## 6 Conclusions and Future Work  
In this paper, a novel method named the MDI-CNN that fuses the multidimensional input data is proposed for fault diagnosis. The main advantage of the proposed model is the feature learning of multidimensional data by introducing a fusion model into the traditional CNN. Due to using multiple input layers, the proposed model can extract the features directly from the original vibration signal and avoid information loss. However, it can also automatically and effectively learn complementary and rich fault features of different data types directly from a signal using the multiple input layers, which greatly enhances the ability of feature extraction and fault recognition. In this paper, two experiments with rolling bearings are presented to verify the performance of the proposed model. Based on the experimental results, the following conclusions can be drawn:  
* Compared with the traditional CNN model, the proposed model converges more quickly, has shorter training time, and achieves very good results in mixed fault identification;
* The environmental noise seriously affects the recognition accuracy of the intelligent diagnostic model, and the proposed model can reduce the influence of noise on the recognition results. By using the noise data for incremental training, the fault recognition accuracy of the model is obviously improved; \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Training Set**} & \multirow{2}{*}{**Number of Epochs**} & \multicolumn{2}{c}{**SNR of Noise in**} & \multirow{2}{*}{**Accuracy (\%)**} \\  & & & & **Test Set** & \\ \hline \multirow{6}{*}{2D-CNN} & Two-dimensional & \multirow{2}{*}{20} & None & 93.85 \\  & raw data & & \(-\)10 dB & 48.35 \\ \cline{3-5}  & Two-dimensional & & & None & 99.00 \\  & FFT data & & \(-\)10 dB & 75.40 \\ \cline{3-5}  & Two-dimensional & & None & 97.50 \\  & ESA data & & \(-\)10 dB & 59.85 \\ \hline \multirow{6}{*}{1D-CNN} & One-dimensional & \multirow{2}{*}{20} & None & 96.15 \\  & raw data & & \(-\)10 dB & 54.35 \\ \cline{3-5}  & One-dimensional & & None & 99.85 \\ \cline{3-5}  & FFT data & & \(-\)10 dB & 94.10 \\ \cline{3-5}  & One-dimensional & & None & 96.50 \\ \cline{3-5}  & ESA data & & \(-\)10 dB & 57.55 \\ \hline \multirow{2}{*}{MDI-CNN} & Raw data, FFT data, & \multirow{2}{*}{5} & None & 99.95 \\  & ESA data & & \(-\)10 dB & 95.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Diagnosis results of different models. * Different data processing methods have different effects on diagnosis results of the traditional CNN models. The proposed model can fuse a variety of data and has high fault recognition accuracy, convergence, robustness, and generalization ability, providing a new method for real-time fault monitoring of mechanical equipment. However, two issues need to be addressed in our future work. (1) In the experiments, the weight coefficient of the fusion model was artificially set to a constant value of one, and the other cases were not discussed. (2) The experimental data were collected in a stable environment, and then the Gaussian white noise was added artificially to the original signal to test the model sensitivity to the environmental noise. However, in the actual machining, the environmental noise is complex and changeable, which is very different from the Gaussian white noise. Accordingly, in our future work, we will consider using an optimization algorithm to select the parameters for weight coefficients of the fusion model; also, we will collect the fault data in the actual machining environment to evaluate further the accuracy and robustness of the proposed model. Conceptualization, T.Z., H.W. and M.W. ; Methodology, T.Z. and H.W. ; Software, H.W. and Z.L. ; Validation, T.Z., X.G. and H.W. ; Formal analysis, H.W. ; Investigation, Z.L. ; Resources, X.G. ; Writing--original draft preparation, H.W. ; Writing--review and editing, H.W., M.W. and T.Z. ; Visualization, Z.L. ; Supervision, X.G.