# Degradation State Recognition of Piston Pump Based on ICEEMDAN and XGBoost
## 4 Test Data Processing of the Vibration Signal  
### Pre-Processing of the Vibration Signal by ICEEMDAN  
The vibration signals with different degradation degrees are shown in Figure 5, from which it can be seen that there are great differences in the characterization of vibration waveforms under the same working conditions. With the increase of slipper wear, the vibration of piston pump becomes more and more intense, and the amplitude of vibration signal is larger and larger.  
The vibration data of the tested pump under different states are selected and decomposed by ICEEMDAN, and the results are shown in Figure 6. The ICEEMDAN algorithm is used to decompose the vibration signals of four states into respective IMFs and a residual component for model development. The IMFs generated by ICEEMDAN have different sensitivity to the degrees of degradation. If the IMFs are analyzed directly, it is difficult to get the effective features related to the original signal. The appearance of illusive components will cause the extraction of useless features, increase the dimension of the feature set, and bring difficulties to the subsequent analysis [41]. By comparing correlation coefficients, the effective components in IMFs were screened out. The IMF component with the largest correlation coefficient is selected as the research object in this paper.  
Figure 5: Vibration signals with four wear degrees. (**a**) vibration signal of slipper under normal condition; (**b**) vibration signal of slipper with slight wear; (**c**) vibration signal of slipper under moderate wear; (**d**) vibration signal of slipper under severe wear.  
Then, the appropriate IMF component is selected by using the correlation coefficient method [42]. The calculation process of the correlation coefficient is shown in Formula (11):  
\[R=\frac{\sum\limits_{n=0}^{\infty}x\left(n\right)y\left(n\right)}{\sqrt{\sum \limits_{n=0}^{\infty}x^{2}\left(n\right)\sum\limits_{n=0}^{\infty}y^{2}\left(n \right)}} \tag{11}\]  
where \(x\left(n\right)\) is the sequence of effective IMF component, \(y\left(n\right)\) is the sequence of the original signal.  
The correlation coefficient method can be used to express the correlation between the selected IMF component and the original signal, the correlation coefficient values of the IMF components of the four states are showed in Table 1. The larger the correlation coefficient is, the greater the correlation between the IMF components and the original signal, the more effective information it contains. On the contrary, the IMF component is more likely to be illusive.  
Figure 6: Decomposition results of ICEEMDAN. (**a**) the vibration signal under normal state are decomposed by ICEEMDAN; (**b**) the vibration signal under slight wear are decomposed by ICEEMDAN; (**c**) the vibration signal under moderate wear are decomposed by ICEEMDAN; (**d**) the vibration signal under severe wear are decomposed by ICEEMDAN.  
From the above table, we can see the correlation coefficient of each IMF component under the four conditions. The IMF\({}_{1}\) component under no wear condition, the IMF\({}_{1}\) component under mild wear condition, the IMF\({}_{2}\) component with moderate wear degree, and the IMF\({}_{2}\) component with severe wear degree are selected respectively, and then the selected IMF is analyzed in time domain, frequency domain, and entropy features.