## 5 Conclusions  
In this paper, a working condition recognition method based on DSFF-DenseNet-DT for the mineral flotation process is proposed, addressing the problem that the shallow  
Figure 14: Comparison of CTD-DT, SD-DT and DenseNet-DT results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Accuracy** & **Precision** & **Recall** & **F1 Score** \\ \hline CTD-DT & 75.3\% & 70.7\% & 72.45\% & 0.716 \\ SD-DT & 80\% & 80.8\% & 77.25\% & 0.789 \\ DenseNet-DT & 86\% & 79.6\% & 80.75\% & 0.802 \\ SFF-DT & 85.3\% & 84.7\% & 84.6\% & 0.847 \\ DSFF-DenseNet-DT & 92.67\% & 93.9\% & 94.2\% & 0.941 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of DSFF-DenseNet-DT with other different methods in terms of accuracy, precision, recall and F1 score.  
features of flotation froth images extracted by digital image processing technology in the past contain excessive redundancy and noisy information. Through the two-stage feature fusion method based on Cat-SAE, extracted shallow features such as color texture and size are first fused to reduce dimensionality, and 15-dimensional fusion features are obtained. Then, the fused 15-dimensional features are fused with the deep features extracted by the deep neural network and reduced to obtain a 205-dimensional feature vector, and the fused features have less noisy information and redundant information. Finally, the fused features are fed into DenseNet-DT to achieve working condition recognition. Classification experiments were conducted by using flotation froth images acquired from industrial sites. Compared with the CTD-DT (75.3%) and SD-DT (80%) recognition methods, the recognition accuracy of DenseNet-DT (86%) has been greatly improved, demonstrating that detailed froth image features can be extracted more effectively using the deep learning network. Compared with other recognition methods, the recognition accuracy of SFF-DT (85.3%) and DSFF-DenseNet-DT (92.67%) is highly improved, indicating that the fusion and dimensionality reduction of features can eliminate redundant features and noisy information so as to improve the robustness of the model. The average recognition accuracy, precision, recall and F1 score of DSFF-DenseNet-DT can reach 92.67%, 93.9%, 94.2% and 0.94, respectively. It is able to accurately pinpoint the working conditions of the mineral flotation process, which is conducive to the optimization control of the flotation process and improves the grade of the concentrate.  
Conceptualization, H.L. and M.H.; methodology, M.H. and W.C.; software, H.L. and G.Z.; validation, H.L. and G.Z.; formal analysis, H.L. and M.H.; investigation, M.H., Y.W. and L.L.; resources, M.H. and G.Z.; writing--original draft preparation, H.L. and M.H.; writing--review and editing, M.H., Y.W. and L.L.; supervision, M.H. and G.Z.; project administration, M.H. and G.Z.; funding acquisition, M.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 61703441, and the Natural Science Foundation of Hunan Province, grant number 2021 JJ41087.  
Not applicable.  
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.  
The authors declare no conflict of interest.