# A Review in Fault Diagnosis and Health Assessment for Railway Traction Drives  
[PERSON]  
1 Faculty of Engineering, Mondragon Uniberstitatea, 20500 Arrasate-Mondragon, Spain; [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (G.A.) 1 Faculty of Engineering, Mondragon Uniberstitatea, 20500 Arrasate-Mondragon, Spain; [EMAIL_ADDRESS] (J.P.); [EMAIL_ADDRESS] (P.M.); [EMAIL_ADDRESS] (J.d.O. ); galmandoz@[EMAIL_ADDRESS] (G.A.) 1 Faculty of Engineering, Mondragon Uniberstitatea, 20500 Arrasate-Mondragon, Spain; [EMAIL_ADDRESS] (J.P.); [EMAIL_ADDRESS] (P.M.); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (G.A.) 1 Faculty of Engineering, Mondragon Uniberstitatea, 20500 Arrasate-Mondragon, Spain; [EMAIL_ADDRESS] (J.P.); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (J.d.O. ); [EMAIL_ADDRESS] (G.A.) 1 Faculty of Engineering, Mondragon Uniberstitatea, 20500 Arrasate-Mondragon, Spain; [EMAIL_ADDRESS] (J.P.); [EMAIL_ADDRESS] (J.d.O. );for fault detection, as it is shown in Figure 1. Analytical models are mainly developed by structural approaches [6], based on consistency relation and observer-based approaches [7]. Residual evaluation is done using norms or statistical methods [8]. Some statistical methods are Hypothesis tests or Likelihood ratio (LR). Likelihood ratio is given by Equation (1), being \(p\) the probability density for a normal distribution \(\mathrm{N}\big{(}\mu,\sigma^{2}\big{)}\), where \(\mu\) is the mean value and \(\sigma^{2}\) is the variance. Probability density is given by Equation (2) to evaluate the residual \(r\). Thus, \(p(r)\) gives the probability of a given sample of the residual to be within the normal distribution \(\mathrm{N}\big{(}\mu,\sigma^{2}\big{)}\). On the other hand, LR shows which of the compared probability densities is more probable. For example, if a faulty case given by \(p_{1}\) is compared to a fault-free case given by \(p_{0}\), as it is shown in Equation (1), in case that the \(LR(r)>0\) faulty case is accepted, as \(p_{1}\) is more probable than \(p_{0}\), otherwise it is a fault-free case. \[LR(r)=\ln\frac{p_{1}(r)}{p_{0}(r)}\, \tag{1}\]  
being \(p_{1}\) and \(p_{0}\) the probability density of the residual for two normal distributions, for example, faulty and a fault-free cases. \[p(r)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(r-\mu)^{2}}{2\sigma^{2}}}, \tag{2}\]  
being \(\mu\) and \(\sigma^{2}\) the mean value and variance of the normal distribution to which the residual will be compared. On the other hand, in data-driven approaches, it is assumed that a fault alters some of the measured signals, so features for fault detection are obtained from those signals, using mainly signal processing or statistics. In case of data-driven approaches, a fault-free training is required in order to get a pattern. In case that fault detection can be done by analysis of just one signal, signal-based approaches can be used. In contrast to other Data-driven approaches, Signal-based approaches are based on signal processing and they do not need a previous training. Fusion of different FDI approaches are presented in [9]. Fusion can benefit from advantages of different FDI approaches. A review of different FDI approaches is presented in [10]. Based on [11], a classification of main FDI approaches is shown in Figure 2, although there are other techniques, such as artificial intelligence based [12], bond graph [13] or hybrid approaches [4], which are not presented. Diagnostic observers for model-based approaches, PCA for data-driven and Motor current signature analysis (MCSA) for signal-based are some of the most usual FDI approaches in electric drives. Figure 1: Model-based fault diagnosis. Furthermore, there are review articles related to fault diagnosis in renewable energies applications [14; 15] and aerospace applications [16], as well as a review in Railway applications but focused on the wheel-rail and suspension health monitoring [17].