2.1

LightGBM model

LightGBM is a lifting framework that supports efficient parallel training to solve the time-consuming problem in large sample and high-dimensional data environments. Both XGBoost and LightGBM use decision trees as their base learners^16,17. The initial form of the XGBoost objective function is shown in equation (1).

where f_i is a feature in the feature space; Ω(f_i) is the regularization term.

where K is the number of leaf nodes of the regression decision tree; λ is the parameter that controls the score of the leaf node; ω_j is the value of the leaf node. XGBoost fits the residuals of the current prediction to the true value by iterations, continuously converging to the true value. the result of each iteration of XGBoost is shown in equation (3).

To determine the optimal structure of the tree, XGBoost selects Gain as the feature splitting criterion and prioritizes the nodes with the largest Gain to be split. The formula for Gain is shown in equation (4).

The regression tree will continue to split until Gain < 0 or reaches the depth threshold of the tree. LightGBM and XGBoost have different ways of splitting leaf nodes. Figure 1a shows the splitting strategy of leaf nodes of XGBoost and LightGBM. The leaf node splitting method of XGBoost is level-wise, which increases the computation and time complexity by calculating the splitting gain when traversing each splitting point. The leaf node splitting method of LightGBM is leaf-wise. The leaf node with the greatest split gain is selected for splitting at each iteration. In addition, the decision tree algorithm based on histogram sorting is another advantage of LightGBM., as shown in figure 1b. The algorithm reduces memory consumption and improves the efficiency of model training.

Figure 1.

(a): Splitting strategy for leaf nodes; (b): Histogram optimization algorithm.

2.2

BOA-LightGBM model construction

The core process of the BOA algorithm is to set the objective function to be optimized, and update the objective function by continuously adding new data points. Then, the next combination of hyperparameters to be sampled is selected based on the posterior distribution. Figure 2 shows the Bayesian-LightGBM model construction process. Firstly, a dataset is constructed for assessing the skid resistance of asphalt pavements. Secondly, the LightGBM model is trained. In this process, the initial values of the model parameters as well as the domain space need to be defined. Then, a BOA algorithm is used to search for the optimal values in the domain space.

Figure 2.

The Bayesian-LightGBM model construction process.

3.1

Data measurement

(1) MTD data measurement. Pavement texture depth data is collected using an electric sand spreader as shown in figure 3a. The sand spreader needs to be calibrated during the test and the average value is recorded as L0 when the calibration is repeated three times. After calibration, the texture depth data is measured at the test location, and the same test point is measured at least 3 times in parallel (All 3 test points are located on the wheel track). The average of three repeated tests is recorded as L. Finally, the texture depth value for this measurement point is calculated using equation (5).

Figure 3.

Data acquisition equipment. (a): Electric sand spreader; (b): DFT.

(2) Dynamic friction coefficient data acquisition. To investigate the trend of the coefficient of friction under wet conditions and high and low speed conditions, skid resistance tests are designed for both dry and wet conditions. The wet condition is simulated by spraying a certain amount of water with a spray bottle in a fixed test area. The values of the pavement water content (ml) are 0, 16, 32, 48, 64, 80, 96, 112, 128, 144, and 160. The size of the spray area is 40 (cm) ×40 (cm). At the same time, the DFT as shown in Figure 3b is used to collect the pavement friction coefficient, which is mainly used for outdoor or indoor testing of large asphalt mixture specimens.

3.2

Data analysis

MTD reflects the height characteristics of the pavement texture structure and is one of the most significant factors impacting surface skid resistance. The Pearson correlation calculation method is used to analyse the degree of association between MTD and skid resistance under different DFT test speed conditions. The results are shown in Figure 4. There is a weak correlation between MTD and friction coefficient at low speeds. When the speed reaches 60 km/h, the correlation coefficient between MTD and friction coefficient is 0.802. The results show that MTD mainly affects the skid resistance at high speed.

Figure 4.

Pearson correlation features analysis results.

4.1

Analysis of friction coefficient prediction results

In this research, the 2333 sets of skid resistance evaluation data are divided into a 70% training set and a 30% test set. A BOA-LightGBM model is trained with MTD, pavement water content, and DFT test speed as input features to predict friction coefficient. Figure 5a shows the results of fitting the predicted values of LightGBM and true values. Figure 5b shows the fitting results of the predicted values of BOA-LightGBM and the true values. The more concentrated the scattered points are around the red line, the better the model prediction results. Analysis of figure 5 shows that the BOA-LightGBM model’s predicted values are closer to the red line. Therefore, the optimized model constructed predicts better.

Figure 5.

The fitting result of predicted value and real value. (a): LightGBM; (b): BOA- LightGBM.

4.2

Evaluation of friction coefficient prediction results

Furthermore, R², root mean square error (RMSE), and mean absolute percentage error (MAPE) are used to quantitatively evaluate the prediction results of the model. The results are shown in table 1. Compared with LightGBM, the R² value of BOA-LightGBM increased by 2.7% and RMSE decreased by 1.2%. It indicates that the BOA-LightGBM model has higher prediction accuracy and the average deviation of its predicted values from the true values. At the same time, it is verified that the BOA algorithm can effectively enhance the precision of the LightGBM model.

Table 1.

Predictive model evaluation.

Thus, taking the predicted results of BOA-LightGBM model as an example, the trends of the predicted and true curves of pavement friction coefficient under DFT20-30 km/h, DFT30-40 km/h, DFT40-50 km/h and DFT50-60 km/h are analysed, and the prediction results are shown in Figure 6. The trends of the real and predicted values of the friction coefficient are basically the same. The BOA-LightGBM model has strong non-linear fitting performance in both low and high-speed conditions, and can accurately assess the pavement skid resistance.

Figure 6.

Forecasting results for dynamic friction coefficients using BOA- LightGBM. (a): DFT20-30 km/h; (b): DFT30-40km/h; (c) DFT40-50 km/h; (d) DFT50-60 km/h.