## 4 CRH5 Gearbox Degradation Feature Extraction and Analysis
### Transient Fault Simulation and Deep Learning of Critical Component Degradation Processes  
To accurately describe the degradation process of the key components of the CRH5 gearbox, this study utilizes the transient process at the key stage of component degradation for dynamics simulation, extracts the time-domain vibration acceleration signals at the key stage of component degradation, and trains the degradation characteristics of the key components over the whole life cycle using deep learning.  
Taking the driving gear as an example, according to the relevant literature and field research [35; 36; 37], the degradation process of the gear is found to be driven by pitting and spalling caused by impact-type failures, leading to the uniform wear state characteristic of stable-type failures. Figure 8 shows a schematic diagram of the key stages of degradation such as pitting, spalling, and wear of a single tooth of the driving gear. After remodeling the degradation critical stage, it is imported into ANSYS for meshing and generating a flexible body. The new flexure is imported into ADAMS to replace the normal state driving  
Figure 7: Comparison of actual and simulation frequency-domain curves.  
gear and a dynamic simulation is performed. Its time-domain vibration acceleration signal is extracted for training.  
Since the degradation process of parts is time-sequential and there is a causal relationship between adjacent degradation stages, the training of each piece of transient fault simulation data can also be carried out using the GRU-HMM model proposed in this paper, but the model is only carried out to the initial vector update stage. A convergence optimization function \(F\) needs to be added to the GRU for gear degradation trend training,  
\[F=\theta-\beta\
abla_{\theta}\sum_{T_{i}\sim p(T)}L_{T_{i}}(f_{\theta_{i}}) \tag{21}\]  
where \(f\) is the convergence function, \(\theta\) is the model update gradient after training a set of tasks, \(\beta\) is the step size of the gated neural network, and \(L_{T_{i}}(f_{\theta})\) is the loss of the function after the task \(T_{i}\).  
The training objective of GRU is to minimize the loss; the objective function and the loss function are as follows:  
\[\underset{\theta}{\text{min}}\sum_{T_{i}\sim p(T)}L_{T_{i}}(f_{\theta_{i}})= \sum_{T_{i}\sim p(T)}L_{T_{i}}(f_{\theta-\beta\
abla_{\theta}L_{T_{i}}(f_{ \theta_{i}})}) \tag{22}\]  
\[L_{T_{i}}(f_{\theta})=\sum_{x^{j},y^{i}\sim T_{i}}\left\|f_{\theta}(x^{j})-y^{ j}\right\| \tag{23}\]  
where \(x^{j}\) denotes the \(j\)th data and \(y^{i}\) denotes the relative predicted data.  
Taking the driving gear at 1500 rpm as an example, the time-domain vibration acceleration of the normal state and three degradation state simulations are shown in Figure 9. After training the GRU-HMM model, the time-domain vibration acceleration of the driving gear at 1500 rpm operating conditions for the whole life cycle is shown in Figure 10. The training model for the full lifecycle of degradation was validated using the gearbox dataset from Southeast University, comparing the relevant literature and EMU on-board monitoring data, which proved that this method is feasible [38; 39].  
After remodeling the critical degradation stages of the universal joints, driving gear, and driven gears, the time-domain vibration acceleration at 500 rpm intervals from 0 to 3500 rpm are calculated separately for each component. These will be used in the construction of the hybrid feature domain.  
Figure 8: Critical stages of a single tooth degradation of driving gear. (**a**) Pitting; (**b**) spalling; (**c**) wear.