Boosting Hot Mix Asphalt Dynamic Modulus Prediction Using Statistical and Machine Learning Regression Modeling Techniques
Abstract
:1. Introduction
2. Literature Review
Ref. | Model | Binder Properties | Mix Properties | Test Conditions | Training | Validation | Testing | Scale | Sensitivity | Goodness-of-Fit Statistics | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Volumetric Parameters | Gradation Parameters | ||||||||||||||||||||||
δ | G* | η | PGL | PGH | AC | VMA | VFA | Va | Vbeff | ρ3/8 | ρ3/4 | ρ4 | ρ200 | Freq. | Temp. | ||||||||
[14] | ANN | - | - | √ | - | - | - | - | - | √ | √ | √ | √ | √ | √ | fc | - | 90% | 3% | 7% | log | N = 7400, R2 = 0.978 | |
[14] | ANN | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | - | 90% | 3% | 7% | log | N = 7400, R2 = 0.959 | |
[6] | DCNN | - | - | √ | - | - | - | - | - | √ | √ | √ | √ | √ | √ | fc | - | 80% | - | 20% | log | N = 6060, R2 = 0.95, Se/Sy = 0.21 | |
[6] | DCNN | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | - | 80% | - | 20% | log | N = 6060, R2 = 0.96, Se/Sy = 0.19 | |
[6] | DCNN | - | - | √ | - | - | - | - | - | √ | √ | √ | √ | √ | √ | fc | 20% | - | 80% | log | N = 1071, R2 = 0.98, Se/Sy = 0.13 | ||
[6] | DCNN | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | 20% | - | 80% | log | N = 1071, R2 = 0.99, Se/Sy = 0.10 | ||
[15] | BTE * | - | √ | - | - | - | √ | - | - | - | - | - | - | - | - | - | 85% | - | 15% | log | √ | N = 1656, R2 = 0.954 | |
[7] | ANN | - | - | √ | - | - | - | - | - | √ | √ | √ | √ | √ | √ | fc | 93% | - | 7% | Ar | N = 7400, R2 = 0.98, Se/Sy = 0.14 | ||
[7] | ANN | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | 93% | - | 7% | Ar | N = 7400, R2 = 0.96, Se/Sy = 0.21 | ||
[23] | SVM | - | - | - | - | - | - | - | - | - | - | - | - | - | - | fr | √ | 99% | - | 1% | Ar | N = 80, R2 = 0.956 | |
[24] | PCA-GEP | - | √ | - | - | - | √ | - | √ | √ | - | √ | √ | √ | - | fc | √ | - | - | - | log | N = 7400, R2 = 0.925 | |
[8] | DRNN | √ | √ | √ | - | - | - | √ | √ | √ | √ | √ | √ | √ | √ | fr | √ | 80% | - | 20% | log | N = 4650, R2 = 0.98, Se/Sy = 0.11 | |
[25] | BBP | - | - | - | √ | - | - | √ | - | - | - | - | - | - | - | fr | √ | 98% | - | 2% | log | √ | N = 4122, R2 = 0.97, MAPE = 2.3% |
[25] | BBP a | - | - | - | √ | √ | √ | √ | - | - | √ | - | - | - | - | fr | √ | 98% | - | 2% | log | √ | N = 4122, R2 = 0.98, MAPE = 2.0% |
[17] | BAS-RF | √ | √ | - | - | - | - | - | - | √ | √ | - | √ | √ | √ | - | - | - | - | - | Ar | N = NA, R2 = 0.98 | |
[26] | RF a,b | - | - | - | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | fr | √ | - | - | - | log | √ | N =4022, R2 = 0.95 |
[27] | ANN | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | - | 85% | - | 15% | log | N = 1656, R2 = 0.99 | |
[27] | ANN | - | √ | - | - | - | - | √ | √ | - | - | - | - | - | - | - | - | 85% | - | 15% | log | N = 1656, R2 = 0.99 | |
[28] | RF | √ | √ | - | - | - | - | - | - | √ | √ | √ | - | √ | √ | - | - | 70% | - | 30% | Ar | N = 144, R2 = 0.98 | |
[29] | BAS | √ | √ | - | - | - | - | - | - | √ | √ | √ | - | √ | √ | - | - | 70% | - | 30% | Ar | N = 144, R2 = 0.92 | |
[30] | GDTB | - | - | √ | - | - | - | - | - | √ | √ | √ | √ | √ | √ | fc | - | 90% | 3% | 7% | log | N = 7400, R2 = 0.98, Se/Sy = 0.14, MAPE = 2.1% | |
[30] | GDTB | √ | √ | - | - | - | - | - | - | √ | √ | √ | √ | √ | √ | - | - | 90% | 3% | 7% | log | N = 7400, R2 = 0.98, Se/Sy = 0.13, MAPE = 3.9% | |
[31] | ANNPSO | √ | √ | - | - | - | - | - | - | √ | √ | √ | - | √ | √ | - | - | - | - | - | Ar | N = 144, R2 = 0.989 | |
[32] | ANN | √ | √ | - | - | - | - | - | - | √ | √ | √ | - | √ | √ | - | - | 75% | - | 25% | Ar | N = 1320, R2 = 0.98 |
3. Research Motivation and Objectives
- Compare the E* prediction accuracy of the most widely used NCHRP 1-37A Witczak model with new developed statistical regression models based on advanced aggregate gradation feeding features.
- Investigate various ML techniques to enhance the E* prediction based on the same alternatives of feeding variables.
- Conduct a sensitivity analysis on the optimized and most accurate ML-based model to its feeding input parameters.
- The approach of using Weibull distribution factors and Bailey method parameters is novel, as both methods employ full aggregate gradation sieve sizes instead of using only four gradation ones. Furthermore, the use of a comprehensive and reliable dataset of measured E* values and feeding parameters promotes trustworthy and dependable predictions of E* based on optimized and accurate ML-based model.
4. Material and Testing Measurements
5. Methodology
- Data preparation: by cleaning, removing outliers, and scaling.
- Feature engineering: by generating new feeding features from the measured data, using the Bailey method and Weibull distribution to characterize aggregate gradation in a better way.
- Modelling phase: by developing both statistical and ML-based models using three different representations of aggregate gradation feeding features; each representation contains different feeding features representing aggregate gradation.
- Model training on the selected dataset.
- Model evaluation on a holdout test dataset, using different types of evaluation techniques such as R2, root mean square error (RMSE), mean absolute error (MAE), and k-fold cross-validation.
- Model selection and optimization: by choosing the outperforming model and adjusting its hyperparameters.
- Feature importance: by analyzing the model results, using the SHAP values to find out the most important feeding features affecting the model predictions.
- Model deployment: by deploying the optimized model. This involves making the model available to users so that they can use it to predict E* for new asphalt mixtures.
5.1. Statistical Models
- Statistical regression model incorporating Bailey method parameters (:
- ii.
- Statistical regression model incorporating Weibull distribution factors (:
5.2. ML-Based Modeling Techniques
5.2.1. Linear Regression (LiR)
Multiple Linear Regression (MLiR)
Regularized Linear Regression (RLiR)
- Regularized Ridge Regression (RRdR):
- Regularized Lasso Regression (RLaR):
5.2.2. K-Nearest Neighbors Regression (KNNR)
5.2.3. Decision Tree Regression (DTR)
5.2.4. Support Vector Machine (SVM)
5.2.5. Ensemble Learning
Bagging Ensemble Learning
Boosting Ensemble Learning
5.3. Model Performance Indicators
5.4. Threats to Validity
- i.
- Selection bias: The dataset was randomly divided into training and testing sets, but it is important to note that the training set may not be fully representative of the population of interest. This could lead to selection bias, which could affect the validity of the results. To mitigate this risk, the authors stratified the training and testing sets by temperature, which is an important factor that affects E*.
- ii.
- Overfitting: The models were trained on the training set, and their performance was evaluated on the testing set. However, there is a risk that the models could overfit the training data, which means that they may not perform well on new data. To mitigate this risk, the authors used a k-fold cross-validation technique.
- iii.
- Imbalanced data: The E* dataset was imbalanced and skewed to the right. This could lead to the models being biased towards the more common values of E*. To mitigate this risk, the authors used ensemble models, such as random forests and gradient-boosted trees. Ensemble models combine multiple decision trees, which can help to mitigate the impact of imbalanced data on individual trees and improve overall performance.
- i.
- The proposed approach can learn complex relationships between the input and output variables as presented by the proposed feeding features for predicting the E* of asphalt mixtures.
- ii.
- The proposed approach can be used to model a wide range of input variables, including both continuous and categorical variables. This makes it more flexible and versatile than traditional regression models.
- iii.
- The proposed approach can be used to handle imbalanced data.
- iv.
- The proposed approach can be used to improve the interpretability of ML-based models.
- v.
- The findings of this research study are essential for practitioners and engineers who are dealing with asphalt mixtures. The proposed models could be used by asphalt engineers to design asphalt mixtures with a desired E*.
- i.
- ML-based regression algorithms can be computationally expensive to train, especially for large datasets.
- ii.
- ML-based regression models are difficult to interpret, as they can learn complex patterns in the data that are not easily understood by humans.
- i.
- The proposed approach has only been evaluated on a single dataset. It is important to evaluate and validate the approach on other datasets to ensure that it is generalizable.
- ii.
- The proposed approach has only been used to predict the E* of asphalt mixtures. It is important to evaluate the approach for other applications.
6. Results and Discussion
6.1. Statistical Regression Models
6.2. ML-Based Regression Models
6.3. K-Fold Cross-Validation
6.4. Learning Curve
6.5. Comparing the Statistical and ML-Based Models
6.6. Model Selection and Hyperparameter Optimization
6.6.1. Hyperparameter Tuning
6.6.2. Residual Analysis
6.6.3. Model Interpretation and Feeding Feature Sensitivity
7. Conclusions and Recommendations
- On the first hand, two statistical regression models incorporating the Bailey method parameters and Weibull distribution factors were developed to predict E* with alternative characterizations of aggregate gradations. The predictions of both proposed models were compared to E* predictions of the NCHRP 1-37A Witczak model. As predicted, the performance of statistical models varied. While the literature-based 1-37A model did not provide satisfactory results, the Weibull-based and Bailey-based models showed significant improvement in predicting E*. The Weibull-based model slightly outperformed the Bailey-based model in terms of adjusted R2.
- On the other hand, 13 ML-based regression algorithms were trained involving the three approaches to aggregate gradation characterizations. The performance of each algorithm was evaluated using goodness-of-fit statistics and k-fold cross-validation techniques. The optimized algorithm underwent hyperparameter tuning and was subjected to the residual analysis and feature importance study.
- Notably, the results indicated that the ML-based models outperformed the statistical models in predicting the E* of asphalt mixtures. Among the ML-based algorithms, ensemble models, particularly boosting techniques such as EGBR and CbR, exhibited superior performance. These models achieved the adjusted R2 values higher than 0.999, using the training dataset.
- The CbR models showed robustness, with minimal differences in accuracy between the training and testing datasets. Furthermore, the k-fold cross-validation analysis revealed that the CbR model had the least variance among the investigated algorithms, indicating their stability and consistency in predicting E*. Additionally, the learning curve analysis demonstrated that the CbR models achieved an optimal balance between bias and variance, indicating their ability to generalize well to unseen data.
- Based on the comprehensive evaluation, the CbR models, particularly the Bailey-based CbR model, were recommended as the most accurate and reliable models for predicting the E* of asphalt mixtures. Hyperparameter optimization was performed to fine-tune the model, while the residual analysis confirmed that the residuals of the optimized model exhibited no identified patterns or heteroscedasticity, supporting the assumption of randomness in the predictive model.
- Moreover, the SHAP values were applied to interpret the optimized Bailey-based CbR model and determine the relative importance of the feeding features. The results highlighted that temperature was the most critical feeding feature, followed by frequency and binder viscosity. The impact of the Bailey method parameters representing aggregate gradation on E* predictions was comparable to that of mixture volumetrics.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Ref. | Binder Properties | Mix Properties | Test Conditions | Calibration | Validation | Scale | Statistics of Goodness-of-Fit | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Volumetric Parameters | Gradation Parameters | ||||||||||||||||
δ | G* | η | VMA | VFA | Va | Vbeff | ρ3/8 | ρ3/4 | ρ4 | ρ200 | Freq | Temp | |||||
[5] | - | √ | - | √ | - | √ | √ | √ | √ | √ | 90% | 10% | N = 223, R2 = 0.95, Se/Sy = 0.22 | ||||
[6] | - | - | √ | - | - | √ | √ | √ | √ | √ | √ | fc | - | 80% | 20% | log | N = 6060, R2 = 0.54, Se/Sy = 0.68 |
[6] | √ | √ | - | - | - | √ | √ | √ | √ | √ | √ | - | - | 80% | 20% | log | N = 6060, R2 = 0.73, Se/Sy = 0.52 |
[6] | - | - | √ | - | - | √ | √ | √ | √ | √ | √ | fc | 20% | 80% | log | N = 1071, R2 = 0.85, Se/Sy = 0.38 | |
[6] | √ | √ | - | - | - | √ | √ | √ | √ | √ | √ | - | 20% | 80% | log | N = 1071, R2 = 0.53, Se/Sy = 0.69 | |
[7] | - | - | √ | - | - | √ | √ | √ | √ | √ | √ | fc | 93% | 7% | Ar | N = 7400, R2 = 0.68, Se/Sy = 0.57 | |
[7] | √ | √ | - | - | - | √ | √ | √ | √ | √ | √ | - | 93% | 7% | Ar | N = 7400, R2 = 0.77, Se/Sy = 0.48 | |
[8] | - | - | √ | - | - | √ | √ | √ | √ | √ | √ | fr | - | - | - | log | N = 4650, R2 = 0.84, Se/Sy = 0.39 |
[8] | √ | √ | - | - | - | √ | √ | √ | √ | √ | √ | fr | - | - | - | log | N = 4650, R2 = 0.92, Se/Sy = 0.29 |
[8] | √ | - | - | √ | √ | - | - | - | - | - | - | - | - | - | - | log | N = 4650, R2 = 0.68, Se/Sy = 0.57 |
Feeding Features | Feature Description | Mean | Standard Deviation | Minimum | Maximum | |
---|---|---|---|---|---|---|
Testing Conditions | T | Temperature (ºC) | 29.43 | 18.65 | 4.40 | 54.40 |
fC | Frequency (Hz) | 6.93 | 8.79 | 0.10 | 25.00 | |
Binder | ηf,T | Viscosity (cP) | 3.1 × 109 | 14.8 × 109 | 0.0001 × 109 | 84.8 × 109 |
Aggregate | ρ3/4 | Retained on the 3/4 in. sieve (%) | 0.96 | 2.49 | 0.00 | 14.00 |
ρ3/8 | Retained on the 3/8 in. sieve (%) | 24.31 | 7.38 | 13.00 | 36.00 | |
ρ4 | Retained on No. 4 sieve (%) | 49.84 | 5.84 | 42.00 | 63.00 | |
ρ200 | Passing No. 200 sieve (%) | 5.42 | 1.62 | 3.50 | 8.20 | |
λ | Weibull distribution factors | 6.04 | 1.15 | 4.65 | 8.67 | |
κ | 0.89 | 0.07 | 0.72 | 1.07 | ||
CA Ratio | Bailey method parameters | 0.82 | 0.15 | 0.53 | 1.31 | |
FAc Ratio | 0.37 | 0.11 | 0.23 | 0.57 | ||
FAf Ratio | 2.05 | 0.37 | 1.60 | 2.90 | ||
Mixture Volumetrics | Va | Volume of the air voids in the mixture (%) | 7.47 | 0.89 | 5.94 | 9.58 |
Vbeff | Volume of effective bitumen content (%) | 10.75 | 1.26 | 9.00 | 16.00 | |
E* | Measured E* (MPa) | 3489.94 | 4117.70 | 14.90 | 18,974.00 |
Ref. | Algorithm | Nonlinear | Data Transformation Is Required? | Hyperparameters | Category |
---|---|---|---|---|---|
[42] | MLiR | √ | - | Linear | |
[49] | RLaR | √ | Alpha | Linear | |
[50] | RRdR | √ | Alpha | Linear | |
[51] | KNNR | √ | √ | K | KNN |
[52] | SVM-L | √ | C | SVM | |
[52] | SVM-RBF | √ | √ | C | SVM |
[52] | SVM-P | √ | √ | C, gamma, and d | SVM |
[53] | DTR | √ | Criterion, depth, and nodes | DT | |
[54] | RFR | √ | Criterion, N, and depth | Bagging | |
[55] | ABR | √ | Base, Lr, and N | Boosting | |
[56] | GBR | √ | Loss, Lr, criterion, N, and depth | Boosting | |
[57] | EGBR | √ | N, Lr, alpha, lambda, CC, and CW | Boosting | |
[58] | CbR | √ | Depth, Lr, and number of iterations | Boosting |
Statistical Regression Model | R2 (Arithmetic) | RMSE | MAE |
---|---|---|---|
Literature-Based 1-37A Prediction Model | 0.52 | 2831.37 | 1706.03 |
Weibull-Based Prediction Model | 0.90 | 1287.49 | 734.03 |
Bailey-Based Prediction Model | 0.89 | 1317.58 | 744.46 |
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Awed, A.M.; Awaad, A.N.; Kaloop, M.R.; Hu, J.W.; El-Badawy, S.M.; Abd El-Hakim, R.T. Boosting Hot Mix Asphalt Dynamic Modulus Prediction Using Statistical and Machine Learning Regression Modeling Techniques. Sustainability 2023, 15, 14464. https://doi.org/10.3390/su151914464
Awed AM, Awaad AN, Kaloop MR, Hu JW, El-Badawy SM, Abd El-Hakim RT. Boosting Hot Mix Asphalt Dynamic Modulus Prediction Using Statistical and Machine Learning Regression Modeling Techniques. Sustainability. 2023; 15(19):14464. https://doi.org/10.3390/su151914464
Chicago/Turabian StyleAwed, Ahmed M., Ahmed N. Awaad, Mosbeh R. Kaloop, Jong Wan Hu, Sherif M. El-Badawy, and Ragaa T. Abd El-Hakim. 2023. "Boosting Hot Mix Asphalt Dynamic Modulus Prediction Using Statistical and Machine Learning Regression Modeling Techniques" Sustainability 15, no. 19: 14464. https://doi.org/10.3390/su151914464