# Fault Prediction of Mechanical Equipment Based on Hilbert-Full-Vector Spectrum and TCDAN
## 5 Conclusions  
In this paper, the Hilbert-full-vector spectrum is used to extract the spectrum information of equipment. Compared with the traditional Hilbert-envelope spectrum, the Hilbert-full-vector spectrum fuses the vibration data of the dual channels of the equipment, which can more comprehensively reflect the actual operational state of the equipment as a fault-prediction feature. In addition, combined with the two-layer attention mechanism, a temporal convolutional network is used to predict the amplitude corresponding to different characteristic frequencies of the device. Compared with TCN, GRU, BiLSTM, and LSTM models, the TCDAN model proposed in this paper can effectively extract the correlation between different variables in historical data, different time step data, and predictor variables, to adjust the corresponding weight size, and has higher prediction accuracy.  
Through the prediction of the amplitude corresponding to the characteristic frequency of the equipment, the fault trend of the equipment can be intuitively seen, and the specific part of the equipment fault can be judged according to the characteristic frequency, which provides a more effective decision-making basis for the predictive maintenance of the equipment. In the future, the correlation between the amplitude corresponding to different characteristic frequencies and the fault degree will be studied, so that the alarm threshold corresponding to the amplitude of different characteristic frequencies can be set for better application in actual production.  
Conceptualization, L.C. and L.W.; Designed and performed the experiments, L.W. and W.L.; Writing--original draft, L.W. and W.L.; Writing--review and editing, D.H. and J.W., Supervision, L.C. All authors have read and agreed to the published version of the manuscript.  
This work is partially supported by the National Natural Science Foundation of China (51775515), Key Scientific and Technological Projects in Henan Province (182102210016) and the National Key Research and Development Project of China (2016 YFP0203104-5).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**MAPE(\%)**} \\ \cline{2-7}  & \(\mathbf{1\times\mathbf{fi}}\) & \(\mathbf{2\times\mathbf{fi}}\) & \(\mathbf{1\times\mathbf{fi}}\) & \(\mathbf{2\times\mathbf{fi}}\) & \(\mathbf{1\times\mathbf{fi}}\) & \(\mathbf{2\times\mathbf{fi}}\) \\ \hline TCDAN & 0.0471 & 0.0496 & 0.0583 & 0.0609 & 9.69 & 6.27 \\ TCN & 0.0534 & 0.0735 & 0.0653 & 0.0836 & 11.39 & 9.09 \\ BiLSTM & 0.0921 & 0.0958 & 0.1151 & 0.1168 & 17.51 & 11.75 \\ LSTM & 0.0926 & 0.1386 & 0.1079 & 0.1704 & 22.79 & 16.55 \\ GRU & 0.1300 & 0.1910 & 0.1522 & 0.2292 & 27.29 & 22.75 \\ \hline \end{tabular}
\end{table}
Table 3: Evaluation metrics of different prediction models for Bearing 2_1.  
Data Availability Statement: Publicly available datasets were analyzed in this study. XJTU-SY bearing datasets are provided by the Institute of Design Science and Basic Component at Xi'an Jiaotong University (XJTU), Shaanxi, China and the Changxing Sumyoung Technology Co., Ltd. (SY), Zhejiang, China. XJTU-SY bearing datasets can be found here: [[http://biowang.tech/xjtu-sy-bearing-datasets](http://biowang.tech/xjtu-sy-bearing-datasets)]([http://biowang.tech/xjtu-sy-bearing-datasets](http://biowang.tech/xjtu-sy-bearing-datasets)) (accessed on 21 February 2023).  
The authors declare no conflict of interest.