## 6 Conclusions  
This paper proposes a passive acoustic method based on deep learning to monitor potential fault states in distillation columns. Acoustic signals from the target distillation column in different operating states were collected, processed, and analyzed using the proposed method, with MFCC feature maps extracted. These feature maps were used as the dataset for training a residual network.  
The trained residual network model achieved an average accuracy, precision, recall, and F1 score of 99.03%, 96.83%, 96.76%, and 96.79% on the test dataset, demonstrating excellent performance. Compared to the 97.25% model accuracy achieved by the MSVM method used in previous similar studies [4], this method shows a significant performance improvement of 1.78 percentage points. The use of MFCC spectrogram datasets eliminates the need for manual design and the selection of multiple features, highlighting the advantage of the proposed deep learning method in reducing the workload of feature engineering. Additionally, by diagnosing three different potential faults, the proposed method effectively predicted faults in upper flooding, lower flooding, and leakage conditions. This research not only improves the accuracy of fault detection but also reduces the complexity of manual feature design, making the technology more efficient for industrial applications.  
Considering that actual distillation processes in production may be more complex, several recommendations for future work include the following:  
Industrial application and promotion should be considered. Collaboration with industry can facilitate experimentation and validation in more real production scenarios, collecting more field data to optimize model parameters and advancing the application of this technology in real production environments.  
Future work could extend the scope to monitoring and diagnosing more types of potential faults, enhancing the comprehensiveness of the system.  
Data augmentation and enhancement should be considered in practical applications. The characteristics of infrequent faults are difficult to capture in actual production, but simulation experiments or data augmentation techniques can enhance the model's robustness against these rare faults.  
The operational states in actual distillation processes might be more finely divided, requiring feature extraction methods with higher performance. Exploring advanced noise reduction techniques could play a crucial role in this context.  
Figure 13: (**a**) The confusion matrix and (**b**) normalized confusion matrix obtained through the CNN model.  
**Author Contributions:** Conceptualization, H.W. and H.Z.; methodology, H.W.; software, H.Z.; validation, Z.Z., G.W. and H.W.; formal analysis, H.Z.; investigation, H.W.; resources, G.W.; data curation, H.Z. and Z.Z.; writing--original draft preparation, H.Z.; writing--review and editing, H.W.; visualization, H.Z.; supervision, H.W. and G.W.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 22308079; the Natural Science Foundation of Hebei Province, China, grant number B2022202008 and B2023202025; the Science and Technology Project of Hebei Education Department, China, grant number BJK2022037.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.