# Research on Prediction Method of Hydraulic Pump Remaining Useful Life Based on KPCA and JITL
## 4 Life-Cycle Test and Signal Acquisition of Gear Pump
### Extraction of Gear Pump Performance Degradation Features  
When extracting the features of the gear pump pressure signals, first, after removing the DC component of the collected pressure signals of gear pumps 1-4, the wavelet packet denoising method is used to remove the influence of noise. Subsequently, 14 time-domain and 4 frequency-domain characteristic indices of a denoised gear pump pressure signal are extracted. After the DC component is removed, the trends of the changes in the time- and frequency-domain characteristic parameters of the pressure signal with time are shown in Figures 8 and 9, respectively. Based on the analysis of Figures 8 and 9, the trends of the characteristic parameters changes with time are different. Focusing only on a certain characteristic parameter or a certain part of the characteristic, parameters cannot fully reflect the performance degradation trends shown in the life-cycle test of the gear pumps. In the actual working process of a gear pump, the tendency of its performance degradation is objective. Over time, its performance continues to degrade. Therefore, for selecting the time- and frequency-domain characteristic parameters, it is necessary to first consider whether the selected characteristic parameter curves can show distinct change characteristics over time. In addition, to more accurately determine the performance degradation initial time of a gear pump, the selected characteristic parameters should meet the requirement that when the gear pump starts to fail, the corresponding curve presents clear tendency changes. Among the 14 time-domain characteristic parameters, which are shown in Figure 8, the mean value, kurtosis, crest factor, impulse factor, and kurtosis index do not show clear changes with the performance degradation of the gear pumps. There are no distinct changes in the early failure of the gear pumps. Among the four-frequency domain characteristic parameters, which are displayed in Figure 9, only the average power shows clear changes with the performance degradation of the gear pumps. Therefore, for the preliminary screening of  
Figure 7: Wear of each component of gear pump: (**a**) End-face wear of driving gear; (**b**) End-face wear of driven gear; (**c**) Side plate wear; and (**d**) Pump body wear. gear pump characteristic parameters, the characteristic parameters that do not meet the requirements are removed. Figure 8: _Cont_. Figure 8: Time-domain characteristic parameters: (**a**) Mean value; (**b**) Variance; (**c**) Root-mean-square value; (**d**) Kurtosis; (**e**) Peak value; (**f**) Root amplitude; (**g**) Peak-to-peak value; (**h**) Absolute mean value; (**i**) Standard deviation; (**j**) Shape factor; (**k**) Crest factor; (**l**) Impulse factor; (**m**) Kurtosis index; and (**n**) Clearance factor. After the preliminary extraction and screening of the characteristic parameters, the remaining time- and frequency-domain characteristic parameters still present different trends with gear pump performance degradation. It is impossible to accurately determine which characteristic parameter is more suitable for the performance degradation evaluation of the gear pumps. Simultaneously, a single characteristic parameter is relatively biased and cannot fully reflect the trend of gear pump performance degradation. Therefore, it is necessary to obtain a state evaluation index that can fully characterize the performance degradation trend of a gear pump and is sufficiently sensitive to early failure. Therefore, the KPCA method is proposed in this paper to analyze and calculate the time- and frequency-domain characteristic parameters after screening, and the first and second principal components are taken as the state evaluation indices of the gear pump performance degradation. The RBF kernel is selected as the kernel function in the analysis and calculation using the KPCA method. The kernel parameter, \(\sigma\), values are taken as 250, 350, 450, 550, and 650, respectively.