## 5 Conclusions  
In this paper, we propose a novel method combining deep learning and multimodal fusion to achieve the robust and accurate fault diagnosis of rolling bearings. The method first extracts essential features from multimodal data through singular spectrum analysis (SSA) then uses different deep learning models to classify data from various modalities. Finally, decision-level multimodal fusion is applied to integrate the outputs of these models, yielding comprehensive and reliable fault diagnosis results. The innovation of our approach lies in its ability to effectively handle and fuse multimodal data, including short-time Fourier images and time series data, using deep learning models. By utilizing recursive gated convolutional neural networks (RGCNNs) and 1D convolutional neural networks (1 DCNNs) as base models, we are able to achieve superior fault classification accuracy compared to conventional methods. Additionally, the decision-level multimodal fusion method based on weighted average fusion optimizes the contributions of both the samples and models, producing a more reliable and accurate diagnosis through weighted voting. Through extensive case analysis of a rolling bearing dataset containing various fault types, we have demonstrated that the proposed method outperforms both individual deep learning models and traditional methods in terms of fault diagnosis accuracy. This improvement is largely due to the integration of multiple deep learning models and the decision-level fusion, which, together, enhance the robustness and accuracy of the diagnostic results. In the future, we plan to expand the scope of this method by incorporating additional time-domain and frequency-domain features for fault diagnosis, as well as exploring its application across the entire lifecycle of rolling bearings, including early-, mid-, and late-stage faults. Furthermore, enhancing the robustness and generalization of the proposed method under different operating conditions will be a critical area of future research. Conceptualization, Y.W. and H.W. ; methodology, Y.W. and H.W. ; software, Y.W. ; formal analysis, X.C. ; investigation, R.B. and Y.S. ; resources, Y.W. ; data curation, Y.W. ; writing--original draft preparation, Y.W. ; writing--review and editing, Y.W. ; visualization, Q.X. ; supervision, Y.W. ; project administration, H.W. ; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript. This work was supported by the Xinjiang Uygur Autonomous Region Natural Science Foundation Project (2022D01C390) and partially by the Xinjiang Uygur Autonomous Region Key Research and Development Project (2022B02016-1). Not applicable. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Dataset** & \multicolumn{6}{c}{**Pade**} & \multicolumn{6}{c}{**Ottawa**} \\ \hline
**Method** & **ResNet34** & **Efficient** & **Mobile** & **Mobile** & **Shuffle** & **MFFD** & **ResNet34** & **Efficient** & **Mobile** & **Mobile** & **Shuffle** & **MFFD** \\  & **Net** & **Net** & **Net-L** & **Net** & **Net** & **Net** & **Net-S** & **Net-L** & **Net** & **Net** & **MFFD** \\ \hline Accuracy & 95.52 & 97.18 & 97.01 & 97.59 & 96.10 & 98.75 & 95.85 & 96.32 & 96.68 & 98.17 & 97.51 & 99.00 \\ \hline Precision & 0.9586 & 0.9722 & 0.9702 & 0.9763 & 0.9627 & 0.9887 & 0.9600 & 0.9629 & 0.9685 & 0.9821 & 0.9753 & 0.9910 \\ \hline Recall & 0.9554 & 0.9733 & 0.9710 & 0.9755 & 0.9609 & 0.9871 & 0.9590 & 0.9733 & 0.967 & 0.9816 & 0.9744 & 0.9898 \\ \hline F1 & 0.9554 & 0.9718 & 0.9698 & 0.9752 & 0.9609 & 0.9877 & 0.9584 & 0.9632 & 0.9667 & 0.9816 & 0.9747 & 0.9903 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison with different models. **Informed Consent Statement:** Not applicable.