Model | Training data | Test data | Total data | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Mean | STD | Min | Max | Mean | STD | Min | Max | ||||
1 | Inputs | WC (%) | 15.78 | 1.02 | 14.23 | 18.86 | 15.78 | 1.03 | 14.23 | 18.86 | 320 |
T (°C) | 30.90 | 15.88 | 10.00 | 60.00 | 32.31 | 17.82 | 10.00 | 60.00 | |||
Outputs | η (Pa.s) | 24.92 | 36.91 | 0.37 | 225.27 | 27.17 | 38.73 | 0.23 | 177.99 | ||
2 | Inputs | WC (%) | 15.82 | 1.03 | 14.23 | 18.86 | 15.75 | 0.99 | 14.23 | 18.86 | 800 |
T (°C) | 39.28 | 21.42 | 3.67 | 74.57 | 39.22 | 21.83 | 3.61 | 74.48 | |||
Outputs | G′ (Pa) | 1.27 | 3.56 | 0.00 | 36.67 | 1.18 | 2.76 | 0.00 | 20.82 | ||
G″ (Pa) | 299.97 | 744.95 | 0.92 | 6174.37 | 308.74 | 676.12 | 1.43 | 4571.52 | |||
η* (Pa.s) | 47.74 | 118.56 | 0.15 | 982.70 | 49.14 | 107.61 | 0.23 | 727.59 | |||
3 | Inputs | WC (%) | 15.80 | 1.03 | 14.23 | 18.86 | 15.73 | 0.99 | 14.23 | 18.86 | 800 |
T (°C) | 35.96 | 21.35 | 0.55 | 71.43 | 35.95 | 21.71 | 0.57 | 71.42 | |||
G′ (Pa) | 28.29 | 70.77 | 0.00 | 772.13 | 22.85 | 48.72 | 0.00 | 354.15 | |||
Outputs | G″(Pa) | 493.78 | 1169.19 | 0.83 | 8455.12 | 530.61 | 1282.02 | 1.02 | 8398.52 | ||
η* (Pa.s) | 78.93 | 186.42 | 0.13 | 1346.14 | 84.66 | 204.16 | 0.16 | 1336.82 | |||
4 | WC (%) | 15.78 | 1.02 | 14.23 | 18.86 | 15.79 | 1.02 | 14.23 | 18.86 | 4160 | |
Inputs | T (°C) | 31.08 | 16.24 | 10.00 | 60.00 | 31.76 | 16.67 | 10.00 | 60.00 | ||
F (Hz) | 2.42 | 2.95 | 0.10 | 10.00 | 2.34 | 2.89 | 0.10 | 10.00 | |||
G′ (Pa) | 2.42 | 8.29 | 0.00 | 233.52 | 2.29 | 7.14 | 0.00 | 151.11 | |||
Outputs | G″ (Pa) | 407.86 | 1081.78 | 0.18 | 16404.51 | 405.20 | 1052.59 | 0.23 | 9751.40 | ||
η* (Pa.s) | 27.74 | 40.98 | 0.28 | 268.32 | 26.94 | 39.96 | 0.28 | 266.10 |
Variable | Model Coefficient | Training data | Test data | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
β0 | β1 | β2 | β3 | β12 | β13 | β23 | β123 | β11 | β22 | β33 | RMSE | r | RMSE | r | |
G′ (Pa) | - | 0.01 | −0.04 | 0.10 | −0.02 | −0.17 | −0.17 | 0.26 | - | 0.05 | 0.06 | 0.0295 | 0.6189 | 0.0170 | 0.6932 |
G″ (Pa) | 0.03 | −0.03 | −0.20 | 0.38 | - | −0.40 | −0.51 | 0.56 | 0.04 | 0.20 | - | 0.0362 | 0.8503 | 0.0293 | 0.8539 |
η* (Pa.s) | 0.49 | −0.53 | −1.29 | - | 0.52 | - | - | - | 0.16 | 0.81 | - | 0.0680 | 0.8964 | 0.0640 | 0.9018 |
Model | Estimated variable | Empirical constants | Exponential Model (Training data) | Exponential Model (Test data) | ANN (Training) | ANN (Test) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | RMSE | r | RMSE | r | RMSE | r | RMSE | r | ||
1 | η (Pa.s) | 0.799 | 2.036 | 6.415 | 0.0101 | 0.9981 | 0.0433 | 0.9700 | 0.0359 | 0.9760 | 0.0430 | 0.9681 |
G′ (Pa) | 0.805 | 3.302 | 14.696 | 0.0343 | 0.9356 | 0.0290 | 0.9293 | 0.0338 | 0.9398 | 0.0261 | 0.9390 | |
2 | G″ (Pa) | 0.881 | 2.549 | 10.953 | 0.0282 | 0.9725 | 0.0272 | 0.9688 | 0.0296 | 0.9704 | 0.0252 | 0.9731 |
η* (Pa.s) | 0.881 | 2.549 | 10.953 | 0.0282 | 0.9725 | 0.0272 | 0.9688 | 0.0295 | 0.9705 | 0.0252 | 0.9731 | |
G′ (Pa) | 0.489 | 2.628 | 8.542 | 0.0659 | 0.6948 | 0.0521 | 0.7055 | 0.0675 | 0.6969 | 0.0486 | 0.6629 | |
3 | G″ (Pa) | 0.911 | 1.684 | 12.549 | 0.0313 | 0.9742 | 0.0320 | 0.9779 | 0.0308 | 0.9758 | 0.0326 | 0.9794 |
η* (Pa.s) | 0.913 | 1.687 | 12.526 | 0.0314 | 0.9742 | 0.0320 | 0.9779 | 0.0309 | 0.9759 | 0.0326 | 0.9794 | |
G′ (Pa) | - | - | - | - | - | - | - | 0.0260 | 0.7244 | 0.0158 | 0.7301 | |
4 | G″ (Pa) | - | - | - | - | - | - | - | 0.0195 | 0.9604 | 0.0176 | 0.9581 |
η* (Pa.s) | - | - | - | - | - | - | - | 0.0420 | 0.9636 | 0.0406 | 0.9647 |