Introduction
Literature review
Materials and methods
Data collection and preprocessing
S. no | Vehicle category | Delhi–Haridwar and Delhi–Haridwar | |||||||
---|---|---|---|---|---|---|---|---|---|
Average speed (km/h) | Traffic volume | ||||||||
Min | Max | Mean | SD | Min | Max | Mean | SD | ||
1 | Car | 14.123 | 43.373 | 18.140 | 4.699 | 38 | 60 | 46.254 | 4.387 |
2 | Bus | 9.56 | 31.4 | 16.000 | 5.716 | 4 | 24 | 10.550 | 3.325 |
3 | Truck | 11.1 | 39.29 | 16.034 | 6.352 | 1 | 17 | 5.847 | 2.838 |
4 | LCV | 13.09 | 29.95 | 19.549 | 4.914 | 3 | 23 | 8.847 | 2.707 |
5 | 3-Wheeler | 9.96 | 31.23 | 18.86 | 5.643 | 1 | 20 | 4.337 | 2.993 |
6 | 2-Wheelers | 9.54 | 34.13 | 18.968 | 5.789 | 98 | 155 | 114.735 | 9.093 |
7 | Cycle | 9.11 | 22.29 | 12.861 | 3.843 | 5 | 25 | 15.0509 | 3.696 |
8 | Rickshaw | 8.59 | 19.63 | 11.256 | 2.899 | 3 | 21 | 13.2777 | 4.563 |
9 | Tractor | 9 | 20.68 | 14.342 | 2.888 | 1 | 12 | 3.643 | 2.068 |
10 | ADV | 0 | 1.42 | 0.2335 | 0.4199 | 0 | 2 | 0.4444 | 0.7573 |
Model development
Development of ANN models
Model | Algorithm | Hidden layer | hidden neurons | Transfer Function | Epochs | Learning | Step size/Mo | Training | Cross validation | Testing | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Min MSE (*104) | Final MSE (*104) | Min MSE (*104) | Final MSE (*104) | MSE | NMSE (*104) | MAE | R (%) | ||||||||
M1 | MLP | 1 | 4 | Tanh | 100 | LM | – | 5.9 | 5.9 | 12.5 | 10.37 | 4.66 | 47.99 | 1.93 | 98.8 |
M2 | MLP | 1 | 4 | Tanh | 200 | LM | – | 5.3 | 5.3 | 15 | 7.13 | 6.00 | 61.81 | 2.14 | 98.4 |
M3 | MLP | 1 | 4 | Tanh | 300 | LM | – | 4 | 4 | 21.1 | 20.94 | 3.25 | 33.49 | 1.26 | 98.7 |
M4 | MLP | 1 | 5 | Tanh | 100 | LM | – | 3.6 | 3.8 | 20.24 | 8.371 | 4.79 | 49.34 | 1.84 | 99.2 |
M5 | MLP | 1 | 5 | Tanh | 200 | LM | – | 2.8 | 2.8 | 16.05 | 16.866 | 19.8 | 204.4 | 3.73 | 93.7 |
M6 | MLP | 1 | 5 | Tanh | 100 | MO | 1/0.7 | 29.9 | 29.9 | 23.19 | 2.506 | 4.12 | 42.43 | 1.64 | 98.3 |
M7 | MLP | 1 | 5 | Tanh | 200 | MO | 1/0.7 | 27.3 | 27.3 | 25.8 | 3.3 | 7.10 | 73.12 | 2.06 | 96.6 |
M8 | MLP | 1 | 3 | SigmoidAxon | 100 | LM | – | 2.6 | 2.6 | 3.09 | 0.832 | 7.980 | 82.1 | 2.32 | 97.9 |
M9 | MLP | 1 | 3 | SigmoidAxon | 200 | LM | – | 1.6 | 1.8 | 2.63 | 0.263 | 17.66 | 181.8 | 3.13 | 92.7 |
M10 | MLP | 1 | 5 | SigmoidAxon | 100 | LM | – | 0.81 | 0.8141 | 3.73 | 1.883 | 15.012 | 154.55 | 3.44 | 95.6 |
M11 | MLP | 1 | 5 | SigmoidAxon | 200 | LM | – | 0.03 | 0.0358 | 4.92 | 13.479 | 151.9 | 1564.4 | 11.18 | 25.5 |
M12 | MLP | 1 | 7 | SigmoidAxon | 150 | LM | – | 0.36 | 0.366 | 4.7 | 2.89 | 0.816 | 8.4 | 0.77 | 99.8 |
Sensitivity analysis of traffic volume parameter to input
Model/parameter | Minimum MSE (T) | Final MSE (T) | Minimum MSE (X) | Final MSE (X) | MSE (Y) | NMSE (Y) | MAE (Y) | r (Y) (%) |
---|---|---|---|---|---|---|---|---|
Proposed model | 3.67E−05 | 3.67E−05 | 0.00047 | 0.00289 | 0.81655 | 0.00840 | 0.7711 | 99.8 |
Sensitivity based model | 9.46E−05 | 9.46E−05 | 0.00040 | 0.00095 | 0.91439 | 0.00941 | 0.6876 | 99.5 |
Results and discussion
Model | Error | CFE | Theil’s U statistic | ||||
---|---|---|---|---|---|---|---|
MAE | MAPE (%) | VAPE (%) | MPE | U1 | U2 | ||
M1 | 1.93 | 0.9010 | 0.0221 | − 0.6872 | − 32.068 | 0.0031 | 0.0450 |
M2 | 2.14 | 0.9917 | 0.0265 | − 0.8014 | − 38.081 | 0.0056 | 1.3689 |
M3 | 1.26 | 0.5889 | 0.0287 | − 0.4358 | − 20.459 | 0.0041 | 0.9605 |
M4 | 1.84 | 0.0386 | 0.0029 | − 0.8498 | − 40.538 | 0.0050 | 0.0441 |
M5 | 3.73 | 1.7325 | 0.2774 | − 1.1564 | − 52.574 | 0.0102 | 0.9964 |
M6 | 1.64 | 0.7689 | 0.0268 | − 0.3665 | − 16.559 | 0.0046 | 0.0425 |
M7 | 2.06 | 0.9546 | 12.690 | − 0.1373 | − 5.1569 | 1.7368 | 0.0563 |
M8 | 2.32 | 1.0963 | 0.0369 | − 0.9114 | − 42.496 | 3.08E−05 | 0.0588 |
M9 | 3.13 | 1.4442 | 0.0607 | − 0.5223 | − 25.028 | 0.0096 | 0.0811 |
M10 | 11.18 | 5.2393 | 0.1217 | − 3.7443 | − 169.104 | 0.0279 | 0.2455 |
M11 | 11.41 | 5.3393 | 0.1241 | − 3.6870 | − 165.905 | 0.0285 | 0.2539 |
M12 | 0.77 | 0.3569 | 0.0102 | − 0.3158 | − 14.937 | 0.0020 | 0.0180 |
Models | MSE | RMSE | MAE | RSE | RRSE | RAE | R2 |
---|---|---|---|---|---|---|---|
Random forest | 217.718 | 14.7553 | 10.9593 | 0.2284 | 0.4779 | 0.4400 | 0.7716 |
Regression tree | 388.380 | 19.7074 | 14.4908 | 0.4074 | 0.6383 | 0.5817 | 0.5926 |
SVM regression | 898.723 | 29.9787 | 23.3781 | 0.9428 | 0.9710 | 0.9385 | 0.0572 |
K nearest neighbors Regression (KNN) | 14.1294 | 3.7589 | 1.4239 | 0.0148 | 0.1217 | 0.0572 | 0.9852 |
Multiple linear regression | 305.536 | 17.4796 | 13.3072 | 0.3205 | 0.5661 | 0.5342 | 0.6795 |
BP neural network | 4.2848 | 2.06999 | 0.77114 | 0.09951 | 0.31546 | 0.16204 | 0.9962 |