Artiﬁcial Intelligence-Based Model for the Prediction of Dynamic Modulus of Stone Mastic Asphalt

: Stone Mastic Asphalt (SMA) is a tough, stable, rut-resistant mixture that takes advantage of the stone-to-stone contact to provide strength and durability for the material. Besides, the warm mix asphalt (WMA) technology allows reducing emissions and energy consumption by reducing the production temperature by 30–50 ◦ C, compared to conventional hot mix asphalt technology (HMA). The dynamic modulus | E* | has been acknowledged as a vital material property in the mechanistic-empirical design and analysis and further reﬂects the strains and displacements of such layered pavement structures. The objective of this study is twofold, aiming at favoring the potential use of SMA with WMA technique. To this aim, ﬁrst, laboratory tests were conducted to compare the performance of SMA and HMA through the dynamic modulus. Second, an advanced hybrid artiﬁcial intelligence technique to accurately predict the dynamic modulus of asphalt mixtures was developed. This hybrid model (ANN-TLBO) was based on an Artiﬁcial Neural Network (ANN) algorithm and Teaching Learning Based Optimization (TLBO) technique. A database containing the as-obtained experimental tests (96 data) was used for the development and assessment of the ANN-TLBO model. The experimental results showed that SMA mixtures exhibited higher values of the dynamic modulus | E* | than HMA, and the WMA technology increased the dynamic modulus values compared with the hot technology. Furthermore, the proposed hybrid algorithm could successfully predict the dynamic modulus with remarkable values of R 2 of 0.989 and 0.985 for the training and testing datasets, respectively. Lastly, the e ﬀ ects of temperature and frequency on the dynamic modulus were evaluated and discussed.


Introduction
In recent decades, the manufacture and application of asphalt mixture have been significantly increasing because of excellent adhesion to mineral aggregates and viscoelastic properties [1,2]. In order to address economic and environmental objectives, a number of asphalt mixtures were proposed, including dense-graded asphalt concrete, stone mastic asphalt (SMA), rubberized asphalt, crumb rubber asphalt concrete, and asphalt concrete incorporated [3][4][5]. Additionally, from a practical viewpoint, mixing techniques were also considered as an important stage for an asphalt mixture, gaining its targeted performances [3,4,6,7]. Among these, dense-graded asphalt and stone mastic asphalt (SMA) and Ceylan et al. [47]. These results showed that the prediction models of the expected dynamic modulus |E*| still need further clarification and investigation.
Considering the modern approach, Ceylan et al. [30] presented and compared a series of Artificial Neural Network (ANN) models with some existing models to predict the dynamic modulus |E*| of HMA. The ANN models indicated a notable accuracy compared with the conventional regression models and can be applied to the mechanistic-empirical pavement design guide. Far et al. [31] attempted to develop novel models to predict the dynamic modulus |E*| of HMA mixtures in the case of long-term pavement performance. The data consisted of measured moduli from many geographical places around the United States. The obtained results indicated that the predicted dynamic modulus |E*| utilizing ANN and measured dynamic modulus |E*| values were well matched. Sakhaeifar et al. [25] also proposed a fundamental modeling framework to predict dynamic modulus |E*| of HMA using viscoelastic principles combined with the physical and mechanical characteristics of the mixture. The proposed dynamic modulus models were verified as reliable and appropriate for a wide scope of temperatures and recommended in the AASHTO TP62-03 test protocol. Despite that, the application of a machine learning approach to SMA mixtures is still limited, and further elaboration of the dynamic modulus in function of the temperature and frequency is required.
On the basis of sustainable development and environmental standpoints, the current study, therefore, aims at favoring the potential use of SMA with warm technology from two different angles. From an experimental point of view, dynamic modulus tests were performed to highlight the beneficial aspect of SMA using warm technology compared with the hot technology, as well as conventional dense-graded asphalt concretes. From a simulation angle, a novel machine learning algorithm was developed to accurately predict the desired mechanical property of the asphalt mixtures, and thus to facilitate the use in the design process or the construction and operation stages. To this aim, a total of 576 experimental tests on dynamic modulus were carried out to construct a database of 96 instances by taking the average values per 6. In parallel, the ANN-TLBO machine learning algorithm was developed, consisting of one well-known machine learning model (ANN) and an effective optimization algorithm, namely Teaching-Learning Based Optimization (TLBO). The performance of the proposed ANN-TLBO model was evaluated by three common statistical criteria, including root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R 2 ).
The present paper is structured as follows: (i) an overview of the state of the art of the problem is presented in the first section; (ii) the significance of the study is given in Section 2; (iii) the experimental procedure is provided in the next section, including the materials, design, mixing, and testing of the asphalt mixtures; (iv) a brief overview of the machine learning algorithms is given in Section 4; and (v) the experimental and simulation results are presented in Section 5. Several conclusions and perspectives are finally given in the last section of the paper.

Significance of the Study
Considering environmental factors and beneficial aspects of SMA using warm technology, an in-depth investigation of such an asphalt concrete is crucial. Nevertheless, only limited reports on the dynamic modulus |E*| of SMA using warm technology have been conducted in the literature [12,48,49]. To the best of the authors' knowledge, only a few contributions were found in the literature. In addition, so far, no direct comparison between the dynamic modulus |E*| of SMA and conventional asphalt concrete applying the hot and warm technologies using machine learning approach has been performed yet. Therefore, benefitting the present study are the various points as follows: (i) a complete experimental comparison between two types of asphalt mixtures (i.e., HMA and SMA) and technologies (i.e., hot and warm) was given for the first time; (ii) success in decreasing the mixing and compacting temperatures was proven in the literature but only for recycled aggregates [12,48], this study showed a similarly successful result of the dynamic modulus of asphalt mixture in using conventional aggregates; (iii) a novel machine learning (ML) algorithm was developed to accurately predict the dynamic modulus of the four mentioned asphalt mixtures; (iv) the dependency of the dynamic modulus on diverse input variables was proposed thanks to the developed ML algorithm.

Material Properties
In this study, crushed aggregates, including fine and coarse aggregates, were collected from a local quarry at Khau Dem, Quan Son commune, Chi Lang district, Lang Son province, in the North of Vietnam. The compressive strength of the bedrock in the saturated condition is reported as 138.26 MPa. The mineral filler was collected from a local quarry at Kien Khe, Ha Nam Province, Vietnam. The physical properties of fine, coarse aggregates and mineral filler were given in Table 1. Besides, Polymer Modified Bitumen III (PMB III) was chosen as the asphalt cement, and the corresponding physical properties are shown in Table 2. They were provided by the Vietnam National Petroleum Group (Petrolimex), Ha Noi, Vietnam. Cellulose fiber used in the SMA mixtures was a type of ARBOCEL ZZ 8/1, provided by JRS Company, JRS, J. RETTENMAIER & SÖHNE Group, Germany. Sasobit, an organic additive based on polymethylene, was obtained from Sasol Company. The physical properties of Sasobit are shown in Table 3.

Mix Design, Sample Preparation, and Testing
In this study, four types of mixtures with the 12.5 mm nominal maximum aggregate size were prepared, including (1) SMA applying the warm mixing techniques (denoted as SMA-W); (2) SMA applying the hot mixing techniques (denoted as SMA-H); (3) Dense-graded asphalt concrete applying the warm mixing techniques (denoted as HMA-W) and (4) Dense-graded asphalt concrete applying the hot mixing techniques (denoted as HMA-H).
The aggregate gradation of SMA-W and SMA-H mixtures was designed according to the AASHTO M325 [50] and plotted in Figure 1a. Besides, the aggregate gradation of HMA-W and HMA-H mixtures were subjected to the Vietnamese standard [51] (Decision 858, Ministry of Transport, Vietnam) and plotted in Figure 1b. For SMA-W and SMA-H mixtures, the optimal asphalt content (i.e., PMB III) was found as 6.7% (% weight of the mixture), whereas for HMA-W and HMA-H mixtures, the optimum asphalt content was 5.1% (% weight of the mixture). The cellulose fiber content in SMA mixtures was kept constant at 0.3% (% weight of the mixture), whereas no cellulose fiber was added in HMA mixtures. The mixtures were manufactured by warm technology using Sasobit additive with 2% weight of PMB III. Prior to the mixing process, Sasobit additives were mixed with PMB III for 20 min at 160 • C-170 • C. The SMA and HMA mixtures applying the warm mixing techniques were mixed and compacted to 160 • C and 140 • C, respectively. The SMA and HMA mixtures using the hot mixing techniques were mixed and compacted to 190 • C and 170 • C, respectively.

Mix Design, Sample Preparation, and Testing
In this study, four types of mixtures with the 12.5 mm nominal maximum aggregate size were prepared, including (1) SMA applying the warm mixing techniques (denoted as SMA-W); (2) SMA applying the hot mixing techniques (denoted as SMA-H); (3) Dense-graded asphalt concrete applying the warm mixing techniques (denoted as HMA-W) and (4) Dense-graded asphalt concrete applying the hot mixing techniques (denoted as HMA-H).
The aggregate gradation of SMA-W and SMA-H mixtures was designed according to the AASHTO M325 [50] and plotted in Figure 1a. Besides, the aggregate gradation of HMA-W and HMA-H mixtures were subjected to the Vietnamese standard [51] (Decision 858, Ministry of Transport, Vietnam) and plotted in Figure 1b. For SMA-W and SMA-H mixtures, the optimal asphalt content (i.e., PMB III) was found as 6.7% (% weight of the mixture), whereas for HMA-W and HMA-H mixtures, the optimum asphalt content was 5.1% (% weight of the mixture). The cellulose fiber content in SMA mixtures was kept constant at 0.3% (% weight of the mixture), whereas no cellulose fiber was added in HMA mixtures. The mixtures were manufactured by warm technology using Sasobit additive with 2% weight of PMB III. Prior to the mixing process, Sasobit additives were mixed with PMB III for 20 min at 160 °C-170 °C. The SMA and HMA mixtures applying the warm mixing techniques were mixed and compacted to 160 °C and 140 °C, respectively. The SMA and HMA mixtures using the hot mixing techniques were mixed and compacted to 190 °C and 170 °C, respectively. Regarding the determination of the dynamic modulus |E*|, laboratory tests in accordance with AASHTO TP 62 [52] were conducted. The short-term aging of asphalt concrete was firstly conducted, followed by the AASHTO R30 standard. The compaction process was next performed on a rotating compactor in order to achieve air void content of 7 ± 0.5%. The specimen, flattened at both ends, had a height of 100 mm and a diameter of 100 mm ( Figure 2). Regarding the determination of the dynamic modulus |E*|, laboratory tests in accordance with AASHTO TP 62 [52] were conducted. The short-term aging of asphalt concrete was firstly conducted, followed by the AASHTO R30 standard. The compaction process was next performed on a rotating compactor in order to achieve air void content of 7 ± 0.5%. The specimen, flattened at both ends, had a height of 100 mm and a diameter of 100 mm ( Figure 2).
All samples were placed in a thermostatic chamber to maintain a constant temperature. The test was conducted on a CRT NU-14 device ( Figure 3). The experimental tests on the dynamic modulus |E*| used six frequency values, i.e., 0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, and 25 Hz and four temperature values, i.e., 10 • C, 25 • C, 45 • C, 60 • C.

Instrumentation
The samples were mixed by an asphalt mixer with 30-L capacity manufactured by Daiwakenko (Tokyo-Japan). The samples were compacted by Gyratory Compactor 4140 manufactured by Troxler (TROXLER, Durham, NC, USA). All samples were placed in a thermostatic chamber to maintain a constant testing temperature. The test was conducted on a CRT NU-14 device (Cooper, London, UK).

Instrumentation
The samples were mixed by an asphalt mixer with 30-L capacity manufactured by Daiwakenko (Tokyo-Japan). The samples were compacted by Gyratory Compactor 4140 manufactured by Troxler (TROXLER, Durham, NC, USA). All samples were placed in a thermostatic chamber to maintain a constant testing temperature. The test was conducted on a CRT NU-14 device (Cooper, London, UK).

Artificial Neural Network
One of the most common machine learning algorithms is Artificial Neural Network (ANN), which is based on the behavior of the biological neural networks' behavior of the human brain to analyze and mine the data for discovering the knowledge for solving the real-world problems [53,54]. Three layers, namely input, hidden, and output, are connected by neurons, representing the main components of the ANN structure and network [55]. Out of these layers, output layers represent the dependent variables, known as the target variables of the problem. Input layers represent the independent variables, known as the input variables of the problem. Hidden layers used computational algorithms, called activation functions, to analyze the relationships between input and output layers. The ANN is known as the black box model with the advantage of extracting the exact pattern between the input and output variables and it does not require additional explanation and assumptions. This model has been applied widely to solve different civil engineering problems and fields, such as geotechnical engineering [56] and material engineering [57,58]. In this study, ANN was used in the hybrid framework and model for the prediction of dynamic modulus |E*| of SMA mixtures.

Teaching Learning Based Optimization
Teaching Learning Based Optimization (TLBO), one of the population-based evolutionary optimization algorithms, is based on the influence of a teacher on the learners in a given class [59]. The advantage of using TLBO is that this algorithm requires no specific parameters except the common control ones, such as the number of generations and population size. In TLBO, the "Teacher" and "Learner" are two critical phases [60]. Particularly, in the Teacher Phase, the teacher of the class is defined as the best solution in the whole population. The teacher teaches the learners by sharing knowledge to improve the learners' performance, such as marks or grades. The quality of the teacher influences the performance of the learners. Besides, in the Learner Phase, the learners learn the knowledge from other learners to improve their performance. In general, the TLBO is an effective optimization algorithm. It has been widely applied in solving different real world problems [61,62]. In the present study, TLBO was used to optimize the ANN performance to predict the values |E*| of SMA mixtures, especially in the selection of the appropriate values of the associated weights and biases.

Dataset Preparation and Statistical Analysis
As mentioned in the experimental section, the dataset used for the development of ANN-TLBO contained 96 instances (Appendix A), in which each result was the average of 6 similar samples. Overall, 576 samples were fabricated and tested in this work. The statistical analysis of the dataset is presented in Table 4, including the min, max, median, average, and standard deviation values of the utilized input and output variables. Table A1 (Appendix A) presents the database used in this study. The dataset was divided into two main parts, namely the training and testing part. Precisely, the training dataset contained 70% of the data and was used for the development of the ML model. On the other hand, the testing dataset contained the remaining 30% samples and was used for the validation of the previously constructed ML model. The chosen 70/30 ratio for the training and testing datasets in this study was selected, as suggested in the works of Khorsheed and Mohammad [63] and Leema et al. [64].

Quality Assessment Criteria
In this study, three common quantitative indicators, namely RMSE, MAE, and R 2 were employed to validate the performance of the model. R indicates the correlation between two values (predicted and actual) from the predictive model and experiment. RMSE and MAE measure and evaluate the error of the models [65][66][67][68][69]. In general, higher values of R 2 show higher performance of the model, while lower values of MAE and RMSE show the higher performance of the model [70][71][72][73]. Mathematically, three indicators (RMSE, MAE, and R 2 ) can be expressed as the following equations [74][75][76][77][78][79]: where, x mei and x me indicate the measured value of the specimen i th and the measured mean value, respectively; x cai and x ca indicate the output value of the specimen i th and the average value of output predicted from the modeling, respectively; k means the sum of samples. Figure 4 shows the experimental results on the dynamic modulus |E*| in highlighting the influence of the testing frequency, whereas Figure 5 shows similar results in highlighting the influence of the testing temperature. Considering a similar testing frequency, an increase of the testing temperature reduced the value of the dynamic modulus |E*|. Besides, at similar testing temperature, an increase of the testing frequency increased the value of the dynamic modulus |E*|. Specifically, the effects of the testing frequency and temperature on the experimental values |E*| are clearly shown in technology at a similar temperature, the difference was more pronounced with the higher frequency. The difference could be neglected at a testing temperature of 60 °C. At a testing temperature of 10 °C, the value of the dynamic modulus |E*| of SMA-W was 1.11-1.22 times higher than HMA-W, whereas it was 1.01-1.15 times at a temperature of 25 °C, 1.09-1.22 times at a temperature of 45 °C, and 1.08-1.26 times at a temperature of 60 °C. It could be concluded that, compared to the HMA, the SMA showed superior performance in terms of the dynamic modulus |E*|. Besides, the warm technology exhibited higher dynamic modulus |E*| than using the hot technology. Considering SMA and the mixtures using the warm technique, similar observations were also reported in the literature [12]. Indeed, Al-Qadi et al. It could be concluded that, compared to the HMA, the SMA showed superior performance in terms of the dynamic modulus |E*|. Besides, the warm technology exhibited higher dynamic modulus |E*| than using the hot technology. Considering SMA and the mixtures using the warm technique, similar observations were also reported in the literature [12]. Indeed, Al-Qadi et al. showed that the SMA-W exhibited significant improvement compared with SMA-H. Moreover, the authors showed that, in terms of additives, Sasobit disclosed the highest performance compared with the control mix, Evotherm, and foamed asphalt. Besides, the curing time was proved to be another critical factor affecting the dynamic modulus. Several curing times using Sasobit were tested in the work, and the results showed that 1-day curing time was optimal. In this study, taking advantage of such a result, the curing time was directly chosen as one day. The analysis of the effect of curing time might be the objective of further research, as different natures of aggregates, filler, or bitumen might have a certain influence on the dynamic modulus. Besides, another study confirmed the addition of additives enhanced the dynamic modulus compared with the control asphalt mixtures, for instance, in the work of Goh and You [80]. Last but not least, the success in decreasing the mixing and compacting temperatures was proven in the literature but only for recycled aggregates [12,48]; this study showed a similarly successful result of the dynamic modulus of asphalt mixture in using conventional aggregates.

Optimization of the ANN-TLBO Model
Regarding the development of ANN-TLBO algorithms, the determination of the parameters of such a model is a crucial step. Indeed, the prediction capability is directly dependent on the choice of the appropriate values of parameters. They could be the activation function of the hidden layer, cost function, the training algorithm of the ANN model, or the population size, the stopping criterion of the optimization algorithm. After trial-and-error tests, the parameters of the proposed ANN-TLBO model were chosen and indicated in Table 5. The final structure of ANN-TLBO was 4-5-1 and denoted as ANN-TLBO [4-5-1]. Three statistical measurements (i.e., R 2 , RMSE, and MAE) were applied for ANN-TLBO to find the best values of the weights and biases associated with the neurons. This means that all the results presented herein were the best performance of the proposed ANN-TLBO model, with the highest value of R 2 and the lowest values of MAE, RMSE concerning one selected dataset. The evaluations of cost functions with respect to R 2 , RMSE, and MAE for predicting the dynamic modulus |E*| are presented in Figure 6. This study focused only on the selection of an appropriate choice of the stopping criterion. Furthermore, the accuracy of the ML algorithm could not be guaranteed by the higher number of iteration, for instance in [81], where the best model was found at 20 over 100 performed iterations. As a result, the convergence of the proposed ANN-TLBO in this study was reached after about 100 iterations, and 200 iterations were sufficient to reach the state of convergence of all the cost functions.

Validation and Comparison of ANN-TLBO with Single ANN
The performance of the ANN model, in comparison with the ANN-TLBO algorithm, is presented under regression plots (Figure 7), showing a comparison between the predicted and actual values of the dynamic modulus |E*|. The ideal regression lines are in discontinuous style, whereas the R 2 between predicted and actual dynamic modulus |E*| are given ( Table 6). The correlation results analysis showed that the R 2 values were 0.907, 0.948 for the training and testing datasets, respectively, for the ANN model. Concerning the ANN-TLBO model, these values were 0.975, 0.981

Validation and Comparison of ANN-TLBO with Single ANN
The performance of the ANN model, in comparison with the ANN-TLBO algorithm, is presented under regression plots (Figure 7), showing a comparison between the predicted and actual values of the dynamic modulus |E*|. The ideal regression lines are in discontinuous style, whereas the R 2 between predicted and actual dynamic modulus |E*| are given ( Table 6). The correlation results analysis showed that the R 2 values were 0.907, 0.948 for the training and testing datasets, respectively, for the ANN model. Concerning the ANN-TLBO model, these values were 0.975, 0.981 for the training and testing datasets, respectively. These results showed a very good prediction performance of the two proposed models. However, using an optimization, the ANN-TLBO was found to be the superior predictor compared with the single ANN. for the training and testing datasets, respectively. These results showed a very good prediction performance of the two proposed models. However, using an optimization, the ANN-TLBO was found to be the superior predictor compared with the single ANN.  The summary of the prediction performance of ANN and ANN-TLBO is presented in Table 6. The values of R 2 , RMSE, and MAE were calculated based on the formulations given in the previous  The summary of the prediction performance of ANN and ANN-TLBO is presented in Table 6. The values of R 2 , RMSE, and MAE were calculated based on the formulations given in the previous section, whereas ErrorMean was the mean values of errors and ErrorStD was the standard deviation of errors. The "Slope" represented the slope between the ideal regression line (discontinuous lines in Figure 7) and the linear fit, given by the models (continuous lines in Figure 7). The two additional error criteria also confirmed that ANN-TLBO is superior to ANN in predicting the dynamic modulus |E*|. For illustration purposes, the values of the dynamic modulus |E*| in function of sample index using individual ANN and ANN-TLBO models are plotted in Figure 8 for the training and testing datasets. It is clearly seen that the predicted values were in excellent agreement with the experimental dynamic modulus |E*| values. Figure 7) and the linear fit, given by the models (continuous lines in Figure 7). The two additional error criteria also confirmed that ANN-TLBO is superior to ANN in predicting the dynamic modulus |E*|. For illustration purposes, the values of the dynamic modulus |E*| in function of sample index using individual ANN and ANN-TLBO models are plotted in Figure 8 for the training and testing datasets. It is clearly seen that the predicted values were in excellent agreement with the experimental dynamic modulus |E*| values. Overall, the prediction capability of ANN-TLBO was quantified based on various performance indicators. The proposed hybrid model showed high prediction capability and outperformed individual ANN, clearly demonstrating the efficiency of using TLBO as an optimization tool.

Sensitivity Analysis of the Prediction Variables
The sensitivity analysis of the input variables used in the prediction process is presented in this Overall, the prediction capability of ANN-TLBO was quantified based on various performance indicators. The proposed hybrid model showed high prediction capability and outperformed individual ANN, clearly demonstrating the efficiency of using TLBO as an optimization tool.

Sensitivity Analysis of the Prediction Variables
The sensitivity analysis of the input variables used in the prediction process is presented in this section. The temperature and frequency were successively varied at their range of value, whereas other inputs were kept constant. Precisely, using the ANN-TLBO model developed previously, a new two-dimensional input space was constructed using the value of each input, recorded at ten different quantile levels: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. The temperature and the frequency were them successively selected, and the model was run eleven times, once for each percentile value. Principally, the method provides quantitative disclosures on the change of output when the selected input changes.
It can be seen that the temperature was the most significant factor influencing the dynamic modulus |E*|, followed by the frequency (Figure 9). While varying two input variables, the sensitivity index varied from    As indicated in many studies [82][83][84][85], exploring the relative importance of inputs might offer better in-depth knowledge of the output, which could directly assist engineers during the preparation phase. Considering the testing temperature and frequency, experimental investigations have been conducted in several works [12,80]. However, a direct linear interpolation of the as-obtained results or missing information on the range of input values could lead to inexact observations. In this work, an attempt was made from an experimental point of view, to cover a broad range of testing temperature and frequency with sufficiently grid points. The dependency of the dynamic modulus on inputs was then analyzed with the developed ML algorithm. For each mixture, a fit equation was proposed to highlight the dependency of the selected variable to dynamic modulus |E*|. With reasonable accuracy, a linear equation was finally adopted to fit the frequency versus the dynamic modulus. On the contrary, a cubic equation was chosen to relate the temperature with the dynamic modulus. Summarized information on the sensitivity analysis of the effect of temperature and frequency is presented in Table 7, including the appropriate fit, equation form, and correlation effect. The proposed equations could facilitate the usage of asphalt mixtures in selecting the desired dynamic modulus in function of the testing temperature and frequency.  As indicated in many studies [82][83][84][85], exploring the relative importance of inputs might offer better in-depth knowledge of the output, which could directly assist engineers during the preparation phase. Considering the testing temperature and frequency, experimental investigations have been conducted in several works [12,80]. However, a direct linear interpolation of the as-obtained results or missing information on the range of input values could lead to inexact observations. In this work, an attempt was made from an experimental point of view, to cover a broad range of testing temperature and frequency with sufficiently grid points. The dependency of the dynamic modulus on inputs was then analyzed with the developed ML algorithm. For each mixture, a fit equation was proposed to highlight the dependency of the selected variable to dynamic modulus |E*|. With reasonable accuracy, a linear equation was finally adopted to fit the frequency versus the dynamic modulus. On the contrary, a cubic equation was chosen to relate the temperature with the dynamic modulus. Summarized information on the sensitivity analysis of the effect of temperature and frequency is presented in Table 7, including the appropriate fit, equation form, and correlation effect. The proposed equations could facilitate the usage of asphalt mixtures in selecting the desired dynamic modulus in function of the testing temperature and frequency.

Conclusions and Outlook
In this study, a novel machine learning algorithm, namely ANN-TLBO, was used to predict the dynamic modulus |E*| of SMA, one of the most critical mechanical properties of the asphalt concrete. The proposed model consisted of one well-known machine learning algorithm (ANN) and an effective optimization algorithm (TLBO). The dataset resulting from experiments consisting of 96 entries (average values per 6 of 576 experimental results) was used for the development of the algorithm. The performance of the proposed model was assessed by various common statistical measurements, such as RMSE, MAE, and R.
The validation results showed that the performance of ANN-TLBO was remarkable with ideal values of R 2 (0.975 for the training part and 0.981 for the testing dataset). Such results were superior to those obtained by a single ANN model (0.907 for the training phase and 0.948 for the testing dataset). In addition, a sensitivity analysis was performed, and the results showed that the testing temperature was the most influential factor in the prediction of the dynamic modulus |E*|. These results indicated that ANN-TLBO could be a promising predictor of the dynamic modulus |E*| of SMA mixtures. It could thus be used in the designing phase of SMA mixtures, aiming at a more effective and efficient process.
Extending the existing database could be a short-term perspective of the present study. This could improve the quality of the dataset and expand the ranges of input variables used in the prediction process. Besides, despite an astonishing performance of ANN-TLBO, the use of alternative machine learning algorithms or optimization techniques should be examined to improve the effectiveness of the prediction algorithm.