Marshall Stability Prediction with Glass and Carbon Fiber Modified Asphalt Mix Using Machine Learning Techniques

Pavement design is a long-term structural analysis that is required to distribute traffic loads throughout all road levels. To construct roads for rising traffic volumes while preserving natural resources and materials, a better knowledge of road paving materials is required. The current study focused on the prediction of Marshall stability of asphalt mixes constituted of glass, carbon, and glass-carbon combination fibers to exploit the best potential of the hybrid asphalt mix by applying five machine learning models, i.e., artificial neural networks, Gaussian processes, M5P, random tree, and multiple linear regression model and further determined the optimum model suitable for prediction of the Marshall stability in hybrid asphalt mixes. It was equally important to determine the suitability of each mix for flexible pavements. Five types of asphalt mixes, i.e., glass fiber asphalt mix, carbon fiber asphalt mix, and three modified asphalt mixes of glass-carbon fiber combination in the proportions of 75:25, 50:50, and 25:75 were utilized in the investigation. To measure the efficiency of the applied models, five statistical indices, i.e., coefficient of correlation, mean absolute error, root mean square error, relative absolute error, and root relative squared error were used in machine learning models. The results indicated that the artificial neural network outperformed other models in predicting the Marshall stability of modified asphalt mix with a higher value of the coefficient of correlation (0.8392), R2 (0.7042), a lower mean absolute error value (1.4996), and root mean square error value (1.8315) in the testing stage with small error band and provided the best optimal fit. Results of the feature importance analysis showed that the first five input variables, i.e., carbon fiber diameter, bitumen content, hybrid asphalt mix of glass-carbon fiber at 75:25 percent, carbon fiber content, and hybrid asphalt mix of glass-carbon fiber at 50:50 percent, are highly sensitive parameters which influence the Marshall strength of the modified asphalt mixes to a greater extent.


Introduction
Scientists and researchers are continuously working on finding ways and means to enhance the performance of flexible pavement for highways for which they have used glass and carbon fibers in asphalt mix to improve its structural performance. Carbon fibers are strong enough due to their high tensile and modulus of elasticity properties, whereas is a common application of machine intelligence techniques such as gaussian process regression, random forest, random tree, M5P tree, gene expression program (GEP), support vector machine (SVM), Gaussian process (GP), fuzzy logic, and ANFIS [16,[18][19][20][21][22][23][24][25][26]. The ANN approach [18] was implemented to predict the sustainability of asphalt concrete at various temperatures, which is better at predicting non-linear data. The study [18] found the efficacy of the generated models and further compared them with the most widely used dynamic modulus prediction and ANN models. The M5P-based models outperform other applied models [19]. In addition, the logarithmic change in the values of elastic stiffness considerably enhances the model performance. The ANN analytic techniques are quick and correct in predicting bending and critical conditions of pavement structures exposed to standard traffic stresses [20]. In a study [21], ML techniques were applied to predict Marshall characteristics, i.e., MS, permanent deformation, and several air voids of asphalt pavement and surface course. On the other hand, study [22] examined the numerical and experimental data of glass-fiber-reinforced polymer (GFRP) mixes. The application of the Gaussian process regression (GPR) technique showed more accuracy in estimating the rutting characteristic [23]. Additionally, the fatigue parameter can be predicted more precisely using unaged input variables. In the study performed by [24], an ANN model was generated to predict the fracture toughness and rutting pavement thickness of reinforced asphalt and showed more effectiveness of the model. The permeability coefficient was estimated using M5P and GP which demonstrated more accuracy in prediction [25]. The study performed by [26] implemented SVMs to improve the asphalt-pavement resilience modulus and structural performance indicators of pavement materials. The authors of [27] developed gene expression analysis and several dimensionality reduction techniques based on matrix factorization. The results show that it is effective and productive for the gene selection function. The study [28] implemented robust graph regularization non-negative matrix factorization for attributed networks incorporating two sources of data, namely network topology and node properties; the results show that the performance of the prediction is greatly improved when attributed and topological information is combined. It was found in the study [29] that by using a search-based technique and a late fusion strategy, appropriate tags are proposed for each test data throughout the prediction phase. The prior studies related to machine learning techniques are shown in Table 1.

4.
Ameri et al., [5] Glass and basalt fiber ANFIS Indirect tensile strength, moisture sensitivity, resilient modulus, and creep tests using the Marshall test The developed ANFIS models are capable of predicting output values that are close to actual data.

5.
Hejazi et al., [33] Glass, nylon 6.6, polypropylene, and polyester ANN Marshall test results in terms of stability, flow, and specific gravity The models concluded that glass, polyester, and nylon were better, and they were suggested for predicting any textile fibers that may be used in AC.

6.
Mirabdolazimi and Shafabakhsh [34] Forta fiber The objective of this study was to predict Marshall stability (MS) with ten input parameters, i.e., BC, GF, 75GF:25CF, 50GF:50CF, 25GF:75CF, CF, VG, FL, FD Glass Fiber, and FD Carbon Fiber by applying five machine learning models, i.e., artificial neural networks, Gaussian processes, M5P, random tree, and multiple linear regression models; a further objective was to determine the optimum model suitable for prediction of the Marshall stability for the same set of input variables. It was equally important to determine the suitability of each mix for flexible pavements by performing the sensitivity analysis.

ANN Model
ANNs are based on the structure and function of biological brains (representing the number of hidden neurons and one output neuron). The weighted connection between two layers stands for the number of nodes in each layer [39]. For a more practical ANN network, we can utilize iterative learning. By using a black box method, the prediction Materials 2022, 15, 8944 5 of 26 equation is obscured. Each layer's contribution to the network's data flow is noted. In the context of training, epochs are cycles of data collection. Training time for ANNs grows exponentially with the size of the dataset [40]. Sigmoid, biased, and linear output layers can approximate finitely discontinuous functions. Sigmoid functions output the products and weights of the preceding neurons' outputs. Division and exponent math make the sigmoid function difficult to directly implement in circuits. Sigmoid is included in neural networks and deep-learning systems in several ways [16]. Figure 1 depicts the ANN structure.

ANN Model
ANNs are based on the structure and function of biological brains (representing the number of hidden neurons and one output neuron). The weighted connection between two layers stands for the number of nodes in each layer [39]. For a more practical ANN network, we can utilize iterative learning. By using a black box method, the prediction equation is obscured. Each layer's contribution to the network's data flow is noted. In the context of training, epochs are cycles of data collection. Training time for ANNs grows exponentially with the size of the dataset [40]. Sigmoid, biased, and linear output layers can approximate finitely discontinuous functions. Sigmoid functions output the products and weights of the preceding neurons' outputs. Division and exponent math make the sigmoid function difficult to directly implement in circuits. Sigmoid is included in neural networks and deep-learning systems in several ways [16]. Figure 1 depicts the ANN structure.

GP Model
GP, a stochastic process, follows a multivariate normal distribution for finite random variables. GP interprets kernel models and kernel machines. Gaussian process log-marginal-likelihood maximizes kernel hyperparameters in regressor fitting (LML). All finite random variables are jointly normal. For GP Bayesian nonparametric modelling, correlation drives this "non-parametric" model. Nonparametric models, unlike geometrical models such as NNs and polynomial iterations, require raw data to make predictions. The kernel hyperparameters are GPoptimized [41].

M5P Tree Model
Quinlan (1992) [42] developed M5P algorithm model trees which efficiently handle large datasets with many dimensions and attributes. Missing data will not create ambiguity. This tree algorithm applies multivariate linear regression at each branching node. Model trees are two-stage. A splitting criterion generates a decision tree. The M5P tree model splits based on predicted error reduction from evaluating each characteristic at a network and error quantization from managed data instances entering a node. After expanding every result, it determines which attribute is the lowest in the normal [43]. This method employs standard deviation to measure terminal node error and creates linear functions at each node, purifying the data. The standard deviation reduction (SDR) formula is:

GP Model
GP, a stochastic process, follows a multivariate normal distribution for finite random variables. GP interprets kernel models and kernel machines. Gaussian process log-marginallikelihood maximizes kernel hyperparameters in regressor fitting (LML). All finite random variables are jointly normal. For GP Bayesian non-parametric modelling, correlation drives this "non-parametric" model. Nonparametric models, unlike geometrical models such as NNs and polynomial iterations, require raw data to make predictions. The kernel hyperparameters are GP-optimized [41].

M5P Tree Model
Quinlan (1992) [42] developed M5P algorithm model trees which efficiently handle large datasets with many dimensions and attributes. Missing data will not create ambiguity. This tree algorithm applies multivariate linear regression at each branching node. Model trees are two-stage. A splitting criterion generates a decision tree. The M5P tree model splits based on predicted error reduction from evaluating each characteristic at a network and error quantization from managed data instances entering a node. After expanding every result, it determines which attribute is the lowest in the normal [43]. This method employs standard deviation to measure terminal node error and creates linear functions at each node, purifying the data. The standard deviation reduction (SDR) formula is: where Y = number of samples; Y i = number of samples representing ith sample having potential rise; and sd = standard deviation.

RT Model
RT node is a tree-based classification and regression method. Bagged decision trees are created using random data. Each tree node uses the best variable split. Random forest separates nodes by the greatest random predictor. Random trees sample using replacement and bootstrap. Sample data generates a tree model. Random trees never resample. Instead, it randomly picks a subset of predictors to divide a tree node. For each tree node, repeat the technique. Random tree growth works like this. Random tree models work well with big data and numerous fields. Bagging and field samples prevent overfitting, making test findings more repeatable (Kalmegh 2015) [44,45].
Parameter values were estimated using least-squares techniques. The best MLR takes into account a variety of statistical criteria, such as the smallest RSME, the highest correlation, the largest F statistic, and the largest number of descriptors [47].

Methodology
The materials used to conduct the experiments included bitumen, glass fiber, carbon fiber, and filler, as well as open-graded coarse aggregates. The detailed methodology of the experiment performed is shown in Figure 2. Specific requirements of the material as shown in Sections 3.1-3.3.
where Y = number of samples; Yi = number of samples representing ith sample having potential rise; and sd = standard deviation.

RT Model
RT node is a tree-based classification and regression method. Bagged decision trees are created using random data. Each tree node uses the best variable split. Random forest separates nodes by the greatest random predictor. Random trees sample using replacement and bootstrap. Sample data generates a tree model. Random trees never resample. Instead, it randomly picks a subset of predictors to divide a tree node. For each tree node, repeat the technique. Random tree growth works like this. Random tree models work well with big data and numerous fields. Bagging and field samples prevent overfitting, making test findings more repeatable (Kalmegh 2015) [44,45].

MLR Model
Multiple linear regression is one modeling technique used to explain the effect of influential variables used independently of one another [46]. Generally, the MLR model can be expressed as in Equation (1): where P = dependent variable; q1 … qn = independent variable; q2 = Regression Coefficient.
Parameter values were estimated using least-squares techniques. The best MLR takes into account a variety of statistical criteria, such as the smallest RSME, the highest correlation, the largest F statistic, and the largest number of descriptors [47].

Methodology
The materials used to conduct the experiments included bitumen, glass fiber, carbon fiber, and filler, as well as open-graded coarse aggregates. The detailed methodology of the experiment performed is shown in Figure 2. Specific requirements of the material as shown in Sections 3.1-3.3.

Glass and Carbon Fibers
Chopped glass and carbon fiber were the two types of fibers utilized. Five different types of asphalt mixes, including GF, CF, and glass and carbon fiber hybrid mixes, were prepared. Table 6 summarizes the properties of glass and carbon fibers.

Experimental Investigation
The asphalt mix was developed following the specifications specified by ASTM D-1559 [57]. Cylindrical specimens with a diameter of 101.6 mm × 63.5 mm in height were used. A total of 1200 gm of open-graded coarse aggregate was utilized and thoroughly oven dried at a temperature between 100-110 • C for 24 h. The aggregate was heated at a temperature of 170 • C to 190 • C and blended with asphalt at 160 • C. In both the control mix and glass-and carbon-fiber-modified asphalt mixtures, the percentages of glass fiber and carbon content that were chosen were 0%, 1.0%, 2.0%, 3.0%, and 4.0%, and the asphalt content varied from 4.5 to 6.0% at 0.5% intervals, respectively. After the mixture was placed into the mould, it was compacted with 75 blows on both sides with 4.5 kg sliding weight after the compacting sample was extracted using a sample extractor. The design mix of glass and carbon is depicted in Table 7. Figure 3a-c shows the samples were made using glass fiber, carbon fiber, 75GF:25CF, 50GF:50CF, and 25GF:75CF hybrid asphalt mix. The Marshall stability testing apparatus as well as the testing of the Marshall specimen are depicted in Figure 4a,b. Table 7. Design mix of glass and carbon fibers.

Experimental Investigation
The asphalt mix was developed following the specifications specified by ASTM D-1559 [57]. Cylindrical specimens with a diameter of 101.6 mm × 63.5 mm in height were used. A total of 1200 gm of open-graded coarse aggregate was utilized and thoroughly oven dried at a temperature between 100-110 °C for 24 h. The aggregate was heated at a temperature of 170 °C to 190 °C and blended with asphalt at 160 °C. In both the control mix and glass-and carbon-fiber-modified asphalt mixtures, the percentages of glass fiber and carbon content that were chosen were 0%, 1.0%, 2.0%, 3.0%, and 4.0%, and the asphalt content varied from 4.5 to 6.0% at 0.5% intervals, respectively. After the mixture was placed into the mould, it was compacted with 75 blows on both sides with 4.5 kg sliding weight after the compacting sample was extracted using a sample extractor. The design mix of glass and carbon is depicted in Table 7. Figure 3a-c shows the samples were made using glass fiber, carbon fiber, 75GF:25CF, 50GF:50CF, and 25GF:75CF hybrid asphalt mix. The Marshall stability testing apparatus as well as the testing of the Marshall specimen are depicted in Figure 4a,b.

Collection of Dataset
For the Marshall stability prediction, a total of 164 observations are incorporated by using experimental data of glass and carbon fibers and variations in both fibers provided in Table 8. After that, the total observations were split, at random, into two different subsets, each of which contained a 70/30 ratio having 110 observations in the training and 54 in the testing dataset, respectively. Table 9 provides a summary of the data sets obtained from the experiments. For the prediction of MS, five types of ML techniques (i.e., ANN, GP, M5P Tree, RT, and MLR) were implemented using Weka 3.9.5 software and ten

Collection of Dataset
For the Marshall stability prediction, a total of 164 observations are incorporated by using experimental data of glass and carbon fibers and variations in both fibers provided in Table 8. After that, the total observations were split, at random, into two different subsets, each of which contained a 70/30 ratio having 110 observations in the training and 54 in the testing dataset, respectively. Table 9 provides a summary of the data sets obtained from the experiments. For the prediction of MS, five types of ML techniques (i.e., ANN, GP, M5P Tree, RT, and MLR) were implemented using Weka 3.9.5 software and ten input parameters including (BC), (GF), (CF), 75GF:25CF, 50GF:50CF, 25GF:75CF, (VG), (FL), and (FD) glass and (FD) carbon, respectively, were assessed. The statistical characteristics of said input parameters are shown in Table 10. The input characteristics were evaluated to predict the outcome, i.e., Marshall stability of hybrid asphalt concrete, using the performance evaluation parameters that are illustrated in Section 5.           Table 9. Details of the experimental dataset.

Performance Evaluating Parameters
The effectiveness of each model was judged with reference to the following five statistical metrics: CC, which can vary from −1 to 1 (higher correlation coefficients indicate more accurate findings), MAE, RMSE, RAE, and RRSE. The RMSE and MAE are two forms of error that represent the average deviation between actual and predicted values. The better the prediction, the lower the error. These statistics measure the difference between actual and predicted results for the same behavior, i.e., a smaller computed error indicates improved output outcomes. This may be determined using the formula stated in Equations (3)-(7) below: (3) where L = actual values; G = average observation; G = predicted value; and n = number of observations.

Results and Discussion
After obtaining the 164 observations from the various experimental work, the total data set was generated for prediction and analyzing the performance of five types of asphalt mixes, i.e., glass fiber asphalt mix, carbon fiber asphalt mix, and three glass-carbon fiber (25:75, 50:50, 75:25 proportions) combination asphalt mixes for Marshall stability.
The performance of such mixes can be assessed by analyzing each applied model and is discussed in the following section.

ANN Model Performance Assessment
A multilayer perceptron model serves as the core of the iterative process that constitutes ANN-based model generation. Several efforts were made to find the ideal value with the maximum defined CC value with the fewest errors for training and testing the dataset for assessing the generated models' predictions. The user-defined parameters that were utilized in the process of evaluating the ANN model included the sigmoid activation function node (1-9), learning rate (0.2), momentum (0.1), number of iterations (1700), hidden layer (1), and number of neurons (20) [58][59][60][61][62][63].  Figure 5a,b represents the training and testing stages; this indicates that the majority of the scattered data points fall inside and lie within perfect line agreement, which shows an ideal match between actual and predicted values and also falls within the ±20% error range.

GP Model Performance Assessment
In Gaussian processes, a regression technique with parameters such as (O = 2.0 and S = 2.0), noise = (1.0), and seed = (1.0) is used in conjunction with a universal kernel (PUK) based on the Pearson VII function. According to the findings presented in  Figure 6a,b shows the agreement line that connects the actual and the predicted values in which it can be seen from the scatter points that most of the predicted values fall within the ±25% error range [64][65][66][67].   Figure 6a,b shows the agreement line that connects the actual and the predicted values in which it can be seen from the scatter points that most of the predicted values fall within the ±25% error range [64][65][66][67]. (a) (b) Figure 5. (a,b). Agreement graph showing actual vs. predicted values of MS using an ANN-based model for both stages.

GP Model Performance Assessment
In Gaussian processes, a regression technique with parameters such as (O = 2.0 and S = 2.0), noise = (1.0), and seed = (1.0) is used in conjunction with a universal kernel (PUK) based on the Pearson VII function. According to the findings presented in Table 11, a GP-PUK-based model appears to be reliable for predicting the MS of modified asphalt concrete, with values of CC as (0.8383, 0.8187), R 2 as (0.7027, 0.6702), MAE as (1.4276, 1.5350), RMSE as (1.7688, 1.8524), RAE as (57.55%, 64.56%), and RRSE as (56.21%, 59.57%) for both stages. Figure 6a,b shows the agreement line that connects the actual and the predicted values in which it can be seen from the scatter points that most of the predicted values fall within the ±25% error range [64][65][66][67].

M5P Model Performance Assessment
The performance assessment of the M5P model was evaluated using a pruned model tree (using smoothed linear models). The outcome of Table 11 depicts that the M5P tree model is consistent in predicting the MS of modified AC with the value of CC as (0.8396, 0.8172), R 2 as (0.7049, 0.6678), MAE as (1.3358, 1.5264), RMSE as (1.7138, 1.8331), RAE as (53.85%, 64.20%), and RRSE as (54.46%, 58.94%) for both stages. Figure 7a,b presents an agreement graph that plots actual and predicted values and shows most of the scatter data points lie closer to the agreement line using M5P tree-based models. The graph displays that the predicted values fall within the margin of error of ±25% at both phases [68][69][70][71][72]. model is consistent in predicting the MS of modified AC with the value of CC as (0.8396, 0.8172), R 2 as (0.7049, 0.6678), MAE as (1.3358, 1.5264), RMSE as (1.7138, 1.8331), RAE as (53.85%, 64.20%), and RRSE as (54.46%, 58.94%) for both stages. Figure 7a,b presents an agreement graph that plots actual and predicted values and shows most of the scatter data points lie closer to the agreement line using M5P tree-based models. The graph displays that the predicted values fall within the margin of error of ±25% at both phases [68][69][70][71][72].

RT Model Performance Assessment
The performance of a random tree is based on the decision tree and class for constructing a tree that considers K randomly chosen attributes at each node, i.e., value of K = 8, number of folds = 4, and number of seed = 8. The performance assessment of the RT model depicted in Table 11 indicates that the RT model is quite competitive with other models in predicting the MS of modified AC, with the value of CC as (0.8414, 0.7936), R 2 as (0.7079, 0.6298), MAE as (1.2008, 1.6573), RMSE as (0.0171, 1.9848), RAE as (48.41%, 69.70%), and RRSE as (54.42%, 63.80%) for both stages, respectively. The agreement graph between the actual value and the predicted value is shown in Figure 8a,b; it shows that most of the data points are relatively near to the actual values in both the training and testing phases which fall within the margin error of ±28% in training and ±30% in the testing stage [73][74][75].

RT Model Performance Assessment
The performance of a random tree is based on the decision tree and class for constructing a tree that considers K randomly chosen attributes at each node, i.e., value of K = 8, number of folds = 4, and number of seed = 8. The performance assessment of the RT model depicted in Table 11 indicates that the RT model is quite competitive with other models in predicting the MS of modified AC, with the value of CC as (0.8414, 0.7936), R 2 as (0.7079, 0.6298), MAE as (1.2008, 1.6573), RMSE as (0.0171, 1.9848), RAE as (48.41%, 69.70%), and RRSE as (54.42%, 63.80%) for both stages, respectively. The agreement graph between the actual value and the predicted value is shown in Figure 8a,b; it shows that most of the data points are relatively near to the actual values in both the training and testing phases which fall within the margin error of ±28% in training and ±30% in the testing stage [73][74][75].

MLR Model Performance Assessment
The MLR analysis was performed and it can be seen from Table 12 that the performance of MLR shows overfitting of datasets in training and testing stages for the prediction of MS, with CC as (0.7647, 0.7976), R 2 as (0.5847, 0.6361), MAE as (1.6509, 1.6387), RMSE as (2.0278, 1.8910), RAE as (66.55%, 68.92%), and RRSE as (64.44%, 60.81%) for both stages. Figure 9a,b shows that the majority of the predicted data points are scattered which falls within the margin of error of ±30% in training and ±25% in the testing stage.

MLR Model Performance Assessment
The MLR analysis was performed and it can be seen from Table 12 that the performance of MLR shows overfitting of datasets in training and testing stages for the prediction of MS, with CC as (0.7647, 0.7976), R 2 as (0.5847, 0.6361), MAE as (1.6509, 1.6387), RMSE as (2.0278, 1.8910), RAE as (66.55%, 68.92%), and RRSE as (64.44%, 60.81%) for both stages. Figure 9a,b shows that the majority of the predicted data points are scattered which falls within the margin of error of ±30% in training and ±25% in the testing stage.

MLR Model Performance Assessment
The MLR analysis was performed and it can be seen from Table 12 that the performance of MLR shows overfitting of datasets in training and testing stages for the prediction of MS, with CC as (0.7647, 0.7976), R 2 as (0.5847, 0.6361), MAE as (1.6509, 1.6387), RMSE as (2.0278, 1.8910), RAE as (66.55%, 68.92%), and RRSE as (64.44%, 60.81%) for both stages. Figure 9a,b shows that the majority of the predicted data points are scattered which falls within the margin of error of ±30% in training and ±25% in the testing stage.  The impact of the hybrid mix 50GF-50CF (%), GF (%), CF (%), FD (glass), type of the bitumen (VG), and fiber length (FL) on the Marshall stability is found to be negligible due to their constant values. Hence, they did not figure in the MLR model equation.

Comparison of Machine Learning Models
The MS predictions of AC incorporating glass and carbon fibers, as well as variations in both fibers with the ratios 75GF:25CF, 50GF:50CF, and 25GF:75CF, were examined in this study by implementing five ML techniques. Ten attributes including BC, GF, CF, 75GF:25CF, 50GF:50CF, and 25GF:75CF, VG, (FL), and (FD) glass, and (FD) carbon, as well as Marshall stability (MS) as an output parameter and Equations (2)-(6) were used to evaluate the input parameters.  Figure 10a,b displays the results of the performance of all the models used in both stages, showing that all models' prediction values are very near to the actual data, with a ±30 error bandwidth in the training and testing stage. The median and quartile values of actual and predicted MS are shown in Table 13, indicating the representation of data central tendency as a function of the first five numbers and depicts the highest predicted model has an IQR of 4.029, which shows the range of scores from the lower to upper quartile. The data distribution for each model is shown in Figure 11 as a boxplot with percentile labels and the red symbol '+' shows outlier point. This plot demonstrates that the ANN model uses more accurate techniques of data distribution, and hence outperforms in predicting the MS of the modified asphalt mix. Predicted Marshall stability and relative error with data set numbers for all training and testing models are shown in Figure 12a,b, indicating that the ANN model has fewer error bands that are within the range of statistical significance (−3 to 3).     The results indicated that the artificial neural network outperformed other models in predicting the Marshall stability of modified asphalt concrete with a higher value of the coefficient of correlation (0.8392), R 2 (0.7042), and a lower mean absolute error value (1.4449) and root mean square error value (1.8315) in the testing stage with a small error band; furthermore, it provided the best optimal fit for predicting the output. The results of the sensitivity analysis show that the carbon-fiber asphalt mix is the most effective parameter, followed by glass-carbon fiber (50:50 proportion) modified asphalt mix, which influences the Marshall strength to a greater extent. The results obtained from the sensitivity analysis performed with the ANN model showed that the carbon-fiber asphalt mix was the most sensitive to Marshall stability among all the five applied asphalt mixes. In the prior study done by [76], results from the research demonstrated that the ANN technique performed better than regression models for predicting rutting performance using carbon nanotubes. The analysis further showed that the glass-fiber asphalt mix is the weakest among all the mixes.

Feature Importance
The feature importance analysis was performed with the MLR model, as shown in Table 14, to determine the sensitivity of each parameter to MS of the modified asphalt mixes as the slight nonlinearity of the problem identified by the NN model being slightly better than the MLR model, making feature importance complex. The purple box in each row represents the impact on the shown indices in the table by non-consideration of the boxed input parameter in the corresponding column, whereas row 1 (without box) represents the consideration of all input parameters in the feature importance analysis. The results of the analysis show that the first five input variables are the top fifth most sensitive parameters in both models. The carbon diameter in asphalt mix, followed by bitumen content, has been proven to be the most sensitive material, having a lower coefficient of correlation with a higher magnitude of errors. Therefore, the first five input variables, i.e., carbon fiber diameter, bitumen content, hybrid asphalt mix of glass-carbon fiber in 75:25 percent, carbon fiber content, and hybrid asphalt mix of glass-carbon fiber in 50:50 percent, are highly sensitive parameters that influence the Marshall strength of the modified asphalt mixes to a greater extent.

Conclusions
The current study examined the Marshall stability of five types of modified asphalt mixes blended with glass, carbon, and glass-carbon fibers using five machine learning techniques, namely ANN, GP-PUK, M5P, RT, and MLR-based models. The performance evaluation results revealed that the artificial neural network (ANN) outperformed the other models in predicting the Marshall stability of modified asphalt mix, with the CC as 0.8392, R 2 as 0.7042, MAE as 1.4996, RMSE as 1.8315, RAE as 63.07%, and RRSE as 58.89% for the testing dataset. An agreement graph showed that ANN had a smaller error band and optimal fit for predicting the Marshall stability. The results of the feature importance analysis indicate that the first five input variables, i.e., carbon fiber diameter, bitumen content, hybrid asphalt mix of glass-carbon fiber in 75:25 percent, carbon fiber content, and hybrid asphalt mix of glass-carbon fiber in 50:50 percent, are highly sensitive parameters which influence the Marshall strength of the modified asphalt mixes to a greater extent. Five types of asphalt mixes, i.e., glass-fiber asphalt mix, carbon-fiber asphalt mix, and three glass-carbon fiber (25:75, 50:50, 75:25 proportions) combination asphalt mixes were utilized in this investigation. The interval of the proportion of the glass-fiber combination in the modified asphalt mix can be shortened for precise results. Furthermore, the machine learning algorithm can be explored for Marshall stability predictions vis-à-vis the sensitivity analysis.