## 4 Discussion  
This comprehensive modeling study confirms that the vibration signals of water pumps can be used to quantitatively evaluate their operating status and the degree of faults they may incur. This paper proposed a method based on a deep learning model to objectively detect and identify such faults, and this model is applied in the field of recirculating aquaculture for the first time. Data from normal operation, minor faults, and serious faults were, respectively, collected to train and test the model, so as to determine the three working condition types of the water pump. The experimental classification results are conveyed in Figure 9, indicating the new model can effectively identify the water pump's working condition types. This demonstrates that the water pump fault detection method based on the CNN-transformer-BiGRU model is effective. To verify the performance and superiority of the model, nine different model validations were carried out and compared (Table 7). It can be seen that the traditional machine learning algorithms, such as the support vector machine (SVM), random forest (RF), and K-nearest neighbors (KNN), perform poorly at the task at hand, likely because the vibration signal data of water pump faults are affected by an array of complex factors, and those algorithms struggle to manually extract the appropriate characteristic information, such as margin factors, pulse factors, and peak-to-peak values [35; 36]. The model proposed in this paper achieved robust performance when applied to the dataset of water pump faults in industrial recirculating aquaculture systems. The results for the test set are consistent with the F1 value curve of the validation set. Compared with the CNN-LSTM, the model in this paper leverages the advantages of the self-attention mechanism and demonstrates better performance. When compared with the Swin-transformer, the model highlights the advantages of the convolutional module in capturing features from time-frequency feature maps. Through experimental tests, we find that several network models, including BiLSTM, KAN-GRU, and CNN-LSTM, attain relatively high accuracy rates. But when these are directly compared with our proposed model, a performance gap persists. Importantly, ablation experiments were also conducted in this study. To conduct these experiments, some of the model's modules were removed for experiments, whose results are compared in Table 8. This clearly shows that removing the CNN led to a significant decline in all indicators of the entire model. The Acc, P, R, and F1 indicators were, respectively, reduced by 8.19%, 7.96%, 8.19%, and 8.07%. From this, we may infer that by converting the complex one-dimensional vibration signals into two-dimensional time-frequency images and then applying the CNN's powerful processing ability to the latter, the fault characteristic information can be efficiently extracted [37; 38]. Hence, the absence of this module has the greatest impact on model performance. After removing the transformer or BiGRU module, all indicators more or less decreased; this suggests \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Acc (\%)** & **P (\%)** & **R (\%)** \\ \hline CNN-Transformer-BiGRU & 91.43 & 91.52 & 91.43 \\ BiGRU & 88.64 & 88.76 & 88.64 \\ Transformer & 87.15 & 87.37 & 87.15 \\ CNN & 83.24 & 83.56 & 83.24 \\ \hline \hline \end{tabular} Note: Acc, accuracy; P, precision; R, recall.  
\end{table} 
Table 8: Results for the accuracy (Acc), precision (P), and recall (R) of the ablation experiment. that the encoder in the transformer improves the model's hierarchical learning ability for features, and the self-attention mechanism strengthens the weights of the key features of the vibration signals. The BiGRU module is capable of more comprehensively capturing the front and back characteristic information in the vibration signal sequence, further enhancing the overall performance of the model [39].