# Railway Vehicle Wheel Flat Detection with Multiple Records Using Spectral Kurtosis Analysis
## 5 Sensitivity of the Layout Schemes to the Signal Noise  
The signal noise can significantly perturb the assessment of the track response. To evaluate its influence in the proposed methodology to detect wheel flats, an artificial noise is generated due to the maximum response (shear or acceleration) of the signal and added to the main signal. Therefore, new signals considering different noise levels of 5%, 10%, and 20% of the maximum amplitude of the initial signal are generated. The unevenness profile of the track (presented in Figure 3) is considered. Moreover, the effectiveness of using shear and acceleration as input parameters for flat detection is compared, with respect to strain gauges (layout scheme 1) and accelerometers (layout scheme 2), considering the Alfa Pendular and the freight wagon.  
Figures 12 and 13 show an envelope spectrum detection analysis for 12 shear and acceleration responses obtained on the rail (position 1 to 12 shown in Figure 5) for different noise intensities and considering a defective and a healthy wheel of the Alfa Pendular train and the freight wagon. As mentioned before, there are usually two indicators that can be used to detect wheel flats, namely the lag between signals and the amplitude value. It can be observed that the first one can also be used in the present scenario since a clear lag between the signals in the presence of a wheel flat is observed, while in the healthy wheel, all signals coincide. However, when looking at the amplitudes of the signals, it is possible to conclude that this indicator is not suitable when the shear is considered as input. In other words, when the signal is contaminated by noise and track responses evaluate by SGs, the only indicator that effectively distinguishes a defective from a healthy wheel is the clear lag between the amplitude of the envelope spectrum obtained with different sensors. On the other hand, the use of accelerometers is clearly more beneficial than using strain gauges  
Figure 11: Envelope spectrum analysis for the 12 accelerometers (layout scheme 2) for the Alfa Pendular and the freight wagon, considering the unevenness profile of the track for (**a**) a defective wheel Alfa Pendular, (**b**) a healthy wheel Alfa Pendular, (**c**) a defective wheel freight wagon, and (**d**) a healthy wheel freight wagon.  
to perform an envelope spectrum analysis for the detection of defective wheels, since the amplitude observed in the scenario with defective wheel scenario is considerably higher than that obtained with a healthy wheel, making the amplitude indicator also suitable when using this kind of layout scheme.  
As demonstrated in a previous study [37], the time-domain response is not suitable to distinguish a healthy from a defective wheel due to the noise contamination of the signal. Therefore, some signal processing is required to extract fault detection under this situation. Figure 14 shows the kurtosis values for signals with and without noise for the Alfa Pendular passage for layout scheme 2. As presented in this figure, the noise-free signal is significantly more impulsive, causing the envelope spectrum analysis to effectively detect the fault. As an example, regarding accelerometer 9, when the signal is not marked by noise, the kurtosis value is approximately 2400.  
When a 20% noise contamination is imputed to the signal, the kurtosis value decreases to 400 in relation to the noise-free signal, but the pattern remains constant, and the maximum kurtosis value corresponds to accelerometer 9, which is closer to the impact of the flat. This means that the framework is effective even when the noise-to-signal ratio is high.  
Figure 12: Envelope spectrum analysis for the 12 strain gauges (layout scheme 1) with different noise intensities and considering a defective and healthy wheel of the Alfa Pendular train and the freight wagon.