## 7 Conclusions  
An axial piston pump anomaly detection method based on pressure signals is proposed in this paper, namely DTW-RCK-IF. Through a theoretical analysis, modeling simulation tests, and extended application tests, the following conclusions were drawn:  
1. Compared with the fixed-length partitioning method, the data partitioning and matching approach using the DTW algorithm resulted in higher similarity between the partitioned data.
2. Compared with traditional time domain feature extraction and dimensionality reduction methods, a CNN with random convolutional kernel feature extraction can better capture the local features of time series data. This enables the model to learn more effective and comprehensive feature representations, thereby enhancing its generalization capability and robustness.
3. Compared with the OCSVM algorithm, the isolation forest anomaly detection method exhibited superior performance in detecting anomalies in large-scale datasets and high-dimensional feature spaces.
4. For real-time anomaly detection in axial piston pumps, pressure signals outperform vibration signals. The DTW-RCK-IF composite method can efficiently detect anomalies using only data from normal operating conditions. This demonstrates its sensitivity to abnormal data, thereby yielding effective fault-warning capabilities.
5. The DTW-RCK-IF composite method consistently exhibits excellent detection performance when applied to various target objects for anomaly detection, demonstrating its robustness and potential for broad and versatile applications.  
However, the method proposed in this study has some inherent limitations. First, it relies on normal-state data for the training of the model. Consequently, in situations with insufficient normal-state data, the performance of the model may be compromised. Second, although the method demonstrates the improved detection of anomalies for certain complex anomaly patterns, additional domain knowledge may be required to design more effective approaches. In summary, this method requires further comprehensive consideration and evaluation based on specific application scenarios and requirements.  
**Author Contributions:** Formal analysis, L.M.; Funding acquisition, W.J. and S.Z.; Investigation, P.Z.; Methodology, L.M.; Project administration, W.J.; Resources, W.J.; Software, L.M. and Y.Z.; Validation, L.M. and P.Z.; Writing--original draft, L.M.; Writing--review and editing, W.J. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the National Natural Science Foundation of China (Grant Nos. 52275067 and 51875498) and the Province Natural Science Foundation of Hebei, China (Grant No. F2020203058 and E2023203030).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**DTW-RCK-IF**} \\  & **P** & **R** & **FI** \\ \hline normal & 100.00 & 99.46 & 99.73 \\ inner ring fault & 99.47 & 100.00 & 99.73 \\ outer ring fault & 99.47 & 100.00 & 99.73 \\ cage fault & 99.47 & 100.00 & 99.73 \\ average & **99.60** & **99.87** & **99.73** \\ \hline \hline \end{tabular}
\end{table}
Table 11: XJTU-SY bearing abnormal detection results.