# Railway Vehicle Wheel Flat Detection with Multiple Records Using Spectral Kurtosis Analysis
## 6 Sensitivity of the Layout Schemes to the Number and Location of the Accelerometers  
As stated above, in order to reduce installation and maintenance costs, it is of the utmost importance to reduce the number of sensors without compromising the quality of the output results. Moreover, it is important to demonstrate that the system, regardless of the position of the sensors, is always effective in detecting wheel flats. Therefore, this section aims to demonstrate the sensitivity of the layout schemes to the number  
Figure 14: Kurtosis values for signals with and without noise for the Alfa Pendular passage for layout scheme 2.  
Figure 13: Envelope spectrum analysis for the 12 accelerometers (layout scheme 2) with different noise intensities and considering a defective and healthy wheel of the Alfa Pendular train and the freight wagon.  
of sensors (strain gauges or accelerometers) and the location where they are installed. Consequently, in addition to the 12 positions selected on the rail between the two sleepers, seven more accelerometers (positions 13 to 19 shown in Figure 5) were considered on the rail located above each sleeper (layout scheme 3). The robustness of the proposed method for detecting a wheel flat with fewer sensors without compromising data quality is discussed in this section.  
Figure 15 shows the envelope spectrum detection analysis for seven accelerometers (positions 13 to 19 shown in Figure 5) considering a high noise intensity level in the signal obtained in a scenario with a healthy and defective wheel of the Alfa Pendular and the freight wagon. The results are consistent with those obtained in previous sections. As depicted in Figure 15, there is a lag between the signals from a defective wheel, and the maximum amplitude corresponds to accelerometer 17. As presented in Figure 5, accelerometer 17 is located just after the flat impact location. Again, another indicator included in this study to distinguish defective wheels from healthy ones is the amplitude of the envelope spectrum. As expected, the amplitude of the envelope spectrum for a defective wheel is significantly higher than for a healthy one. Regardless of the position of the sensors (between two sleepers or above each sleeper), the system is efficient in detecting wheel flats. Figure 16 presents an additional optimization of the sensor layout, specifying the optimum number and positions of the accelerometers.  
Figure 15: Envelope spectrum analysis for seven accelerometers (layout scheme 3) considering a defective and a healthy wheel of the Alfa Pendular and the freight wagon (noise = 10%).  
The installation along an equivalent wheel perimeter length (\(2\pi r_{w}=2.7\) m) is useful for monitoring the entire perimeter of the wheel. Figure 16 shows that from an economic point of view, two accelerometers are needed to distinguish a defective from a healthy wheel. Regarding the position of the sensors, it is better to install them so that, with every rotation of the wheel, each sensor monitors half the length of the wheel perimeter. The length of the wheel perimeter is \(2\pi r_{w}=2.7\) m. Therefore, each time the defective wheel contacts the surface of the rail, the same impact will occur again 2.7 m later. For example, if the flat impact location occurs before accelerometer 19 (see Figure 5), it means that in the previous rotation of the wheel, the accelerometer 14, which is located 3.0 m away, could also detect the impact at a close distance. For this reason, it is recommended that accelerometers should be installed in such a way that for each wheel rotation, one accelerometer could monitor half of the wheel circumference (2.7/2 = 1.35 m), which is the distance between three sleepers, to guarantee that at least one accelerometer is close to the location of the flat impact. In the actual installation, it is not necessary to install 12 sensors along the rail to identify the profiles of the wheels during the operation of the vehicle.