# Research on Remaining Useful Life Prediction of Bearings Based on MBCNN-BiLSTM
## 3 Proposed Method  
Although the CNN network has a powerful spatial feature extraction capability, precisely because of its excellent feature learning capability, it may also tend to learn some useless information which is not conducive to the extraction of rolling bearing degradation features. On the other hand, although the BiLSTM network has strong temporal feature extraction ability, its spatial feature extraction ability is inferior to that of the CNN network. Therefore, this paper combines the two and uses a multi-branch approach. The main function of the MBCNN network is to extract spatial features and downsample the data, which plays the role of information refinement. The output is a feature map that is sparser than the original signal, but retains the spatial feature information of the data. The BiLSTM network extracts information that may be ignored by the CNN from both directions of the time series data. The structure of the MBCNN-BiLSTM model is illustrated in Figure 5. The original data and the frequency domain data obtained by fast Fourier transform are used as two branches of input to fully exploit the spatial and temporal feature information. An attention mechanism, GAM, is used to pay more attention to the important features in time and space. Finally, the RUL of the bearing is mapped by full connection to achieve the purpose of improving the accuracy of life prediction.  
Figure 4: GAM network structure.  
Figure 3: BiLSTM network structure.  
Figure 6 presents the flow chart of the proposed prognostic method.  
The exact steps for the proposed approach to prediction are listed in the following:  
* Step 1. The fast Fourier transform is performed on the bearings' originally vibrating signal to acquire the frequency domain signal, dividing the dataset into training set and test set based on the original signal and frequency domain signal. With the aim of improving the speed of training convergence of the network, the original vibration signal and the frequency domain signal are normalized. The data are preprocessed with the Z-Score normalization method. After normalization, the data exhibit a  
Figure 5: MBCNN-BiLSTM model network structure.  
Figure 6: Flow chart of the proposed method for prognostics.  
distribution with a mean of 1 and a standard deviation of 0. The equation is shown as follows: \[x_{norm}=\frac{x-\mu}{\delta}\] (9) where \(x\) denotes the data sample; \(\mu\) denotes the mean of the data sample; \(\delta\) denotes the standard deviation of the data sample; \(x_{norm}\) denotes the normalized data sample.
* Step 2. According to the RUL \"end-to-end\" prediction method, the bearing RUL labels are normalized and mapped to the range of 0-1, as follows: \[L_{i}=\frac{N-T_{i}}{N}\] (10) where \(N\) denotes the total number of sampling points of the vibration signal for the whole life cycle of the bearing, that is, the actual RUL length of the bearing; \(T_{i}\) is the \(i\)-th sampling point; \(L_{i}\) is the bearing life label of the \(i\)-th sampling point. In this paper, the full-life degradation data of the bearing are mapped between 0 and 1. When the life label \(L_{i}\) = 1 at the \(i\)-th time point, the bearing is a brand-new bearing. When \(L_{i}\) = 0, the bearing has been completely damaged.
* Step 3. The data are divided according to the length of the set time window, and the data in each time window have a time order.
* Step 4. Model training. According to the MBCNN-BiLSTM model structure, the training hyperparameters are configured. The optimization algorithm of back propagation is used in the training period to optimize the network weights according to the loss function taking the minimum value, i.e., the minimum error of RUL between the true and the predicted.
* Step 5. Model evaluation. The data from the test set are input to the trained model to acquire the prediction results. The RUL prediction evaluation metrics are calculated according to the predicted and true values to get the RUL prediction performance of the model.