## 6 Results and Discussion  
### Random-Forest Model Results  
In this section, the results of the random-forest model and the model parameter optimization are presented. As mentioned in the previous section, fiber optic accelerometers are installed adjacent to the operating HSR to continuously acquire vibration data of the track slab in the normal and deformed states continuously. First, raw data are preprocessed with data interception, denoising, and segmentation. Then, the data are decomposed by LMD, and the characteristic PFs are selected on the basis of Pearson correlation coefficients. Finally, six time-domain feature parameters and one time-frequency-domain feature parameter are calculated of the selected characteristic PFs. Therefore, seven features can be extracted from the dataset to form the characteristic parameter vector matrix. For conducting evaluation analysis after the model development, the total dataset is divided into training and testing datasets. In this study, the dataset comprises 2534 samples, that is, 1875 and 659 samples for the normal and deformed states of track slab, respectively. Of the total data, 70% is used for the training set and the rest for the testing and validation of the results. During the development of the random-forest model, the number of decision trees \(T\) and the split features \(mtry\) are determined. In general, the split features \(mtry=(M)^{1/2}\); in this paper, \(M=7\), so we let \(mtry=3\). The number of decision trees in random-forest model is determined according to the relationship between the number of decision trees and the classification accuracy, as shown in Figure 8. The classification accuracy tends to be stable when the number of decision trees reaches 1300. Given that the more decision trees, the better the randomization performance of the model, the number of decision trees in this paper is set to be 2000. After the number of decision trees in the random-forest model is determined, the split features \(mtry\) need to be determined. When the classification accuracy reaches the maximum, the number of split features is considered to be optimal. Table 3 shows the effect of the number of split features \(mtry\) on the classification accuracy when the number of decision trees \(T\) is equal to 2000. Figure 8: Relationship between the number of decision trees and classification accuracy. The best performance of the random-forest model to recognize Class 1 reaches 98.18% accuracy when \(mtry\) is set to 1. Similarly, the random-forest model using 3 split features (\(mtry=3\)) can well identify Class 2 with 95.59% accuracy. Considering the average classifying accuracy, the random-forest models employing 3, 4, and 7 split features can achieve relatively higher accuracy (96.09%, 95.79%, and 94.58%) compared with other cases. It is also worth noting that more attention should be paid to the recognition accuracy of Class 2, because the deformed state may affect the safe operation of the HSR. From the model perspective, the split features \(mtry\) balances the strength of the trees as well as the correlation of the trees in the random-forest model. Therefore, in this paper, the split features \(mtry=3\) and the number of decision trees \(T=2000\) are used as the optimization parameters of the random-forest model. Figure 9 illustrates the results of random-forest classification using these optimized parameters (\(mtry=3\), \(T=2000\)). The points in Figure 9 represent the number of decision trees for both classifications, the horizontal coordinate represents the number of decision trees whose voting result is Class 1, and the vertical coordinate represents the number of decision trees whose voting result is Class 2. Since the total number of decision trees is 2000, all points are on the diagonal (\(x+y=2000\), \(x\) represents the number of decision trees whose voting result is Class 1, and \(y\) represents the number of decision trees whose voting result is Class 2).