## 5 Axial Piston Pump Simulation Test
### Performance of the Proposed DTW-RCK-IF Composite Method in This Article  
#### 5.3.1 Overall Performance  
Following the aforementioned comparative validations, it was found that compared to the fixed-length partitioning method, the DTW algorithm for data partitioning yielded more similar data segments. In contrast to traditional time domain feature extraction and dimensionality reduction methods, the random convolutional kernel feature extraction method of the CNN was proven to be more effective in capturing local features in time series data, thereby enhancing the model generalization and robustness. Furthermore, compared with the OCSVM algorithm, the isolation forest anomaly detection method demonstrated excellent performance for large-scale datasets and high-dimensional feature spaces. The operational data of axial piston pumps are typically manifested as time series data. Considering the dynamism and variability within the data, the DTW algorithm was introduced to delineate matching data patterns. The CNN, which automatically extracts features and captures local patterns from time series data, proved effective in discerning key features for enhanced anomaly detection. The incorporation of random convolutional kernels introduced a degree of randomness that fostered model diversity and robustness. This became particularly significant in the context of potentially complex patterns and noise within the axial piston pump data, thereby improving the adaptability of the model. The isolation forest algorithm is an effective anomaly detection method that can swiftly \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**OCSVM**} & \multicolumn{3}{c}{**Isolation Forest**} \\  & **P** & **R** & **F1** & **P** & **R** & **F1** \\ \hline normal & 100.00 & 65.85 & 79.41 & 100.00 & 73.17 & 84.51 \\ swashplate wear & 74.55 & 100.00 & 85.42 & 78.85 & 100.00 & 88.17 \\ sliding shoe wear & 74.55 & 100.00 & 85.42 & 78.85 & 100.00 & 88.17 \\ single-plunger loose shoe & 74.55 & 100.00 & 85.42 & 78.85 & 100.00 & 88.17 \\ average & 80.91 & 91.46 & 83.92 & **84.14** & **93.29** & **86.51** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of different anomaly detection methods. and accurately identify anomalous samples. Given the critical nature of promptly detecting abnormal patterns or fault states in data collected from axial piston pumps, the isolation forest algorithm provides valuable support. In summary, the combination of DTW, a CNN with random convolutional kernels, and the isolation forest algorithm effectively leverages their respective strengths. This combination proved to be highly applicable to the anomaly detection problem of axial piston pumps. These methods handle time series data in depth, automatically extract features, enhance model robustness, and facilitate efficient anomaly detection. Consequently, the final experiment adopted the DTW-RCK-IF composite method for anomaly detection. A baseline comparison was performed with traditional anomaly detection methods, such as the LOF, OCSVM, and isolation forest algorithms, and the results are presented in Table 5.  
The results show that the anomaly detection method combining the DTW algorithm and random convolutional kernel feature extraction, as well as the isolation forest algorithm, has an average of 98.22% precision, 99.39% recall, and 98.79% F1 score for the four working conditions compared with the isolation forest algorithm. For the same dataset, the average precision increased by 14.08%, the average recall increased by 6.1%, and the average F1 score increased by 12.28%. This further validates the superior performance of the CNN with random convolutional kernels for feature extraction. This also underscores the enhanced capability of the method in recognizing normal data and its high accuracy in identifying various abnormal states, thereby affirming its robustness.