## 1 Introduction
The dynamic stiffness of rail pads was predicted using several machine learning methodologies (multilinear regression, \(K\) nearest neighbors, regression tree, random forest, gradient boosting, multilayer perceptron, and support vector machine (SVM)) [45]. The fault detection approach for the HSR turnout based on a deep denoising auto-encoder and one-class SVM [46] was also proposed. Being subjected to repeated temperature load and train load, the track structure suffers from track slab cracks, track slab deformation, CA mortar layer damage, and so on. Although these damages do not necessarily affect the safe train operation directly, they could pose considerable threat to the safe operation if they are not identified in time. For the timely detection of such damages, machine learning methods have been used. The track slab cracks were detected on the basis of the region proposal network and fully convolutional networks [47] and the different severity levels of track slab cracks were studied on the basis of the Inception-ResNet-v2 network [48]. The arching deformation of track slabs was detected on the basis of CNN [11] using track geometry data. The damage of CA mortar layer was identified on the basis of SVM by using the acceleration of wheelset [9], the back propagation neural network by using vibration data obtained from modal analysis [49], and CNN by using Hilbert spectrum [34]. In summary, intelligent identification techniques based on random-forest model for track slab deformation identification by using track-side vibration acceleration signals acquired from HSRs field have not been sufficiently explored. This study uses track-side vibration signals for track slab deformation identification without interrupting the normal operation of HSRs. Track-side vibration signals contain information of not only train vibration and track slab deformation but also noise and environmental vibration, which can be eliminated by adopting data preprocessing methods. The train group, running speed, and load of high-speed trains are different, and the wheel-rail vibration signal decays layer by layer from the rail through track slab, CA mortar layer, supporting concrete layer and bridge deck slab to reach the cable trough. Therefore, many factors influence track-side vibration signals [50], resulting in many attributes; hence, more parameters are required for using machine learning methods [51]. Compared with other traditional models, such as SVMs and neural networks, a random-forest model requires fewer parameters, i.e., only the number of decision trees and split features, in the modeling process regardless of the number of attributes [52]. Although the number of parameters of the SVM model (i.e., kernel function parameter and penalty parameter [53]) is the same as that of the random-forest model, in practical applications, different kernel functions and corresponding kernel function parameters must be selected according to the actual situation, and the parameters need to be optimized several times. Neural networks have two types of parameters, weights and thresholds, and the number of parameters increases exponentially with the number of neurons [54]. Both the traditional methods require complex parameter optimization algorithms to obtain the appropriate parameters. Owing to the simpler parameter determination process and greater advantages in practical applications of a random-forest model compared with the two traditional methods, we use it in this study for track slab deformation identification. In addition, [PERSON]. [55] has demonstrated through both theoretical and extensive empirical studies that a random-forest model has lower generalization errors, higher prediction accuracies, and better robustness to noise compared with other methods such as SVMs, neural networks, and k-nearest neighbor. In summary, a random-forest model is suitable for the identification of track slab deformation.