# Research on the Remaining Life Prediction Method of Rolling Bearings Based on Multi-Feature Fusion
## 3 Prediction of RUL Based on the Multi-Feature Fusion Method
### RUL Forecast  
Figure 5 illustrates the procedure for model training and predicting the RUL. The fusion of bearing vibration data obtained from multiple sensors yields multi-sensor fusion data. Consequently, this leads to the fulfillment of the prediction objective. In the RUL prediction process in Figure 5, the gathered bearing vibration data from many sensors is combined via fusion, resulting in multi-sensor fusion data. This data is then separated into training-bearing data and test-bearing data to construct the prediction network. In the offline modeling process, the training data are input into the parallel feature extractor and trained several times. The training process calculates the loss function and backpropagation to adjust the model parameters, and once the number of training iterations exceeds the total number of training iterations, the model finishes the training process. In the online prediction process, the trained prediction network model is used to make real-time predictions by inputting test data. Furthermore, assessment indicators are established to validate the model's predictive performance. Ultimately, the forecast outcomes are presented in a graphical representation. In this study, bearings' complete life cycle information is used to educate the network. The advantages are: (1) Complete life cycle data encompasses every conceivable bearing failure. Therefore, the examination of complete life cycle data will facilitate a more exhaustive surveillance of the bearing's condition. (2) It has been noted that the duration between the initial injury and the ultimate failure of a bearing is exceptionally brief. Damage can spread rapidly, particularly when the bearing is on the verge of total failure. Hence, predicting the RUL before the onset of deterioration may provide enough time to schedule equipment repair. (3) [PERSON] et al. (2016) used the concept of first prediction time (FPT) to classify life cycle data into two distinct stages: healthy and deteriorated. However, accurately establishing the FPT is a challenging endeavor that may require a significant increase in effort to calculate it manually. This research circumvents this issue by training the network utilizing comprehensive data over the whole lifespan. The assessment metrics consist of mean absolute error (\(MAE\)) and root mean square error (\(RMSE\)). These metrics are described as follows:  
\[MAE=\frac{1}{n}\frac{n}{i=1}\Big{|}Rul_{i}^{pre}-Rul_{i}^{act}\Big{|} \tag{19}\]  
\[RMSE=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\sum}}\left(Rul_{i}^{pre}-Rul _{i}^{act}\right)^{2}} \tag{20}\]  
where \(Rul_{i}^{act}\) represents the actual value of the remaining life, \(Rul_{i}^{pre}\) represents the predicted value of the remaining life, and \(n\) represents the overall duration of the prediction, which is equivalent to the number of samples. In addition, early RUL predictions and late RUL predictions have different impacts on the machine during the machinery and equipment's actual operation. Therefore, in the early stages of the machine's life cycle, the weight of the predicted results is reduced, while in the later stages, the weight of the predicted results is increased to capture possible malfunctions and failures of the machine more accurately. The scoring function's definition is extracted from reference ([PERSON] and [PERSON], 2017). The scoring function designed in reference ([PERSON] and [PERSON], 2017) differs from the scoring function in PHM 2012 ([PERSON] and [PERSON], 2017) in that it takes into account the effects of the early stages of the machine lifecycle, the later stages of the machine lifecycle, and the whole lifecycle operation stages. The specific descriptions are shown in Equations (21) and (22):  
\[A_{i}=\left\{ \begin{array}{l}\exp(-\ln(0.6)\cdot\frac{(Rul_{i}^{pre}-Rul_{i }^{act})}{10}),er_{i}\leq 0\\ \exp(\ln(0.6)\cdot(\frac{Rul_{i}^{pre}-Rul_{i}^{act}}{40})),er_{i}>0\end{array} \right.