## 5 Axial Piston Pump Simulation Test
### Comparative Analysis of Experimental Data
#### 5.2.3 Performance Comparison of Different Feature Extraction Methods  
The dataset postsegmented using DTW was directly utilized for anomaly detection using the OCSVM algorithm. Each sample within this dataset comprises continuous time series data encompassing many sampling points. Considering the inherent continuity and high dimensionality of the data, anomaly detection often entails high computational complexity. Consequently, feature extraction was conducted on the segmented data to extract the relevant features. This feature extraction process serves several critical objectives, including bolstering the model's generalization capabilities, optimizing the computational efficiency, and, most importantly, enhancing the precision of the detection outcomes.  
Conventional time domain feature extraction was performed on the partitioned dataset, resulting in a collection of extracted time domain features. This feature set comprised eight quantitative characteristics: maximum, minimum, peak, mean, variance, standard deviation, mean square, and root mean square. In addition, it encompassed six dimensionless features, namely kurtosis, skewness, the waveform factor, the peak factor, the impulse factor, and the margin factor--totaling 14 feature parameters. Subsequently, while ensuring that essential information was retained, principal component analysis (PCA) was employed to reduce the dimensionality of the dataset. After the dimensionality reduction, the number of principal components was set to four.  
Deep learning offers substantial advantages in feature extraction. When a CNN with random convolutional kernels is used for feature extraction, it automatically learns the features present in the data specific to the task. The combination of numerous random convolutional kernels effectively captures discriminative patterns in time series data. For the dataset obtained by applying the DTW algorithm for partitioning and matching, feature extraction was performed using a CNN with random convolutional kernels. To generate the 2000 feature dimensions that comprised the feature dataset, 1000 one-dimensional random convolutional kernels were selected. Subsequently, the two feature datasets obtained from the distinct feature extraction methods were subjected to anomaly detection using the OCSVM algorithm. The results presented in Table 3 validate the advantages of the CNN with random convolutional kernels for feature extraction.  
The results demonstrate that feature extraction from the divided dataset, when compared with the time domain features, led to an average increase of 8.16% in precision, a 4.27% boost in recall, and a remarkable 7.85% improvement in the average F1 score. This  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Traditional Time Domain**} & \multicolumn{3}{c}{**Random Convolution Kernels**} \\
**Feature** & \multicolumn{3}{c}{**Feature + PCA**} & \multicolumn{3}{c}{**Feature Extraction**} \\  & **P** & **R** & **F1** & **P** & **R** & **F1** \\ \hline normal & 100.00 & 65.85 & 79.41 & 100.00 & 82.93 & 90.67 \\ swashplate wear & 74.55 & 100.00 & 85.42 & 85.42 & 100.00 & 92.13 \\ sliding shoe wear & 74.55 & 100.00 & 85.42 & 85.42 & 100.00 & 92.13 \\ single-plunger loose shoe & 74.55 & 100.00 & 85.42 & 85.42 & 100.00 & 92.13 \\ average & 80.91 & 91.46 & 83.92 & **89.07** & **95.73** & **91.77** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance comparison of different feature selection methods.  
indicates that feature extraction using the CNN with random convolution kernels significantly enhanced the information content derived from the original data. The extraction method for time domain features often adopts a global perspective, whereas CNNs with random convolution kernels prioritize local feature characteristics during the convolution process. This enhances the algorithmic efficiency and fortifies the robustness and generalization capabilities of the model.