# A Review in Fault Diagnosis and Health Assessment for Railway Traction Drives
## 3 Fault Diagnosis in Railway Systems  
A variety of fault diagnosis approaches has been used for electric and mechanical parts in Railway Systems. Apart from Railway Traction drives, which will be reviewed in the following section, previously mentioned FDI approaches have been applied to other parts of Railway Systems. In [52; 53], a vision-based condition monitoring is applied in order to detect faults in railway lines. An online-monitoring is proposed in [54] for rail fasteners, analysing acceleration signals with wavelet transform. Wavelet transform [55] allows analysing a signal by mean of a variable time  
Figure 7: Integration of failure mode and effects analysis (FMEA) and fault injection for maintenance [48]. window and different scaling, inversely proportional to frequency, as it is shown in (3) for continuous wavelet transform. \[wt(s,\tau)=\frac{1}{\sqrt{s}}\int_{-\infty}^{\infty}x(t)\Psi^{*}\bigg{(}\frac{t- \tau}{s}\bigg{)}dt, \tag{3}\]  
being \(\Psi^{*}\big{(}\frac{t-\tau}{s}\big{)}\) the complex conjugate of wavelet basis for the time translation \(\tau\) and scaling \(s\) and \(x(t)\) the signal to transform. One of the applications of wavelet transform is the suppression of the noise in the original signal. Based on wavelet transform, Wavelet Packet Transform (WPT) improves the resolution for high-frequency region. The signal is decomposed into approximation and detail signals, then the detail signals are limited to a threshold and finally the signal is reconstructed based on approximation and detail signals. In case of fault detection applications, a suitable wavelet basis should be chose in order to classify between fault-free and faulty cases. Wavelet basis could be selected to identify changes in entropy, energy and so forth. In [56] WPT energy is applied to vibrations signals in combination with neural networks, in order to detect faults in the axle of bogies. Vibration signals are analysed by mean of another signal-based approach, an improved Minimum Entropy Deconvolution (MED) [57], in order to detect faults in bearing. The method presented improves the fault diagnosis in case of low signal-to-noise ratio compared to classical MED. On the other hand, among the statistics-based approaches, in [58] Principal component analysis (PCA) is used for railway line fault detection. PCA [59] is multivariate statistical method, where the data, normally normalized and based on a large quantity of observations and variables, are representing in a new space, with a lower dimension than the original one and given by principal vectors. PCA decomposes the data into two matrices, one including the score vectors, which represent the data in the new space and another one for the loading or principal vectors. A variety of decomposition algorithms are used to obtain the principal components, in order to improve the detectability of variations in the data, setting the component with major changes in horizontal axis and the second one with major changes in vertical axis, as it is shown in the example, based on motor phase currents, in Figure 8. PCA approach needs historical fault-free data for fault detection. First, an offline step based on fault-free data, in order to obtain the fault detection threshold, then an online step to compare the actual data to the threshold for fault detection. Among others, [PERSON]'s T\({}^{2}\) and squared prediction error (SPE) statistics tests are used for threshold setting and fault detection. A variation of PCA is applied in [60] in order to detect faults in transformers, being more adequate when data have complex non-linear relationship. In [20] the data for railway point machine (RPM) replacement is obtained based on electric current monitoring and Shapelet method. Training data is required for its application too. Figure 8: Scores of principal component analysis (PCA) application for an unbalance in an induction motor phases for an operation point.