# Railway Vehicle Wheel Flat Detection with Multiple Records Using Spectral Kurtosis Analysis
## 1 Introduction  
The presence of a geometric defect in the interface between the rail and the wheel is one of the sources of dynamic train interaction. Wheel profiles have a significant effect on the safety and dynamic performance of the vehicle, for instance, in terms of the dynamic stability of the vehicle, the magnitude of the wheel-rail contact force, and riding comfort. Wheel travel imperfections are usually divided into two main categories: (i) defect along part of the wheel circumference and (ii) defect around the entire wheel. These are both regarded as types of wheel out-of-roundness (OOR) phenomena. The first category includes wheel flat, spalling, shelling, etc., and is mainly caused by braking damage and rolling contact fatigue cracking. The second category involves wheel corrugation and polygonal wheel, which are periodic irregularities around the wheel that can be caused by unbalanced loads [1]. The non-roundness of railway wheels creates an unfavorable effect on the components of track and vehicle [2]. In recent decades, several researchers [3; 4; 5; 6] have focused on the development mechanism of OOR. However, the main focus of this research is the development of techniques that accurately identify the presence of defective wheels, namely with flats [7; 8; 9; 10; 11; 12]. When the wheelsets are locked and slides along the rails as a result of poorly adjusted or defective brakes, the wheel flats are created. Therefore, the surface of the wheels becomes flat rather than round due to the friction between the wheels and the rails [13]. Wheel flats induce high dynamic impact loads on the railway infrastructure, which causes significant damage to the vehicles and the track, such as broken axles, hot axle boxes, damaged rolling bearings, and cracks in the wheels, rails, and sleepers. Moreover, this type of wheel defectgenerates high levels of noise and excessive vibration. These large magnitude vibrations are heavily transmitted to the rolling stock, inducing forces way above the permitted values, causing damage to the suspension system, frame, and car body of the rolling stock [8; 14]. In addition, the irregularity of the wheel and track also results in the deterioration of the interaction performance of the train and overhead contact line [15]. Therefore, to tackle this issue, railway administrations take the necessary measures to make sure all required precautions and renovations are in place. In terms of precautions, most passenger trains are currently equipped with advanced anti-slip systems that slightly reduce wheel-rail sliding [16]. However, as operating speeds and axle loads increase, wheel flats cannot be completely avoided. Moreover, since freight trains do not have a non-slip system, the condition of the wheels is usually worse, having a significant impact on the long-term service of trains and infrastructure. Several researchers have proposed different in-service methods for measuring wheel defects in the last few decades, namely onboard and wayside measurements. Most onboard techniques are based on vibration, acoustic, image detection, and ultrasonic technologies [17; 18; 19; 20]. However, for a comprehensive diagnosis and effective management of the wheels, sensors must be installed on all wheels. The installation of sensors on wheels is seldom used due to cost and maintenance issues, while onboard detection methods are commonly used to monitor the track condition and not for monitoring wheel condition. In contrast, wayside measurement systems are currently a preferable solution to detect wheel flats, as the condition of all wheels evaluates during the passage of trains [21; 22; 23; 24; 25; 26; 27; 28]. [PERSON] et al. [29] proposed a quantitative decision approach based on wheel impact data that illustrates the actual condition of the wheels. According to the proposed method, the critical wheels should be removed while wheels that are not in critical condition remain in operation.