Table 4.
ANN models | Training algorithm | Number of total hidden nodes | Hidden activation function | Output activation function | Architecture | Training | Testing | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
R2 | RMSE | MAE | VAF | Accuracy | R2 | RMSE | MAE | VAF | Accuracy | ||||||
ANN1 | TrainSCG | 4 | Tansig | Tansig | 7-4-1 | 0.934 | 0.660 | 0.428 | 93.415 | 91.471 | 0.724 | 1.193 | 0.724 | 68.725 | 87.644 |
ANN2 | TrainSCG | 7 | Logsig | Tansig | 7-7-1 | 0.937 | 0.693 | 0.283 | 93.100 | 94.829 | 0.643 | 1.459 | 0.756 | 57.458 | 85.260 |
ANN3 | TrainLM | 10 | Tansig | Tansig | 7-4-6-1 | 0.948 | 0.567 | 0.350 | 94.767 | 94.247 | 0.928 | 0.293 | 0.487 | 92.773 | 90.254 |
ANN4 | TrainLM | 12 | Purelin | Tansig | 7-5-7-1 | 0.883 | 0.864 | 0.535 | 87.290 | 89.503 | 0.802 | 1.395 | 0.820 | 77.386 | 85.371 |
ANN5 | TrainOSS | 13 | Logsig | Logsig | 7-5-8-1 | 0.932 | 0.672 | 0.411 | 93.213 | 91.816 | 0.850 | 0.492 | 0.508 | 84.935 | 90.061 |
ANN6 | TrainGDX | 14 | Tansig | Logsig | 7-7-7-1 | 0.939 | 0.684 | 0.483 | 93.774 | 91.529 | 0.906 | 0.754 | 0.666 | 89.952 | 87.247 |
ANN7 | TrainLM | 16 | Logsig | Logsig | 7-7-9-1 | 0.930 | 0.643 | 0.332 | 92.783 | 94.510 | 0.924 | 0.589 | 0.360 | 96.392 | 90.164 |
ANN8 | TrainGDX | 14 | Purelin | Purelin | 7-9-5-1 | 0.906 | 0.799 | 0.499 | 90.543 | 91.588 | 0.841 | 0.850 | 0.622 | 83.640 | 87.034 |
ANN9 | TrainSCG | 17 | Tansig | Purelin | 7-9-8-1 | 0.947 | 0.677 | 0.432 | 94.696 | 91.873 | 0.816 | 0.993 | 0.606 | 80.912 | 88.465 |
ANN10 | TrainGDX | 24 | Logsig | Logsig | 7-11-13-1 | 0.915 | 0.913 | 0.624 | 88.188 | 88.413 | 0.879 | 1.126 | 0.985 | 80.926 | 79.481 |
ANN11 | TrainSCG | 26 | Tansig | Tansig | 7-11-15-1 | 0.938 | 0.619 | 0.336 | 93.654 | 93.553 | 0.882 | 1.023 | 0.586 | 88.018 | 90.555 |
ANN12 | TrainGDX | 32 | Purelin | Tansig | 7-15-17-1 | 0.922 | 0.680 | 0.387 | 92.201 | 93.114 | 0.866 | 0.978 | 0.392 | 86.559 | 88.953 |
ANN13 | TrainLM | 37 | Tansig | Tansig | 7-17-20-1 | 0.906 | 0.900 | 0.628 | 88.409 | 87.744 | 0.763 | 0.992 | 0.822 | 73.105 | 85.883 |
ANN14 | TrainSCG | 39 | Purelin | Logsig | 7-17-22-1 | 0.855 | 0.916 | 1.501 | 87.608 | 64.877 | 0.765 | 0.596 | 1.357 | 79.748 | 87.901 |
ANN15 | TrainLM | 42 | Tansig | Logsig | 7-17-25-1 | 0.913 | 1.035 | 0.844 | 90.418 | 87.033 | 0.758 | 0.981 | 0.893 | 75.765 | 82.328 |
LM Levenberg–Marquardt, GDX Adaptive learning rate, SCG Scaled conjugate gradient, OSS One-step secant.