Evaluation of Multiple Linear Regression and Machine Learning Approaches to Predict Soil Compaction and Shear Stress Based on Electrical Parameters
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Data Acquisition
2.2. Multiple Linear Regression
- The explanation objective examines the regression coefficients and their magnitude, sign, and statistical inference for each predictor variable;
- The forecast objective examines the extent to which the explanatory variables can estimate the explicative variable [55].
2.3. Artificial Neural Networks
2.4. Sensitivity Analysis
2.5. Support Vector Machines
2.6. Criteria of Accuracy Assessment of Models
- The model is perfect if GA = 1;
- The model is excellent if 0.75 ≤ GA < 1 or 1 < GA ≤ 1.35;
- The model is good if 1.35 < GA ≤ 2 or 0.5 ≤ GA < 0.75;
- The model is poor and unsuitable for prediction if GA > 2 or GA < 0.5.
3. Results
3.1. Multiple Linear Regression
3.2. Artificial Neural Networks
3.3. Sensitivity Analysis (SA)
3.4. Support Vector Machines
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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The Parameter | Minimum | Maximum | Mean | Standard Deviation |
---|---|---|---|---|
Soil compaction (depth 0–0.5 m) (MPa) | 0.65 | 2.20 | 1.41 | 0.28 |
Soil compaction (depth 0.4–0.5 m) (MPa) | 0.17 | 3.39 | 1.14 | 0.58 |
Shear stress (kPa) | 96.00 | 248.00 | 163.40 | 32.88 |
Factor | RSC_0.4_0.5 Constant Term = 1.812 | RSC_0_0.5 Constant Term = 1.545 | RSS Constant Term = 124.587 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
b Coefficient | Standard Error b | p-Value | Significance | b Coefficient | Standard Error b | p-Value | Significance | b Coefficient | Standard Error b | p-Value | Significance | |
Apparent soil electrical conductivity 0.5 m (ECa0.5) | 0.390 | 0.094 | 0.017 | + | −0.040 | 0.008 | <0.001 | + | 5.530 | 1.065 | <0.001 | + |
Magnetic susceptibility 0.5 m (MS0.5) | −0.837 | 0.089 | 0.749 | − | −1.868 | 1.238 | 0.133 | − | 146.434 | 147.712 | 0.323 | - |
Apparent soil electrical conductivity 1 m (ECa1) | 0.390 | 0.132 | 0.038 | + | 0.009 | 0.005 | 0.083 | − | −1.192 | 0.644 | 0.066 | - |
Magnetic susceptibility 1 m (MS1) | −0.077 | 0.139 | 0.502 | − | −0.025 | 0.054 | 0.642 | − | −18.247 | 6.549 | 0.006 | + |
Model | RMSE | MAE | MAPE | NSC | R |
---|---|---|---|---|---|
RSC_0.4_0.5 | 0.535 | 0.401 | 28.468 | 0.152 | 0.408 |
RSC_0_0.5 | 0.335 | 0.261 | 18.187 | 0.072 | 0.469 |
RSS | 37.794 | 30.433 | 21.299 | 0.073 | 0.423 |
Model | Model Structure | Train | Validation | GA | OBJ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | MAPE | NSC | R | RMSE | MAE | MAPE | NSC | R | ||||
MLPSC_0_0.5 | 4-12-1 | 0.246 | 0.191 | 15.416 | 0.297 | 0.545 | 0.153 | 0.134 | 9.550 | 0.555 | 0.790 | 0.621 | 0.281 |
MLPSC_0.4_0.5 | 4-10-1 | 0.471 | 0.355 | 21.302 | 0.319 | 0.567 | 0.387 | 0.323 | 20.246 | 0.546 | 0.772 | 0.821 | 0.562 |
MLP_SS | 4-19-1 | 29.363 | 23.289 | 14.699 | 0.236 | 0.486 | 24.210 | 20.120 | 12.912 | 0.408 | 0.680 | 0.824 | 38.280 |
Model | Model Structure | Train | Validation | GA | OBJ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | MAPE | NSC | R | RMSE | MAE | MAPE | NSC | R | ||||
RBFSC_0_0.5 | 4-17-1 | 0.264 | 0.210 | 16.779 | 0.187 | 0.432 | 0.160 | 0.138 | 9.398 | 0.603 | 0.812 | 0.606 | 0.322 |
RBFSC_0.4_0.5 | 4-16-1 | 0.526 | 0.387 | 31.574 | 0.149 | 0.386 | 0.405 | 0.316 | 17.085 | 0.511 | 0.846 | 0.769 | 0.663 |
RBF_SS | 4-25-1 | 29.637 | 22.765 | 14.511 | 0.221 | 0.470 | 26.484 | 22.313 | 15.314 | 0.311 | 0.648 | 0.893 | 39.917 |
Model | Train | Validation | GA | OBJ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | MAPE | NSC | R | RMSE | MAE | MAPE | NSC | R | |||
SVMSC_0_0.5 | 0.251 | 0.198 | 15.605 | 0.208 | 0.457 | 0.216 | 0.074 | 6.415 | 0.242 | 0.709 | 0.860 | 0.281 |
SVMSC_0.4_0.5 | 0.539 | 0.393 | 29.897 | 0.187 | 0.437 | 0.437 | 0.207 | 14.061 | 0.086 | 0.555 | 0.810 | 0.636 |
SVM_SS | 29.690 | 23.624 | 15.466 | 0.228 | 0.478 | 31.125 | 15.345 | 9.044 | 0.016 | 0.243 | 1.048 | 43.642 |
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Pentoś, K.; Mbah, J.T.; Pieczarka, K.; Niedbała, G.; Wojciechowski, T. Evaluation of Multiple Linear Regression and Machine Learning Approaches to Predict Soil Compaction and Shear Stress Based on Electrical Parameters. Appl. Sci. 2022, 12, 8791. https://doi.org/10.3390/app12178791
Pentoś K, Mbah JT, Pieczarka K, Niedbała G, Wojciechowski T. Evaluation of Multiple Linear Regression and Machine Learning Approaches to Predict Soil Compaction and Shear Stress Based on Electrical Parameters. Applied Sciences. 2022; 12(17):8791. https://doi.org/10.3390/app12178791
Chicago/Turabian StylePentoś, Katarzyna, Jasper Tembeck Mbah, Krzysztof Pieczarka, Gniewko Niedbała, and Tomasz Wojciechowski. 2022. "Evaluation of Multiple Linear Regression and Machine Learning Approaches to Predict Soil Compaction and Shear Stress Based on Electrical Parameters" Applied Sciences 12, no. 17: 8791. https://doi.org/10.3390/app12178791
APA StylePentoś, K., Mbah, J. T., Pieczarka, K., Niedbała, G., & Wojciechowski, T. (2022). Evaluation of Multiple Linear Regression and Machine Learning Approaches to Predict Soil Compaction and Shear Stress Based on Electrical Parameters. Applied Sciences, 12(17), 8791. https://doi.org/10.3390/app12178791