## 6 Extended Applications of the DTW-RCK-IF Composite Method
### CWRU Bearing Dataset  
This test used bearing data sourced from Case Western Reserve University in the United States [18], and the test platform is illustrated in Figure 17. Damage was induced in the bearings using electrical discharge machining, resulting in deliberate damage to the inner race, rolling elements, and outer race. The collected signals were recorded using an accelerometer. Three types of bearing faults, namely an inner ring fault, rolling element fault, and outer ring fault at the 6 o'clock position, as well as the normal-state data, were selected for validation, with a motor load of 0 hp, speed of 1797 r/min, sampling frequency of 12 kHz, and fault diameter of 0.1778 mm. SKF bearings were used in this study. The  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Sample Length** & **Number of Samples** & **Training Dataset** & **Testing Dataset** & **Target Abnormal Samples** \\ \hline normal & 259 & 192 & 144 & 48 & - \\ swashplate wear & 259 & 191 & 0 & - & 48 \\ sliding shoe wear & 259 & 193 & 0 & - & 48 \\ single-plunger & & & & & \\ loose shoe & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Axial piston pump vibration signal data set partitioning.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Signal** & \multicolumn{2}{c}{**Vibration Signal**} & \multicolumn{2}{c}{**Pressure Signal**} \\
**P** & **R** & **F1** & **P** & **R** & **F1** \\ \hline normal & 100.00 & 93.75 & 96.77 & 100.00 & 97.56 & 98.77 \\ swashplate wear & 94.12 & 100.00 & 96.97 & 97.62 & 100.00 & 98.80 \\ sliding shoe wear & 94.12 & 100.00 & 96.97 & 97.62 & 100.00 & 98.80 \\ single-plunger loose shoe & 94.12 & 100.00 & 96.97 & 97.62 & 100.00 & 98.80 \\ average & 95.59 & 98.44 & 96.92 & **98.22** & **99.39** & **98.79** \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the detection performance for pressure and vibration signals.  
first 1.2 \(\times\) 10\({}^{5}\) data points of each state were selected. The time domain waveforms of the original signals under the four conditions are shown in Figure 18.  
In Experiment 1, the DTW-RCK-IF anomaly detection method was extended to practical applications. Using the DTW algorithm for data partitioning, each sample had a length of 801. Under normal operating conditions, the dataset comprised 149 samples with a training-to-testing ratio of 3:1, resulting in 111 samples for training and 38 samples for testing. After completing the data partitioning for the three abnormal operating states, 38 random samples were selected from each target abnormal sample, as listed in Table 8. Subsequently, a CNN with random convolutional kernels was used to extract features from the partitioned data. A total of 1000 one-dimensional random convolutional kernels were employed, generating 2000 feature dimensions that constituted the dataset. Finally, the isolation forest algorithm was used to perform anomaly detection and calculate the performance metrics for the extracted feature dataset. The anomaly detection results are listed in Table 9.  
Figure 17: Bearing failure test bench of CWRU.  
Figure 18: Bearing vibration signal time domain waveform diagram of CWRU: (**a**) normal; (**b**) inner ring fault; (**c**) rolling element fault; (**d**) outer ring fault.  
The results demonstrated that the average precision across the four operating conditions was 99.03%, the average recall was 99.67%, and the average F1 score reached 99.35%. This suggests that the DTW-RCK-IF composite method exhibits high applicability to and stability for bearing anomaly detection.