 0.47 8-5-1 
7 Total Coliform (MPN/100 ml) 22.66 0.29 0.45 14.93 0.56 0.29 8-3-1 
8 Turbidity (NTU) 7.38 0.15 −0.34 3.75 −0.02 0.15 8-6-1 
9 Total Alk. (mg/L) 32.05 0.73 0.92 22.76 −3.52 0.72 8-5-1 
10 Chloride (mg/L) 25.76 0.66 0.87 15.82 −0.04 0.66 8-5-1 
11 Hardness (mg/L) 42.62 0.66 0.88 30.07 −1.30 0.65 8-5-1 
12 Calcium (mg/L) 9.995 0.66 0.88 7.58 −0.808 0.65 8-5-1 
13 Magnesium (mg/L) 6.42 0.48 0.78 4.801 0.32 0.48 8-8-1 
14 Sulphate (mg/L) 13.34 0.66 0.89 9.44 −0.189 0.66 8-8-1 
15 Sodium (mg/L) 17.09 0.78 0.94 11.70 0.80 0.78 8-8-1 
16 TDS (mg/L) 84.88 0.76 0.929 59.35 5.76 0.76 8-8-1 
17 TSS (mg/L) 12.26 0.56 0.78 7.29 −0.79 0.56 8-7-1 
18 Total Phosphate (mg/L) 0.27 0.67 0.88 0.16 0.01 0.67 8-5-1 
19 Potassium (mg/L) 1.61 0.64 0.85 1.04 −0.12 0.61 8-6-1 
20 Fluoride (mg/L) 0.27 0.10 0.3 0.20 0.01 0.10 8-5-1 
21 Sodium % 7.99 0.35 0.55 6.15 −0.41 0.35 8-4-1 
22 SAR 0.44 0.72 0.91 0.31 0.00 0.71 8-5-1 
S. No.ParameterRMSEOverall R2DMAEMBENSENetwork architecture
1 DO (mg/L) 0.50 0.52 0.71 0.40 0.04 0.51 8-5-1 
2 pH 0.33 0.35 0.21 0.24 0.01 0.21 8-5-1 
3 Electrical conductivity (mS/cm) 133.07 0.79 0.92 91.43 −2.76 0.78 8-5-1 
4 BOD (mg/L) 0.94 0.64 0.82 0.50 −0.02 0.63 8-5-1 
5 COD (mg/L) 6.63 0.83 0.95 5.12 −0.188 0.83 8-8-1 
6 Nitrate 0.87 0.47 0.78 0.60 0.04 0.47 8-5-1 
7 Total Coliform (MPN/100 ml) 22.66 0.29 0.45 14.93 0.56 0.29 8-3-1 
8 Turbidity (NTU) 7.38 0.15 −0.34 3.75 −0.02 0.15 8-6-1 
9 Total Alk. (mg/L) 32.05 0.73 0.92 22.76 −3.52 0.72 8-5-1 
10 Chloride (mg/L) 25.76 0.66 0.87 15.82 −0.04 0.66 8-5-1 
11 Hardness (mg/L) 42.62 0.66 0.88 30.07 −1.30 0.65 8-5-1 
12 Calcium (mg/L) 9.995 0.66 0.88 7.58 −0.808 0.65 8-5-1 
13 Magnesium (mg/L) 6.42 0.48 0.78 4.801 0.32 0.48 8-8-1 
14 Sulphate (mg/L) 13.34 0.66 0.89 9.44 −0.189 0.66 8-8-1 
15 Sodium (mg/L) 17.09 0.78 0.94 11.70 0.80 0.78 8-8-1 
16 TDS (mg/L) 84.88 0.76 0.929 59.35 5.76 0.76 8-8-1 
17 TSS (mg/L) 12.26 0.56 0.78 7.29 −0.79 0.56 8-7-1 
18 Total Phosphate (mg/L) 0.27 0.67 0.88 0.16 0.01 0.67 8-5-1 
19 Potassium (mg/L) 1.61 0.64 0.85 1.04 −0.12 0.61 8-6-1 
20 Fluoride (mg/L) 0.27 0.10 0.3 0.20 0.01 0.10 8-5-1 
21 Sodium % 7.99 0.35 0.55 6.15 −0.41 0.35 8-4-1 
22 SAR 0.44 0.72 0.91 0.31 0.00 0.71 8-5-1 
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