Prediction of marshall design parameters of asphalt mixtures via machine learning algorithms based on literature data

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Road Materials and Pavement Design ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/trmp20 Prediction of Marshall design parameters of asphalt mixtures via machine learning algorithms based on literature data Mert Atakan & Kürşat Yıldız To cite this article: Mert Atakan & Kürşat Yıldız (2024) Prediction of Marshall design parameters of asphalt mixtures via machine learning algorithms based on literature data, Road Materials and Pavement Design, 25:3, 454-473, DOI: 10.1080/14680629.2023.2213774 To link to this article: https://doi.org/10.1080/14680629.2023.2213774 Published online: 23 May 2023 Submit your article to this journal Article views: 237 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=trmp20 ROAD MATERIALS AND PAVEMENT DESIGN 2024, VOL 25, NO 3, 454–473 https://doi.org/10.1080/14680629.2023.2213774 Prediction of Marshall design parameters of asphalt mixtures via machine learning algorithms based on literature data Mert Atakan and Kürşat Yıldız Department of Civil Engineering, Faculty of Technology, Gazi University, Ankara, Turkey ABSTRACT ARTICLE HISTORY Received 21 November 2021 Previous studies have achieved accurate predictions for Marshall design Accepted May 2023 parameters (MDPs), but their limited data and input variables might restrict generalization In this study, machine learning (ML) was used to predict KEYWORDS MDPs with more generalised models To achieve this, a dataset was col- Asphalt mixture design; lected from six different papers Inputs were material properties and their machine learning; Marshall ratios in the mixture, while target features were six MDPs used in mixture design; prediction model; design Four ML algorithms were used including linear regression, polyno- virtual design mial regression, k nearest neighbour (KNN) and support vector regression (SVR) Also, the cross-validation (CV) method was used to detect the gen- eralisation capability of the models Accuracy of the SVR was the highest, however, in nested CV its performance was highly reduced Therefore, KNN was recommended due to its second highest performance The results demonstrated that prediction of MDPs from only material properties is possible and promising to use in mixture design Abbreviations: ANN: artificial neural network; BC: bitumen content; BP: bitumen penetration (1/10 mm); CV: cross-validation; DEM: discrete ele- ment method; GA: genetic algorithm; Gmb: Bulk specific gravity of mixture; Gmm: Maximum specific gravity of mixture; Gsb: bulk specific gravity of aggregate; KNN: k nearest neighbour; LA: Los Angeles abrasion; LR: linear regression; MARS: multivariate adaptive regression spline; MDP: Marshall design parameter; MF: Marshall flow; MQ: Marshall quotient (kN/mm); MS: Marshall stability; NMAS: nominal maximum aggregate size; NoB: number of blows; PI: penetration index; PR: polynomial regression; R2: coefficient of determination; SP: softening point (°C); SVR: support vector regression; UPVT: ultrasonic pulse velocity–time; Va: air voids percentage; VFA: voids filled with asphalt; VMA: voids in mineral aggregate; WA: water absorption Introduction The durability and performance of the asphalt pavement are highly affected by the mechanical and volumetric properties of the mixture (Sebaaly et al., 2018) In order to provide required mechanical and volumetric characteristics, asphalt mixture design is carried out In other words, mixture design is the most significant factor that affects road performance Today, Marshall, Hveem, and Superpave methods are commonly used design methods in the world (Jiang et al., 2018) There are some differences between these methods such as compaction style, size of the specimen and mechanical tests applied to the specimen But basically, mixture design starts by producing various asphalt mixture specimens in different binder content and gradation Then, it CONTACT Mert Atakan mertatakan@gazi.edu.tr © 2023 Informa UK Limited, trading as Taylor & Francis Group ROAD MATERIALS AND PAVEMENT DESIGN 455 is determined which of the specimens meet the necessary performance criteria These methods are very time-consuming, demanding and expensive For example a Superpave mixture design might take approximately 7.5 working day (Ozturk & Emin Kutay, 2014) That is why, a prediction-based approach in mixture design is vitally important Accordingly, predicting the physical and mechanical properties of the asphalt mixture from its material characteristics without excessive laboratory work is essential In this regard, researchers have employed two basic approaches: numerical simulations (e.g Discrete element method (DEM), finite element method, and user defined algorithms) and soft computing methods like machine learning (ML) (Liu et al., 2022) There have been many studies using numerical methods to predict characteristics of asphalt con- crete such as air voids, density, rutting, etc Li and Wang (2017) have performed a Marshall design by predicting Marshall characteristics of the virtual specimens produced in the DEM simulation Similarly, Shen and Yu (2011) have used DEM to predict voids in mineral aggregate (VMA) of the asphalt con- crete Jin et al (2022) have used a user defined algorithm to produce internal structure of the asphalt concrete based on aggregate contacts Also, a large and growing body of literature has investigated physics engine simulation to produce virtual asphalt specimens Garcia-Hernandez et al (2021) have produced virtual Marshall specimens via a physic engine called as Nvidia PhysX to predict air void content of the asphalt specimens Likewise, Komaragiri et al (2021) have used bullet physics engine to simulate gyratory compaction to predict density of the asphalt specimens ML basically means extracting knowledge from data (Müller & Guido, 2016) To achieve this, the data are arranged as a table where columns represent features and rows represent a single observation or a case (Theobald, 2017) Then, input and target variables are selected After that, data was split into two as training and test data Once the data are split, a prediction model is trained using the training data via various learning algorithms This model can predict target values from the input values Finally, the performance of the model is measured with test data by comparing prediction values and the real values Many studies have been done to predict the mechanical and physical properties of asphalt mix- ture using either ML algorithms or soft computing techniques such as artificial neural network (ANN), genetic algorithm (GA) and fuzzy logic Majidifard et al (2019, 2020) have built a gene expression and a deep learning ML model to predict the rut depth and the fracture energy Therefore, they have been able to make asphalt mixture designs based on these predictions Miani et al (2021) have created an ANN model to predict basic characteristics of the asphalt such as stiffness modulus, Marshall stability (MS), Marshall flow (MF) and air voids percentage (Va) Some other previous studies are listed in Table Volumetric characteristics of asphalt specimens (e.g Va, VMA, voids filled with asphalt (VFA)) have been used to predict mechanical properties such as MS, MF and stiffness in a considerable amount of litera- ture For instance, Aksoy et al (2012) used some Marshall design parameters (MDPs) such as Va, density, VMA, etc as inputs to predict MS, MF and Marshall quotient (MQ) These parameters are well corre- lated with Marshall test results, however, they are obtained with experiments Unless produce Marshall specimens, we cannot predict MS, MF and MQ with this type of model In other words, although these kinds of models have made successful predictions, they are not sufficient to reduce laboratory labour and time Thus, it is necessary to build a prediction model that does not require any experimental input variable such as Va, VMA or VFA More specifically, a better prediction model should use mate- rial properties as inputs such as bitumen type, aggregate gradation, etc In this way, it is possible to predict all MDPs without producing any specimen For example, Azarhoosh and Pouresmaeil (2020), Nguyen et al (2019), Sebaaly et al (2018), Khuntia et al (2014) and Ozgan (2009) have not used volu- metric parameters as inputs Therefore, their models could be used to predict design parameters in the future without any laboratory work with high prediction accuracy However, these studies might not be generalised with high accuracy due to limited input features, feature range (e.g a couple of bitumen type or aggregate type) or small dataset size To sum up, a part of the previous studies has used some MDPs as input variables that cannot reduce laboratory labour Others have created high-performance prediction models, but their models might not be generalised In other words, they may not work properly with other bitumen types and aggregate types or in another laboratory environment Ozgan (2009) Tapkin et al (2009) Tapkin et al (2010) Mirzahosseini et al (2011) Ozgan (2011) Gandomi et al (2011) Aksoy et al (2012) Khuntia et al (2014) Sebaaly et al (2018) Baldo et al (2018) Nguyen et al (2019) Ghanizadeh et al (2020) Azarhoosh and Pouresmaeil (2020) Shah et al (2020) Reference Table Summary of the previous studies •• • • • • • Coarse/fine aggregate percentage Filler percentage • Aggregate type Aggregate shape and texture • Gsb Filler/bitumen ratio • Binder type Binder ratio • • • •• •• • •• • •• Marshall test temperature Exposure time to test temperature •• •• • Ultrasonic pulse velocity–time of sample Sample volume •• Sample height Input variables Sample production method • • • Number of blows in compaction Saturated surface dry specific gravity • Gmb MS • MF MQ • • •• • •• Va VMA •• •• VFA Other additives type/ratio •••• • •••• • •• • •• ••• ••• •• Repeated creep test properties • • M ATAKAN AND K YILDIZ 456 Table Continued Predicted variables Method Reference Gmm MS MF MQ Va VMA VFA Indirect tensile strength Stiffness modulus Flow number GA Particle swarm optimisation Support vector machine ANN KNN Multiple LR Multivariate adaptiveregression spline Fuzzy inference systems Shah et al (2020) • • • • • Azarhoosh and Pouresmaeil (2020) • • • • • • • ROAD MATERIALS AND PAVEMENT DESIGN Ghanizadeh et al (2020) • • Nguyen et al (2019) • • • • • • • Baldo et al (2018) • • • • • Sebaaly et al (2018) • • • • • • Khuntia et al (2014) • • • • • Aksoy et al (2012) • • • • • Gandomi et al (2011) • • • Ozgan (2011) • • Mirzahosseini et al (2011) • • • Tapkin et al (2010) • • • • Tapkin et al (2009) • • Ozgan (2009) • • 457 458 M ATAKAN AND K YILDIZ In this study, one of the aims is to establish a prediction model whose inputs are composed merely of material properties, in order to achieve producing virtual Marshall specimens without any laboratory effort in the future Therefore, it is considered more input variables at the same time than previous studies, and some of them are used for the first time such as Los Angeles abrasion (LA), penetra- tion index (PI), softening point (SP) and bitumen penetration (BP) The other aim is to obtain a more generalised model To achieve this, various datasets were combined from different studies In this way, there will be various data from different laboratories and the constructed dataset will be more representative Methodology First of all, it is important to state that in this study, Python programming language and its libraries such as scikit-learn were used The methodology that we followed in this study is demonstrated with a flow chart in Figure First of all, data from different studies were collected, then they were modified and combined in a dataset After that, two columns were added to the dataset The first one was the PI calculated using SP and BP values The second one was the MQ which was calculated as the proportion of the MS and MF values Once these two columns were added, missing values were imputed using DataWig library which is later explained in detail on the title 2.1.2 After that, another column named VFA was added to the dataset VFA was calculated by using VMA and Va values It is important to state a point here Because some of the Va and VMA values were missing at the beginning, we could not add the VFA column before imputing missing values Instead, we add after imputation the missing values Once the dataset was completed, input and target features were determined Next, the data were divided into train and test sets without any scaling Then, linear regression (LR) was applied to training data However, for the other models, the data were scaled using the standard scaler function in the scikit-learn library before training In the training process, two different approaches were employed At the first one, the dataset was randomly divided as train and test sets with the train–test split function Then the models were trained with the train set In the second approach, the dataset was divided into more than one train and test group using k-fold cross-validation (k-fold CV) and coefficient of determination (R2) values were calculated for each model The differences between these approaches are explained further in the related titles 2.1 Dataset 2.1.1 Data collection Data from six different studies were used to create a bigger dataset (Table 2) In total, there were 407 rows, namely specimens, in the dataset The steps of creating the dataset are as follows: Choosing features Getting data from each study for the chosen features Joining the data from all studies into one dataset First, we determined 14 specimen features in total considering previous studies and important fea- tures that might affect the mixture design results In other words, basic material characteristics that can change MDPs such as Va, MS or MF were used as input features Also, when choosing input features, we attached importance especially not to choose a MDP as an input Although MDPs like Va might highly correlate with MS and MF, the real aim of this study was to predict all MDPs without producing any Marshall specimens That is why all of six MDPs were chosen as target features Once all features were determined, it has generated three additional features (i.e PI, VFA and MQ) from current column values These features are demonstrated in Table ROAD MATERIALS AND PAVEMENT DESIGN 459 Figure Workflow diagram of the current study The challenges we encountered when creating the data set are given below: • Some of the researchers shared the gradation of aggregates as a graphic We used a software named Get Data Graph Digitilizer to get the exact percent of the coarse and fine aggregates This software can scale the image and draw a new readable graphic over again In this way, necessary values can be read from the graphs • While some researchers have defined coarse aggregate as bigger than 4.75 mm, others have defined it as bigger than 2.36 mm We assumed coarse aggregate as bigger than 2.36 mm That is why, when creating the dataset, all data that we got from the studies was modified according to this assumption 460 M ATAKAN AND K YILDIZ Table Number of specimens of the studies that comprise this study’s dataset Reference Number of specimens Mirzahosseini et al (2011) 118 Azarhoosh and Pouresmaeil (2020) 90 Nguyen et al (2019) 60 Baldo et al (2018) 60 Aksoy et al (2012) 63 Tapkin et al (2010) 16 Total 407 Table Features of the created dataset Bitumen Mixture Aggregate Nominal maximum aggregate size (NMAS) (mm) BP (1/10 mm) 10 BC (%) Coarse agg (%) SP (°C) 11 Va (%) Filler (%) 12 VMA (%) LA (%) Number of blows 13 VFA (%)a WA (%) PIa 14 MS (kN) 15 MF (mm) aFeatures generated from other columns 16 MQ (kN/mm)a 17 Gsb (g/cm3) • In some studies, bitumen content (BC) was presented by the weight of the mixture (e.g Baldo et al., 2018) These values were transformed into by weight of the aggregate to provide equivalency among the different studies • In Baldo et al (2018), the number of blows used in the compaction has not been presented It has been said that specimens were prepared according to EN 12697-30 This standard states that the number of blows should be between 25 and 100, but it also states it is generally used as 50 blows Therefore, the number of blows for compaction was assumed as 50 blows for the study named (Baldo et al., 2018) • Units were converted to the same unit for each feature 2.1.2 Handling missing values There were some missing values in the dataset because some features were not presented in the stud- ies we used DataWig library was used to impute missing values This approach employs automatic hyperparameter tuning in deep learning feature extraction Therefore, even users who not have deep learning background can benefit from the library (Biessmann et al., 2019) We used one of DataWig functions named ‘SimpleImputer.complete’ to impute missing values This function fits an imputation model for each column by choosing all other columns as inputs The statistical description of the data with missing values and after imputation are presented in Tables and Once missing values were imputed, the dataset had been created completely However, some fea- tures were not used in the model such as water absorption (WA) and bulk specific gravity of aggregate (Gsb) since they have a high number of missing values in the first place In other words, using these features might have led to high bias in the models, therefore they were not used in the models 2.1.3 Splitting the data as train and test sets The ‘train_test_split method’ in the scikit-learn library was used to split the data into train and test sets Train and test sizes were chosen as 0.67 and 0.33 Random state number, which provides the same splitting state every time the code runs, was selected as Table Statistical description of the data with missing values Count NMAS (mm) Coarse agg (%) Filler (%) BC (%) Va (%) VMA (%) MS (kN) MF (mm) LA (%) WA (%) Gsb (g/cm3) BP (1/10 mm) SP (°C) NoB MQ PI Mean Std 407 407 407 407 347 347 407 407 391 289 257 407 407 407 407 407 Min 13.84 63.70 6.28 5.50 4.83 15.96 11.15 3.19 20.24 1.35 2.58 63.78 52.82 64.32 3.72 −0.02 25% 3.63 11.98 2.41 0.81 1.60 1.37 2.85 0.77 5.54 0.73 0.09 11.39 8.55 12.06 1.34 0.06 50% 9.50 33.00 1.00 3.50 0.40 12.10 2.73 1.60 12.00 0.57 2.49 45.00 45.60 45.00 0.61 −0.12 75% 12.50 56.00 5.00 5.00 3.73 14.90 8.98 2.66 16.22 0.80 2.49 62.00 49.00 50.00 2.72 −0.06 Max 12.50 67.00 6.00 5.40 4.60 16.00 10.90 3.10 25.00 0.90 2.62 63.00 49.00 75.00 3.44 −0.05 19.00 68.00 7.00 6.00 6.03 17.03 13.22 3.60 25.00 2.20 2.66 65.00 52.05 75.00 4.53 0.01 19.00 83.00 10.50 7.50 9.44 19.04 18.33 6.90 26.00 2.40 2.71 91.00 78.80 75.00 7.35 0.13 Table Statistical description of the data with imputed values Count NMAS (mm) Coarse agg (%) Filler (%) BC (%) Va (%) VMA (%) MS (kN) MF (mm) LA (%) WA (%) Gsb (g/cm3) BP (1/10 mm) SP (°C) NoB MQ PI ROAD MATERIALS AND PAVEMENT DESIGN Mean std 407 407 407 407 407 407 407 407 407 407 407 407 407 407 407 407 Min 13.84 63.70 6.28 5.50 4.83 16.30 11.15 3.19 20.12 1.92 2.61 63.78 52.82 64.32 3.72 −0.02 25% 3.63 11.98 2.41 0.81 1.50 1.54 2.85 0.77 5.47 1.10 0.09 11.39 8.55 12.06 1.34 0.06 50% 9.50 33.00 1.00 3.50 0.40 12.10 2.73 1.60 12.00 0.57 2.49 45.00 45.60 45.00 0.61 −0.12 75% 12.50 56.00 5.00 5.00 3.80 15.12 8.98 2.66 16.22 0.80 2.49 62.00 49.00 50.00 2.72 −0.06 Max 12.50 67.00 6.00 5.40 4.70 16.26 10.90 3.10 25.00 2.20 2.62 63.00 49.00 75.00 3.44 −0.05 19.00 68.00 7.00 6.00 5.78 17.47 13.22 3.60 25.00 2.96 2.71 65.00 52.05 75.00 4.53 0.01 19.00 83.00 10.50 7.50 9.44 19.77 18.33 6.90 26.00 4.07 2.73 91.00 78.80 75.00 7.35 0.13 461 462 M ATAKAN AND K YILDIZ 2.1.4 Scaling the data The data were scaled before training for all models except for LR We used the standard scaler in the sckit-learn library It standardises features by transforming the data into which has a mean value of and standard deviation value of The standard scaled value of sample X was calculated as Equation (1) where x¯ is the mean of the samples and σ is the standard deviation of the samples z = x − x¯ (1) σ 2.2 Model performance assessment 2.2.1 Prediction performance In order to assess the prediction performance of the models, we used the score function in the scikit- learn library This function returns the coefficient of determination, namely R2 value It was calculated as Equation (4) where RSS is the residual sum of squares and TSS is the total sum of squares In Equation (2), yi is ith value to be predicted, f (Xi) is the predicted value of yi, and n is the upper limit of summation In Equation (3), yi is ith value in sample, y¯ is the mean value of the sample and n is the upper limit of summation The value of R2 can be as high as 1.00 at maximum It can be also negative when the prediction performance is poor Therefore, the closer this value is to 1.00, the higher the prediction performance of the model n RSS = ((yi − f (Xi))2, (2) i=1 n TSS = (yi − y¯)2, (3) i=1 R2 = − RSS (4) TSS 2.2.2 k-Fold CV CV is used to assess the generalisation performance of the prediction model It is more stable and comprehensive than the basic train/test split method One of the most common CV methods is k-fold CV The k number is to be decided by the user which is commonly chosen as or 10 (Müller & Guido, 2016) We used the cross_val_score function in the scikit-learn library to perform CV The number for k was selected as except for the support vector regression (SVR) model In addition, the random state was 1, and the shuffle option was true Once parameters were decided, this function divided the data into five parts which are called folds Then, five different training were accomplished which are called splits (Figure 2) For instance, in split 1, training data were composed of fold 2–5 and test data were composed of fold Finally, the CV score was calculated as an average of the accuracy scores of five models established in every split 2.2.3 Grid search in SVR Grid search is a function that tries certain parameters one by one and gives the best parameters We used GridSearchCV function in the scikit-learn library to make the grid search This function also uses CV to reduce overfitting and bias Therefore, we selected a five-fold CV option First, the data were scaled and divided into test and training sections The training set was to use in the grid search and the test set was to use in calculating the test set score Next, a parameter grid was created as seen in Table There were six different parameters for C and γ , which are both hyperparameters used in SVR algorithm, it made up 6∗6 = 36 combination Since five-fold CV was also used, 36∗5 = 180 models were built to choose the best parameters Then, the model accuracy is calculated in every model and ROAD MATERIALS AND PAVEMENT DESIGN 463 Figure Illustration of k-fold CV when k = Table Parameters used in grid search # C γ 0.0001 10 0.001 100 0.01 1000 0.1 10,000 100,000 10 the best parameters were found Finally, test set scores were calculated on the test set data when the best parameters are used This process was repeated for every target value 2.2.4 Nested CV in SVR As mentioned before, when GridSearchCV function was used, first we divided the data training and test section Then we used the test set to obtain model performance However, results relied on too much that single split in this method The actual score of the more generalised model might be a lot different In order to obtain a more generalised accuracy score, we used multiple CVs which are called nested CV In this method, first data were divided with k-fold CV, then grid search CV was applied in every fold Since k was chosen as 5, that number of accuracy scores was found for every target variable Therefore, while there were 180 models in the normal grid search CV, in nested CV, there were 180 ∗ = 900 models for every target variable 2.3 Algorithms We used four different techniques to create prediction models, namely, LR, polynomial regression (PR), k nearest neighbour (KNN) and SVR These algorithms were chosen based on previous studies The model performance was measured with the coefficient of determination 2.3.1 LR The ‘linear_model.LinearRegression’ method in scikit-learn library was used to carry out LR The model was trained with the training set of data obtained by the train/test split method Differently from other 464 M ATAKAN AND K YILDIZ algorithms, the data were used without scaling, because it was found to be not necessary for the LR Lastly, model performance was evaluated according to R2 values 2.3.2 PR First of all, the data were scaled and divided into training and test sections Next, the polynomial feature method was used in the scikit-learn library to obtain a certain degree of the input variables Then, vari- ous degrees up to 10 were tried for all target values and the second-degree option was selected due to providing the best results After that, the linear_model.LinearRegression function was applied to the train set in order to create the model Once the model was trained, model accuracy was determined using test data Besides, k-fold CV score was calculated to detect the generalisation performance of the second-degree PR 2.3.3 KNN First of all, the data were scaled, then it was split into train and test sections KNeighborsRegressor function was used to train the model KNN has two important parameters The first one is the number of neighbours and the second one is the measuring method of the distance between data points (Müller & Guido, 2016) We tried 10 different neighbour numbers from to 10 and the distance function was chosen as Minkowski, which is the default value Besides, k-fold CV scores were calculated where the number of splits was 5, the shuffle was true and the random state was 2.3.4 SVR Because SVR is sensitive to chosen parameters, grid search was applied in the SVR model First, the data were scaled, and then it was split into train and test sections Then, grid search was carried out with the train section of the data, and the best parameters were chosen After using the best parameters, model performance was determined on test data It was also applied nested CV in the SVR model In this method, k-fold CV and grid search functions were performed as nested Results and discussion 3.1 Limitations There are two major limitations in this study that could be addressed in future research First, we used data from previous papers in this study Therefore, the data are not well structured in terms of the dis- tribution of the values and the variety of the variables Second, there were some missing values in the dataset because these values were not presented in the past studies That is why we used data impu- tation to handle the missing values which might create some bias in the prediction models Future research can focus on using a more organised dataset by producing the specimens all together in the laboratories As an alternative, the data imputation method used in this study can be verified experimentally in future research 3.2 LR Regression analysis was used to predict the target parameters of the asphalt mixture The performance of the LR model on the test set is presented in Figure What stands out in the graphs is that the accu- racy score for the prediction of MF is 0.36 which is the lowest score among the predicted parameters Similarly, the accuracy of predicted MS values is also not very high which is 0.54 Interestingly, the accuracy score of predicted MQ is particularly higher than both those of MS and MF Moving on to vol- umetric parameters, VMA and VFA were predicted more accurately than Marshall parameters On the other hand, the prediction performance of Va is similar to Marshall parameters Overall, the accuracy of the LR was not very high But it may give an idea about the relationship between input and output variables especially when it is applied every input parameter separately ROAD MATERIALS AND PAVEMENT DESIGN 465 Figure Performance of first-degree LR 3.3 PR Second-degree PR was used to predict the target parameters of the asphalt mixture The performance of the PR model on the test set is presented in Figure The most significant aspect of these results is that prediction performance is much better than LR for all parameters Besides, accuracy scores of all parameters are higher than 0.80 except for MS It can be considered a high score Furthermore, the k-fold CV method was used to measure the performance of the PR model The results are shown in Table There were five folds and their R2 values are presented in the table for each target value A closer inspection of the table shows that some of R2 values are high and some of them are low Therefore, it is better to consider mean values for each target parameter When these mean values of R2 are examined, they are observed to be parallel with those of normal test data scores Then again there was an apparent decrease in model accuracy of MS differently from other output variables 466 M ATAKAN AND K YILDIZ Figure Performance of second-degree PR 3.4 KNNs KNN algorithm was used in order to predict target parameters of asphalt mixture Using a random train–test set, the relationship of model accuracy and the neighbour number was plotted for all target values in Figure As expected, the accuracy of the train set was clearly higher than those of the test set in all output variables As the neighbour number was increased, model accuracy increased at first but afterward, there was a steady decrease beginning from a certain point This point can be considered as an optimum neighbour number The optimum neighbour numbers according to test sets and their R2 values are presented in Table Prediction accuracy of most of the target parameters was better at the two-neighbour option, therefore the performance of all the output variables was evaluated using the two-neighbour option (Figure 6) ROAD MATERIALS AND PAVEMENT DESIGN 467 Figure KNN model accuracy according to neighbours numbers Moreover, CV was applied to the model in different neighbour numbers (Figure 7) Except for MS and MF, the best performance was seen in the two-neighbour option MS and MF, on the other hand, showed the best performance in and neighbours, respectively Accuracy scores of CV are resem- bling the test set scores which were calculated from the normal train–test split Therefore, these scores might be generalised, and using these KNN models in mixture design could be beneficial 3.5 Support vector regressor SVR was used to predict the target parameters of the asphalt mixture First, grid search CV was carried out to determine the best parameters of the SVR model Accuracy scores obtained from grid search CV are illustrated in Figure for a range of C and γ parameters In the figure, the best score represents the mean value of the splits in the CV scores obtained from training data Parameters that provide the 468 M ATAKAN AND K YILDIZ Table Second-degree regression scores with k-fold CV Target k-fold regression scores (R2) parameter Mean MS 0.70 0.90 0.19 0.76 0.77 0.66 0.81 MF 0.79 0.86 0.81 0.79 0.78 0.81 0.80 MQ 0.76 0.91 0.65 0.85 0.87 0.85 0.86 Va 0.90 0.89 0.69 0.81 0.74 VMA 0.88 0.92 0.80 0.88 0.78 VFA 0.93 0.92 0.77 0.87 0.82 Table Prediction accuracy of KNN models at their best neighbour numbers Target parameter Best neighbour number Test set score (R2) MS 0.86 MF 0.83 MQ 0.89 Va 0.87 VMA 0.93 VFA 0.87 Table Nested CV scores for SVR Target Scores (R2) of each split parameter Mean MS 0.79 0.88 0.4 0.76 0.81 0.73 0.32 MF 0.86 0.12 0.18 0.23 0.2 0.71 0.78 MQ 0.61 0.89 0.58 0.57 0.88 0.89 0.86 Va 0.52 0.86 0.95 0.65 0.9 VMA 0.9 0.91 0.94 0.86 0.86 VFA 0.93 0.92 0.96 0.81 0.66 best scores are selected as best parameters which can be seen in the figure as lighter tones These are the values closest to and written as the best score above the color maps The other two accuracy scores were calculated using the best parameters The first one, namely train set score, is the model accuracy in the train set, and the second one, namely test set score, is model accuracy for the test set which is not used in the grid search Also, nested CV scores for each target parameter are presented in Table The difference of this method from the former one is that CV and grid search CV were used as nested; in other words one within the other The accuracy scores in the table were slightly lower than the normal grid search CV scores for all target variables except for MF A major drop was seen in the accuracy score of MF Thus, the prediction performance of SVR in MF cannot be generalised with this dataset 3.6 Comparisons of the algorithms The prediction performance of all the models for six target variables were presented in Figure Over- all, LR showed the worst performance for all targets The performance of the PR was far better than LR KNN and SVR had clearly higher performance than both linear and PR models Among KNN and SVR, the latter one has a slightly better accuracy score However, nested CV scores for SVR were lower than both KNN and SVR with grid search It means SVR showed worse generalisation performance than KNN Therefore, KNN might be the best option to predict the MDPs of asphalt specimens ROAD MATERIALS AND PAVEMENT DESIGN 469 Figure KNN model accuracy when neighbour number is (train–test split, random size = 0) Conclusions The purpose of the current study was to create a more generalised model to predict MDPs of the asphalt mixture The following conclusions can be drawn from the present study: • Prediction accuracy of the LR was not high, but it may be used to get a general idea about data • Second-degree PR had better prediction performance than LR, but it was still low in comparison to KNN • In the KNN algorithm, the two-neighbour option gave the best results for most of the target variables 470 M ATAKAN AND K YILDIZ Figure k-Fold CV scores according to neighbour number • KNN algorithm showed a good correlation between prediction and real values even in the CV method Therefore, KNN might be used in mixture design to reduce laboratory work • Although SVR with grid search CV had the best prediction score, KNN might be preferred instead of SVR Because SVR is a parameter-sensitive method, and its prediction performance was reduced in nested CV, its generalisation performance was fairly worse than KNN • The KNN algorithm is a better choice to predict MDPs in collected datasets like in this study compared to SVR However, SVR might be useful in datasets produced in the same laboratory • Making CV is important to reduce the bias and overfitting which stem from the selection of the train and test groups In spite of its limitations, the study certainly adds to our understanding of the prediction physical and mechanical properties of the asphalt mixture The study showed it is possible to make accurate ROAD MATERIALS AND PAVEMENT DESIGN 471 Figure Grid search CV scores of SVR predictions from only material properties with a generalised model In other words, once a ML model that can predict MDPs is built, it is possible to produce virtual Marshall specimens in computer Then these specimens can be used to make asphalt mixture design However, this kind of design method should be verified with an experimental study Research is also required to determine necessary inputs and their importance to model using a well-organised dataset in future studies As well as efficiency of the data imputation method used in this study should be evaluated with laboratory work in further research 472 M ATAKAN AND K YILDIZ Figure Comparisons of the model scores for all the target parameters Disclosure statement No potential conflict of interest was reported by the authors ORCID http://orcid.org/0000-0003-1878-2111 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