Predicting the International Roughness Index of JPCP and CRCP Rigid Pavement: A Random Forest (RF) Model Hybridized with Modified Beetle Antennae Search (MBAS) for Higher Accuracy

Abbreviation

1  Introduction

In recent years, with the development of road transportation, the total amount of road freight is also growing, and the phenomenon of overload of large trucks is common [1,2]. Cement pavement refers to pavement composed of cement concrete panels or base, also known as rigid pavement, which is widely used in heavy traffic because of its advantages of large stiffness, strong bearing capacity, good stability, good durability, high compressive strength, and tensile strength [3–5]. JPCP is a pavement consisting of a concrete surface layer and a base or substratum, with reinforced concrete pavement only in the joint zone and local areas, also known as white pavement [6,7], and JPCP has the advantages of low initial cost and low maintenance cost compared with other cement pavement, so it is widely used [8]. CRCP is a pavement form that controls cracks caused by longitudinal shrinkage of concrete pavement by placing sufficient continuous reinforcement in the longitudinal direction [9–11], and also a kind of high-performance cement pavement that can effectively overcome the diseases caused by the weak links such as transverse shrinkage joints in the joint concrete pavement [12].

The smoothness of the pavement is the main factor in the vehicle running environment and is one of the important indexes of pavement performance [13], the road is not flat will increase the vehicle vibration and resistance in the process of moving, which affects the service life of the dynamic vehicle system and transmission system [14]. The research shows that the smoothness of the pavement, especially the initial smoothness of the pavement, seriously influences the service life of the road surface [15]. Therefore, it is of great practical significance to study the roughness of road surfaces [16]. The MEPDG, developed by the American Association of State Highway and Transportation Officials and the National Cooperative Highway Research Program, is one of the most commonly used models for predicting pavement performance [17–20], which adopts to evaluate the smoothness of the pavement [21]. However, with the development of the times, researchers have found that the accuracy of MEDPG in predicting pavement performance has certain limitations [22,23]. Hence, it is extremely important to develop a more accurate model for predicting pavement performance [24–26].

In recent years, machine learning has been applied in various fields (including slope stability classification, compressive strength prediction, rock joint shear strength prediction, and loading-bearing capacity of structures) because of its excellent performance. Also, proposed soft computing approaches, such as tree-based intelligent techniques, regression models, and nonlinear models were applied [27–32]. Researchers have also introduced it into the research of pavement performance direction and achieved remarkable results [33,34]. Yan et al. proposed a hybrid machine learning model of Particle Swarm Optimization and Support Vector Machine to establish the evaluation model of the performance of asphalt pavement, with Pavement Condition Index, Pavement Structure Strength Index, Skidding Resistance Index and IRI as evaluation indexes. The PCI prediction model based on machine learning was established by using SSI, SRI, and IRI. The results showed that the model can evaluate the performance of asphalt pavement simply and efficiently [35]. Wang et al. researched a fuzzy regression method to predict the IRI and compared the results of MEPDG, conventional grey model, and fuzzy grey model with the actual long-term pavement performance (LTPP) data. The results showed that the fuzzy regression model based on the grey theory has a better prediction effect on the IRI [36]. Kaloop et al. improved the results of optimal pruning extreme learning machine by combining optimal pruning extreme learning machine and wavelet analysis [37]. Li et al. studied the sensitivity of different variables to the creep of concrete based on the existing data and the SVM model re-selected the indicators based on the results, and re-trained the SVM model based on the newly selected parameters, verifying that the parameters with low sensitivity and strongly correlated parameters have a positive impact on improving the robustness of the model [38]. Zounemat-Kermani et al. proposed to use new machine learning models to simulate the degradation of concrete caused by environmental factors used machine learning models to analyze the sensitivity of parameters causing concrete corrosion and confirmed the effectiveness of machine learning in performance prediction and sensitivity analysis [39]. However, currently, much research on machine learning in the direction of the smoothness pavement was based on single machine learning models [33,40,41], which had low prediction accuracy and did not involve the important analysis of variables.

To improve the prediction accuracy on the smoothness of JPCP and CRCP and explore the influence of input indexes on output index, this study proposed the smoothness prediction model of JPCP and CRCP based on RF-MBAS and the main contents of the study are as follows. Firstly, dataset used to evaluate JPCP and CRCP are selected based on LTPP, and the feasibility of indicators and dataset selection was verified through statistical analysis and correlation analysis. Then, based on hyperparameter tuning [42], the accuracy of the models are proved by the analysis of the consistency between the predicted value and the actual value. Finally, the sensitivity of all input indexes and human intervention indexes to the IRI of the two types of pavement are creatively analyzed. The research process is shown in Fig. 1.

Figure 1: Flow chart of the study

In order to solve the problem of low prediction accuracy and efficiency of traditional evaluation methods on the smoothness of JPCP and CRCP, this study proposed RF-MBAS. The prediction accuracy of RF-MBAS needs to be evaluated by the hyperparameter tuning effect of MBAS on RF and the prediction accuracy of the RF-MBAS on the IRI of JPCP and CRCP. Further analysis of the importance of the indicators to the IRI of the JPCP and CRCP is necessary to assess the extent to which they affect the smoothness on the two types of pavement. Hence, the specific research objectives are summarized as follows:

•   Evaluate the hyperparameter tuning effect of MBAS on FA that predicts the IRI of JPCP and CRCP.

•   Compare and analyze the accuracy of RF-MBAS and MEPDG in predicting the IRI of JPCP and CRCP.

•   Analyze the importance score of input indicators on IRI of JPCP and CRCP, and provide feasible suggestions for civil engineers to build and maintain JPCP and CRCP.

2  Research Methods

2.1 Description of the Dataset

A reliable database is a basis to verify the accuracy of the prediction of IRI for JPCP and CRCP. The data of the database established in this study came from the LTPP database, which is a large and reliable database of different pavement structures in the United States, Canada, and other regions. LTPP includes the data on the performance of pavement related to summary, structural, climatic, traffic, and road performance modules. Considering the influence mechanism of JPCP and CRCP comprehensively, including pavement disease, traffic load, pavement structure, and field condition, and considering the IRI evaluation index of JPCP and CRCP by MEPDG to ensure the reliability of model comparison results, this study finally selected initial smoothness measured as IRI (IRII), pavement age in years (AGE), percentage of slabs with transverse cracking (all severities) (TC), percentage of joints spalled (SPALL), PATCH, TFAULT, freezing index (FI), P200 as input variables to predict the IRI of JPCP, and IRII, AGE, TC, PATCH, all severities of Punchouts number per mile (PUNCH), FI, and P200 as input variables to predict the IRI of JPCP and CRCP (as shown in Appendix A). The rationality of data distribution is the basis to evaluate the accuracy of the prediction model, this study analyzed the mathematical statistical and frequency histograms of the variables of JPCP and CRCP, and the results are shown in Table 1 and Fig. 2. Fig. 2 mainly depicts the data coverage and distribution of the variables, as can be seen, the frequency distribution histogram of IRII and AGE in input variables of JPCP show the single-peak pattern, and the frequency distribution of P200 is relatively stable. In short, the data distribution of each input variable have the wide and reasonable coverage. Hence, the frequency distribution histogram of IRI in the corresponding database is the single-peak type. The frequency distribution histograms of IRII, AGE, and P200 in the input variables of CRCP are single-peak type, and the final data distribution frequency histogram of IRI also shows the single-peak pattern.

Figure 2: Frequency distribution histogram of the variables of JPCP and CRCP (JPCP: a–i, CRCP: j–r)

2.2 Correlation Analysis

The analysis of two or more variables that are correlated is called correlation analysis [43,44]. Correlation analysis can measure the degree of closeness between two factors [42,45,46], and the existence of certain connections or probability between elements is the basis for correlation analysis of elements [47]. The correlation analysis results between the input variables of JPCP and CRCP are shown in Fig. 3. It is obvious that the correlation values on the diagonal line from the bottom left to the top right of JPCP and CRCP are all 1, indicating that the correlation coefficients between the same variables are 1, while the correlation coefficients at other positions except the diagonal are all less than 0.5, manifesting that the correlation coefficients between different variables are all less than 0.5. The above analysis results show that there is a certain correlation between the input variables used to predict the IRI of JPCP and CRCP in this study, and the correlation between the variables is low, thus the prediction effect of the model will not be affected by the multicollinearity between the input variables [48–50].

Figure 3: Correlation analysis of input variables

2.3 Algorithm

2.3.1 Mechanistic-Empirical Pavement Design Guide (MEPDG)

MEPDG was first proposed by the American Association of State Highway and Transportation Officials and the U.S [51]. National Highway Research Program, Since then, researchers have carried out more in-depth studies on MEPDG and made corresponding updates and improvements. Currently, MEDPG has been widely used in the United States and also attracted the attention of transportation experts worldwide [52]. The subject of MEDPG involves a wide range of research directions. At present, the research mainly focuses on the four directions of structure, material, model, and mechanical analysis [53].

2.3.2 Improved Beetle Antennae Search (MBAS)

(1)   Basic BAS

BAS algorithm is a meta-heuristic algorithm proposed by researchers inspired by the foraging behavior of beetles [54,55]. The beetles swing their scent-picking whiskers to get the location of the food, choose the direction of their next flight based on the concentration of food odor received by their left and right whiskers, and keep updating their position until they find food [56]. In the BAS algorithm, the objective function to be optimized is regarded as food, and the variables in the objective function are regarded as the position of the beetle [57,58]. The flow chart of BAS is performed in Fig. 4.

(2)   Improvement of BAS

Figure 4: Flow chart of BAS

BAS has been widely used to solve practical problems in engineering due to its good optimization ability [59]. However, the BAS algorithm has some shortcomings such as the limited ability of the individual to search for optimal value, and the individual cannot make full use of the obtained optimal value information [60]. The optimization of BAS relies too much on parameter setting, which is related to the convergence and solution accuracy of the algorithm [20,61]. However, there are few types of research on the improvement of the BAS algorithm. This study proposed the MBAS based on Levy flight and self-inertial weight optimization. Levy flight was used to update the position of individual beetle in the process of beetle position update, to expand the search capability, which jump out of the local optimal solution. The formula for increasing beetle step size is as follows:

x(i)=∂|Levy|⊗x(i−1)(1)

In the formula, x is a random parameter, and x∈[0,1], ⊗ means term by term multiplication, |Levy| represents the levy distribution with infinite variance, and infinity is defined as Levyu=t−λ,(1<λ≤3). The levy flight formula is as follows:

|f(i)−f(i−1)|<10−5(fw−fb)(2)

In the formula, fb and fw represent the historical best fitness value and the historical worst fitness value, respectively.

In this study, the adaptive weight method with exponential change was used to ensure the search range. With the increment of the number of iterations, the weight decreases exponentially, which greatly increases the local optimization capability of the algorithm. The adaptive weight monotone decreasing equation is:

xi+1=ηi×xi(3)

In the formula, Xi represents the step size of the current position, ηi represents the inertia weight of the adaptive function, and its calculation formula is as follows:

ηi=(1−∂)0.95+αfwi−fifwi−fbi(4)

In the formula, fi is used to represent the fitting equation of the current position, fbi and fwi are used to represent the best fitting value and the worst fitting value, and ∂ is the parameter used for the tradeoff between (1−∂)0.95 and ∂fwi−fifwi−fbi, and ∂=0.2.

2.3.3 Random Forest (RF)

RF is a common classification machine learning method combining Bagging ensemble learning and based on multiple decision trees [62,63]. Firstly, RF needs to learn the sub-model of the trained weak classifier, then combine the weak classifier according to the results, and finally get the final result of the model according to the voting result of the subset or average value [64]. The steps of RF are shown in Fig. 5.

Figure 5: The framework flow chart of the RF

3  Result and Analysis

3.1 Hyperparameter Tuning

In this study, root mean square error (RMSE) was used to measure the results of hyperparameter tuning [65]. RMSE is calculated as follows:

RSME=1m∑i=1m⁡(yi′−yi)2(5)

where yi′ is the predicted value, yi is the actual value, and m is the number of samples.

In the process of training, the model often matches the training data well but fails to predict the data outside the training set, which is called overfitting [66–69]. Therefore, it is necessary to verify the effect on the hyperparameter tuning of the model. According to previous studies, this study chose 10-fold cross-validation to verify and further optimize the effect of MBAS on RF. The diagram of 10-fold cross-validation is shown in Fig. 6, the original data used for validation was divided into 10 groups, and each group of data in 10 groups was taken as the validation set in turn, and the remaining 9 groups were taken as the training set, and obtained 10 models [70]. As can be seen from Fig. 7, the RMSE values of the IRI prediction models of the two kinds of pavement with MBAS hyperparameter optimization are all low at each cross-validationthe, which proves the effectiveness of hyperparameter tuning, and the minimum RSME value of JPCP is obtained at the 7th iteration, the minimum RSME value of CRCP is obtained at the 10th iteration, which reflects at the 7th iteration and 10th iteration models with the most accuracy.

Figure 6: 10-fold cross-validation method process

Figure 7: RMSE results of the hyperparameter tuning

3.2 Results of the Model

To verify the accuracy of the prediction on IRI of JPCP and CRCP by the newly developed RF-MBAS, we analyzed the fitting effect between the predicted and actual values and the result are shown in Fig. 8. We can clearly see that the consistency between the predicted values and the actual values of the test set of JPCP and CRCP is high, only a few points with large errors exist, but these points do not affect the prediction effect of the model on the whole. The test set of JPCP had a high R-value (0.9476) and low RSME-value (0.2732), and the test set of CRCP also had a high R-value (0.9182) and low RSME-value (0.1863). Also, from the above calculation, it can be obtained the MAE values of 0.2358 and 0.1657 for the IRI prediction of the JPCP and CRCP, respectively. The above results proved that RF-MBAS has high prediction accuracy on the IRI of JPCP and CRCP.

Figure 8: Actual measured vs. predicted measured values of the IRI

To more intuitively prove that the prediction accuracy of RF-MBAS is significantly improved compared with that of MEPDG, this study analyzed the predicted values and actual values on the IRI of JPCP and CRCP by RF-MBAS and MEPDG, respectively, and the comparison results are shown in Fig. 9. It can be clearly seen from Fig. 9 that the fitting effect of RF-MBAS on the predicted values and actual values on the IRI of the two kinds of road pavement is better than that of the traditional MEPDG, which proves once again that the RF-MBAS developed in this study has better prediction effect.

Figure 9: Comparison of the actual value and predicted value of IRI of RF-MBAS and MEPDG

3.3 Importance of Variables

Fig. 10 shows the analysis results of importance scores of input variables on the IRI of JPCP and CRCP. The importance scores of the eight input variables for the IRI of JPCP decrease in order of IRII, TFAULT, FI, AGE, P200, SPALL, TC, and PATCH, and for the IRI of CRCP decreases in the order of IRII, FI, P200, AGE, TC, PATCH and PUNCH.

Figure 10: The importance score of the input variable

Through further analysis of the input variables of JPCP and CRCP, it can be found that IRII, FI, and AGE cannot be manually interfered with, so engineers cannot increase IRI by changing the above variables when designing and maintaining JPCP and CRCP. It is important to analyze the importance of the variables that can be manipulated for engineers to enhance the IRI during design and maintenance. In the input variables of JPCP and CRCP, the importance score of the variables that can be manipulated is shown in Fig. 11. It can be seen that the input variables of JPCP that can be manually intervened are TFAULT, P200, PATCH, TC, and SPALL, respectively, and their importance scores to IRI are 2.0089, 0.9715, 0.4523, 0.4439, and 0.3122, respectively. The importance score of TFAULT and P200 to the IRI of JPCP is high, that is, engineers can focus on the fineness of TFAULT and P200 to increase the IRI when designing and maintaining JPCP. The variables of CRCP that can be interfered with are P200, PATCH, TC, and PUNCH, respectively, among which P200 and PATCH have relatively high importance scores to the IRI, with 1.4444 and 1.0539, indicating that the IRI of CRCP shows higher sensitivity to P200 and PATCH.

Figure 11: The importance score of the input variable that can be artificially interfered with

4  Conclusions

To overcome the weakness of the prediction models in the previous MEPDG, this study developed RF-MBAS to predict the IRI of JPCP and CRCP and compared the prediction effect of RF-MBAS and MEPDG. The 10-fold cross-validation was applied to verify the reliability and accuracy of the model. In addition, this study creatively proposes to analyze the importance score of all input variables that can be interfered with by humans. After the above research, the following conclusions are drawn:

(1)   To achieve the two goals of jumping out of the optimal local solution and improving the convergence accuracy, levy flight, and adaptive weight methods were used to improve the basic BAS algorithm. From the relationship between the number of iterations and RSME values, the RSME values converge rapidly and drop to a lower value with the increase of iterations proving MBAS shows a good efficiency on the hyperparameter tuning of RF. The proposed evolved RF-MBAS model was an important innovation point of this study to characterize and predict pavement IRI.

(2)   The predicted values predicted by RF-MBAS have high consistency with the actual values for IRI of JPCP and CRCP. This study compared the prediction effects of MEPDG and RF-MBAS, and the results further proved that the RF-MBAS has better prediction effects on the IRI of JPCP and CRCP, and the machine learning model shows great superiority in predicting IRI compared to the traditional MEPDG.

(3)   The importance of the input variables of IRI used to evaluate JPCP and CRCP is ranked from highest to lowest as IRII, TFAULT, FI, AGE, P200, SPALL, TC, PATCH and IRII, FI, P200, AGE, TC, PATCH, PUNCH, the higher scores of JPCP were TFAULT and P200 (2.0089 and 0.9715) and the highest scores of CRCP were P200 and PATCH (1.4444 and 1.0539), respectively. The IRI of JPCP and CRCP was proportional to the corresponding input variables in this study, including TFAULT, P200, PATCH which scored higher.

The RF-MBAS model developed in this study has satisfactory accuracy in the evaluation of the IRI of JPCP and CRCP. However, the optimization of JPCP and CRCP involves multiple conflicting goals such as usage performance and economic performance. Hence, in the future, researchers need to develop multi-objective optimization models that can simultaneously optimize multiple conflicting objectives of JPCP and CRCP.

Acknowledgement: This research was supported by the Fundamental Research Funds for the Central Universities. The writers are grateful for this support.

Funding Statement: This research was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2021QN1006), Natural Science Foundation of Hunan (Grant No. 2023JJ50418), and Hunan Provincial Transportation Technology Project (Grant No. 202109). The writers are grateful for this support.

Author Contributions: The authors confirm contribution to the paper as follows: study conception and design: Jiandong Huang, Mengmeng Zhou; data collection: Jiandong Huang, Qiang Wang; analysis and interpretation of results: Jiandong Huang, Mengmeng Zhou, Qiang Wang; draft manuscript preparation: Jiandong Huang, Mengmeng Zhou. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: The data supporting this study’s findings are available on request from the corresponding author, upon reasonable request.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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Appendix A: Input and Output Variables Employed in the Study

(a) JPCP

(b) CRCP