Table 4 The relative rank values of r, AAE, max. AE, RMSE, RMSE%, Bias, Bias%, FI, AIC and BIC for the best predictive DLA models with best predictive number of neuron alternative according to each hidden layer choices, the ITH-DBH functions based on NLRM, M5 based on NLME with f random, FFB-ANN and CC-ANN
AI alternatives and regression models | The number of hidden layers | RMSE | RMSE% (%) | AIC | BIC | FI | AAE | Max. AE | BIAS | BIAS% (%) | ∑ |
|---|---|---|---|---|---|---|---|---|---|---|---|
50 # neuron | 3 | 6.854 | 6.854 | 7.698 | 7.698 | 6.057 | 9.495 | 1.051 | 5.916 | 5.916 | 57.538 |
90 # neuron | 4 | 4.725 | 4.725 | 5.370 | 5.370 | 4.136 | 5.734 | 1.000 | 3.723 | 3.723 | 38.504 |
90 # neuron | 5 | 3.556 | 3.556 | 4.042 | 4.042 | 3.121 | 4.467 | 6.035 | 1.748 | 1.748 | 32.315 |
100 # neuron | 6 | 2.973 | 2.973 | 3.364 | 3.364 | 2.625 | 3.342 | 3.104 | 4.124 | 4.124 | 29.991 |
70 # neuron | 7 | 3.541 | 3.541 | 4.024 | 4.024 | 3.108 | 4.963 | 1.687 | 1.335 | 1.335 | 27.559 |
90 # neuron | 8 | 2.550 | 2.550 | 2.868 | 2.868 | 2.270 | 3.256 | 1.202 | 2.824 | 2.824 | 23.211 |
100 # neuron | 9 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 2.349 | 1.362 | 1.362 | 11.073 |
80 # neuron | 10 | 3.203 | 3.203 | 3.632 | 3.632 | 2.820 | 2.825 | 2.921 | 4.580 | 4.580 | 31.395 |
M1 NLRM | 19.213 | 19.213 | 19.347 | 19.347 | 19.065 | 18.283 | 20.000 | 18.380 | 18.380 | 171.228 | |
M2 NLRM | 19.433 | 19.433 | 19.530 | 19.530 | 19.325 | 18.666 | 18.900 | 19.397 | 19.397 | 173.612 | |
M3 NLRM | 20.000 | 20.000 | 20.000 | 20.000 | 20.000 | 19.261 | 17.662 | 20.000 | 20.000 | 176.923 | |
M4 NLRM | 15.419 | 15.419 | 16.064 | 16.064 | 14.735 | 18.337 | 16.081 | 1.101 | 1.101 | 114.322 | |
M5 NLRM | 15.237 | 15.237 | 15.900 | 15.900 | 14.535 | 18.936 | 14.699 | 1.000 | 1.000 | 112.445 | |
M6 NLRM | 17.330 | 17.330 | 17.745 | 17.745 | 16.878 | 20.000 | 17.363 | 1.116 | 1.116 | 126.623 | |
M7 NLRM | 18.973 | 18.973 | 19.146 | 19.146 | 18.782 | 18.395 | 19.745 | 18.905 | 18.905 | 170.971 | |
M5 NLME with f random | 11.425 | 11.425 | 12.345 | 12.345 | 10.499 | 15.764 | 10.378 | 1.003 | 1.003 | 86.185 | |
FFB-ANN based on A3 activation function alternative and 85 # neuron | 12.027 | 12.027 | 12.925 | 12.925 | 11.117 | 15.814 | 3.025 | 2.201 | 2.201 | 84.263 | |
CC-ANN based on A3 activation function alternative and 73 # neuron | 11.679 | 11.679 | 12.591 | 12.591 | 10.759 | 14.623 | 5.849 | 1.983 | 1.983 | 83.736 | |