# A Hierarchical Decision Fusion Diagnosis Method for Rolling Bearings
## 2 Method
### Hierarchical Fault Diagnosis Strategy  
The traditional fault diagnosis method based on machine learning is to consider the fault position and severity synthetically. However, most of the rolling bearings are in normal condition, the fault occurs by chance and the evolution of the fault degree is nonlinear. In addition, in the actual process, the complete bearing fault samples are difficult to obtain. In this case, the fault diagnosis network that can judge the fault at the same time is often difficult to train because of the complexity of its network structure. In this paper, the hierarchical fault diagnosis architecture of rolling bearings is proposed, and the hierarchical diagnosis of rolling bearings is carried out in the progressive way. Further, the fault diagnosis of rolling bearings is divided into three layers: the first layer is the fault detection layer, which is used to judge whether the current state of the bearing is normal or not. The second layer is the fault isolation layer, and its goal is to identify the fault position of the bearing diagnosed as having a faulty state in the first layer. The third layer is the fault degree estimation layer, which is to further estimate the severity of the fault position of the rolling bearing. The advantages of the hierarchical diagnosis proposed in this paper are as follows: the function of each layer of the neural network is relatively simple, the corresponding level of fault diagnosis network is trained by using the obtained fault samples, and the network training time is reduced. It is also relatively easy to improve the accuracy of fault identification. In addition, updating the fault algorithm is relatively easy, as it is only necessary to retrain the affected neural network to achieve the algorithm update, compared with the traditional diagnosis method; it also has better flexibility. Hierarchical decision fusion fault diagnosis methods include a training stage and a diagnosis stage. Step 1: Generate training samples. According to the hierarchical fault diagnosis architecture, five kinds of training samples are designed, including a bearing state training sample, fault position training sample, inner race fault degree training sample, ball fault degree training sample and an outer race fault degree training sample. Step 2: Wavelet packet decomposition. Selecting the appropriate wavelet basis and the number of decomposition layers, each kind of sample data is decomposed into a wavelet packet, and the raw signal is decomposed into a series of reconstructed signals with equal bandwidth. Step 3: Feature extraction. There are \(m\) features extracted from the wavelet packet reconstruction signal, and the feature set \(F=\{F_{1},F_{2},\ldots,F_{m}\}\) is obtained. The dimension of the feature subset \(F_{j}\) (\(j=1,2,\)\(\ldots,m\)) depends on the number of decomposition layers \(n\) by the wavelet packet. In this paper, all the training samples are decomposed by three-layer wavelet packets. Hence, \(s=8\), and the feature subset can be described as \(F_{j}=\{F_{j}^{1},F_{j}^{2},\ldots,F_{j}^{8}\}^{T}\). Step 4: Normalization. Because neurons are highly sensitive to numbers in the range of \([-1,1]\), the bearing feature data cannot be directly input into the BPNN, so it is necessary to normalize the feature set. The min-max normalization method is used in this paper. \[\overline{u}=\frac{u-u_{\text{min}}}{u_{\text{max}}-u_{\text{min}}} \tag{12}\]  
Figure 4: Training process of the hierarchical decision fusion fault diagnosis method. where \(u\) and \(\overline{u}\) are the original data of the feature set and the normalized data, respectively. \(u_{\text{max}}\) is the maximum value in the original feature set, and \(u_{\text{min}}\) is the minimum value in the original feature set. Here, \(u\) represents the feature value \(F_{j}^{s}\) and \(\overline{u}\) represents the normalized eigenvalue \(X_{j}^{s}\). Step 5: Train BPNNs.