# Research on the Remaining Life Prediction Method of Rolling Bearings Based on Multi-Feature Fusion
## 4 Experimental Verification
### Case Study 1: Predicting the RUL of Bearings Using the PHM 2012 Dataset
#### 4.2.2 Analysis of Projected Results  
To comprehensively evaluate the performance of our prediction network, we carefully selected bearing vibration data from two different operating conditions, namely Condition 1 and Condition 2. Under these two conditions, we conducted five test experiments on each bearing to ensure the reliability of the data and the stability of the experimental results. Notably, in each experiment, we used a brand-new, untrained network. This approach was taken to ensure the consistency and repeatability of our experimental results. When testing a specific bearing data set, we used the data from all other bearings to train the network. For example, if bearing A1-1 was chosen as the test set, then bearings A1-2, A1-3, A1-4, A1-5, A1-6, and A1-7 were used as the training set. This strategy ensured \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Operating Condition**} & **A1** & **A2** & **A3** \\ \cline{2-4}  & **1800 r/min** & **1650 r/min** & **1500 r/min** \\  & **4000 N** & **4200 N** & **5000 N** \\ \hline \multirow{4}{*}{Bearing} & Bearing A1-1 & Bearing A2-1 & Bearing A3-1 \\  & Bearing A1-2 & Bearing A2-2 & Bearing A3-2 \\ \cline{1-1}  & Bearing A1-3 & Bearing A2-3 & Bearing A3-3 \\ \cline{1-1}  & Bearing A1-4 & Bearing A2-4 & \\ \cline{1-1}  & Bearing A1-5 & Bearing A2-5 & \\ \cline{1-1}  & Bearing A1-6 & Bearing A2-6 & \\ \cline{1-1}  & Bearing A1-7 & Bearing A2-7 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The FEMTO-ST bearing dataset’s operating conditions. Figure 9: PHM 2012 dataset-bearing test bench. that each bearing data set could be used both for training and testing, maximizing the utilization of data and enhancing the effectiveness of the experiments. To demonstrate the effectiveness of our method, we selected four different approaches and compared their RUL prediction results with our multi-feature fusion-based prediction results. The specific comparison results are shown in Table 3.  
In this experiment, a total of 14 bearings were examined. As Table 3 illustrates, for most of the tested bearings, the proposed approach's MAE and RMSE are less than those of the comparison method, and as Figure 10 illustrates, the proposed method's average RMSE and MAE are the lowest while its score is the greatest. The approach suggested in this paper has greater score values than the comparable methods, except that the score of tests bearing A1-1 is lower than that of TCN-RSCB and the score of tests bearing A2-3 is the same as that of TCN-RSCB. The aforementioned experimental findings demonstrate that the proposed method has the greatest prediction performance because the multi-sensor data fusion method effectively fuses multi-sensor data, and in the multi-feature fusion network, we designed a parallel TCN-LSTM-Transformer feature extractor. Where TCN extracts the data's long-term sequence features, LSTM captures the time-dependent features in the sequence data, and Transformer extracts the global feature representation of the bearing data. Meanwhile, a parallel multi-scale attention mechanism is designed that captures both local and global dependencies to go a step further in capturing the global and local contextual information of the sequence in order to accomplish the three feature extractors' output features' adaptive weighted fusion. Secondly, the shallow features obtained from the parallel feature extractor are residually connected to the deep features through the attention mechanism to improve the efficiency of utilizing the information of the front and back features, and finally, the RUL's output is used in the fully connected layer. Among them, CNNs face the drawbacks of insufficient modeling power for long-term dependence, fixed sense field size, a large number of parameters, and translational invariance, leading to poor RUL prediction when dealing with time series data.