## 3 Experiments and Datasets
### Case 2: Validation with Rail Crack Signals and Actual Additive Railway Noises  
In order to investigate the proposed method in real operating conditions, AE wheel-rail noise signals were acquired from an actual rail line in Jiaozuo, Henan province [30]. The rail tracks were made up of 60 kg/m rails and the material U75V. The tracks were examined to ensure they were intact in advance. As is shown in Figure 6a, the experiment is carried out when a passenger train is passing. The speed of the passenger locomotive is about 55 km/h. The sensor was fixed on the rail waist by the mechanical clamp, and couplant was used to fill between the sensor and rail surface for better signal transmissibility.  
AE signals were obtained through the acquisition system with a sampling rate of 5 MHz (Model: Vallen AMSY-6 ASIP-2/A; Vallen Systeme GmbH; Wolfratshausen, Germany). One receiving sensor is attached to the rail waist with a wideband of 100-900 kHz (Model: PAC WS\(\alpha\); Mistras Group, Inc.; Princeton Junction, NJ, USA). The signals were continuously collected under the interference of a variety of real noises caused by wheel-rail contact movements. An example of 9 s of continuous, pure, actual railway noise is shown in Figure 6b, and the noise test sets with 100 test noise samples were randomly selected and truncated from the raw continuous noise signal, as shown in the subfigure. Each sample was truncated to a length of 0.4 ms and used to generated synthetized noisy signals with 100 random AE crack signals for a systematic evaluation of the different methods. In on-site railways, the AE noise components are typically complex. In practice, noise signals comprise both stationary/periodic noise and non-stationary/impulsive noise [31]. The stationary noise is generally attributed to normal wheel-rail interactions, such as rolling contacts. In contrast, impulsive noise arises from abnormal interactions, such as braking, impacts, and severe friction, often exhibiting characteristics in the high-frequency band and even overlapping with the defect spectrum.  
Using the smoothed pseudo Wigner-Ville distribution for time-frequency transformation, the spatial time-frequency distributions of an exemplified rail crack signal, periodic, and abnormal noise signals from the datasets are shown in Figure 7. A typical observation mixture of the actual signals, composed of the sources in Figure 7, is shown in Figure 8. In Figure 7a, the rail crack signal exhibits a non-stationary, wideband characteristic, and the dominant component of actual railway noise shows a relatively low-frequency characteristic. Moreover, as shown in Figure 7c, there also exists some unpredictable short-term abnormal impulsive noise, which also has an obvious non-stationary characteristic and overlap band with the defect signals, further hindering the separation with typical linear filters. Therefore, the overall separation performance will be illustrated later.  
Figure 6: (**a**) Photo of acquiring actual AE noise signals from the on-site experiment with a passing locomotive; (**b**) an example of 9 s of continuous pure actual railway noise and generated noise test sets.