# RUL Prediction of Rolling Bearings Based on a DCAE and CNN
## 4 Prediction of the RUL Based on 1D-CNN  
The prediction process of the RUL of the rolling bearing based on the 1D-CNN is shown in Figure 11. After the segmented processing of the original data, labels were added to the original data using the constructed HI value. The labeled data were directly input into the 1D-CNN model, and the output of the model was the predicted value of the remaining life of the bearing reflected by the vibration signal at the input time. There are two key factors in training a good intelligent diagnosis model or RUL prediction model based on deep learning methods: one is whether the selection of the algorithm is suitable for the data sample, and the second consideration is the data quality. This is because in an actual industrial environment, the data volume of the whole life cycle of the mechanical equipment will be enormous. A CNN is characterized by weight sharing and local connections between neurons, making it ideal for processing copious amounts of data. Simultaneously, the original data are the vibration data of a one-dimensional time series. The model uses a one-dimensional convolution operation to directly input the original data into the model, which will not destroy the correlation between data and allows it to acquire the feature information in the data to the maximum extent. Empirically, a model trained on inferior quality data will lead to problems such as low model accuracy, poor generalization ability and overfitting. Currently, in the model training of supervised learning, the data are input into the model with labels, which means that when the data are input into the model, the data are artificially judged, and labels are added [37]. The ability to accurately add labels to the data influences the data's quality and thus affects the effect of the training model. In the problem of predicting the remaining life of mechanical equipment based on a supervised learning model, adding labels to the data is equivalent to modeling the degradation state of the equipment. At present, there are two main ways to add labels [38; 39; 40; 41; 42]. One is to use a linear function, as shown in Figure 12a. The linear function is employed to simulate the linear degradation trend of the bearing, which is defined as  
\[f(t_{i})=-\bigg{(}\frac{1}{t_{n}}*t_{i}\bigg{)}+1 \tag{11}\]  
where \(t_{n}\) is the full lifetime of the bearing and \(t_{i}\) is the current time in the bearing life cycle. In Figure 12a, the ordinate is the label value, and the actual meaning is the RUL. The trend of the degradation rate is linear, which illustrates that the degradation rate is steady. However, the degradation rate of the bearing will not remain unchanged during the operation of the bearing. Figure 11: 1D-CNN structure diagram. The second way is to design a piecewise function to describe the degradation process of the bearing, as shown in Figure 12b. Its definition is written as  
\[f(t_{i})= \begin{cases}1&t_{i}\leq t_{j}\\ \left(\frac{1}{t_{j}-t_{n}}\right)*t_{i}+\left(\frac{t_{n}}{t_{n}-t_{j}}\right) &t_{i}>t_{j}\end{cases}  \tag{12}\]  
where \(t_{j}\) is the initial degradation time of the bearing (i.e., the initial failure point). From Figure 12b, the health degree always remained the same before the time \(t_{j}\) and then linearly descended until the time of \(t_{n}\) (i.e., the total failure of the bearing). This method is also inaccurate. First, it is difficult to select critical points. Secondly, this method ignores the weak information hidden in the early data, and the degradation rate in the accelerated degradation stage is not linear. The model trained by these two ways of adding labels can fit the actual labels in some working conditions, but there are problems in the expression of meaning and practical application. The predicted value of the model only predicts the tag well but may not accurately predict the actual remaining life, and the generalization ability of the model is weak.