## 2 Basic Theory
### Stepwise Intelligent Diagnosis Method Based on SAE  
In the case of sliding bearing fault diagnosis, the fault characteristics of contact rubbing (C) and the oil whirl (O) centralize in low frequency in spectrum; the static unbalance (SU) and the dynamic unbalance (DU) centralize in mid-low frequency in spectrum. Moreover, the characteristics in two kinds of unbalance faults are similar, with no obvious boundaries between each other. Therefore, it can be difficult to identify all of them simultaneously to lead to low diagnosis precision. Inversely, if we identify two states in one step, it can effectively reduce the impact from the shortcomings of fault feature and obtain optimal diagnostic accuracy and efficiency. Therefore, a stepwise diagnosis process is proposed and shown in Figure 4, and there are totally four steps in the diagnosis process. Firstly, the signal is divided into normal state (N) and the abnormal state (AN) according to the health condition of the sliding bearing, if the SAE can correctly distinguish the two states (N and AN), the contact rubbing (C) and the other three faults are structured a set of data to distinguish the contact rubbing (C) and the other two faults (OA). If the diagnosis process can be performed successfully, the oil whirl (O) and the unbalance (U) construct a set of data. If the accuracy can meet the requirements of the practical equipment fault diagnosis, we continue to distinguish the static unbalance (SU) and the dynamic unbalance (DU) according to the same method.  
Figure 4: Stepwise diagnosis process.  
Figure 3: Detailed description of auto-encode (AE).  
Figure 2: Conceptual diagram of the auto-encoder.  
The main tool in stepwise intelligent diagnosis method is SAE that is generated by stacking multiple AEs. It is an effective way to imitate the human brain learning process, and it shows great superiority in capturing the representative information from raw signal [24]. The architecture of SAE is shown in the Figure 5.  
As shown in Figure 5, the fault feature can be extracted by those AEs and the learned features are inputted into the classifier to perform the fault type identification. In this regard, the greedy layer-wise unsupervised learning is employed to extract better feature representations based on AE, receiving an initial parameters for the first layer, and the output of the first hidden layer is employed (a compressive characterization for the inputted signal) as the input for the next AE, similarly initializing the other AEs. Moreover, the simple architecture of the SAE network training learning process is shown in Figure 6, and the black rectangle is the learned AEs.  
As shown in the Figure 6, the output layer of each AE can be removed after finishing the decoder process, remaining a series of cascading models named auto-encoders. Then the successive AEs follow the same transformation conception, and the back-propagation algorithm is applied to globally fine-tune the network parameters to improve the performance of fault diagnosis further. Therefore, SAE is superior to traditional neural network when traditional signal processing method faces with big data contaminated with strong noise, and it can learn the weak features in the raw signal and magnify the useful fault feature information. Therefore, it is suitable to apply to the process of sliding bearing fault diagnosis.