# Selection Strategy of Vibration Feature Target under Centrifugal Pumps Cavitation
## 4 Analysis and Methodology
Figure 5: Grey slope correlation coefficient: (**a**) Maximum, (**b**) Minimum, (**c**) Mean, (**d**) Peak, (**e**) Absolute mean, (**f**) Variance, (**g**) Standard deviation, (**h**) Kurtosis, (**i**) Skewness, (**j**) Root mean square, (**k**) Shape factor, (**l**) Crest factor, (**m**) Kurtosis factor, (**n**) Impulse factor, (**o**) Margin factor. Figure 6: Heat map of translated value: (**a**) 40 m\({}^{3}\)/h, (**b**) 50 m\({}^{3}\)/h, (**c**) 60 m\({}^{3}\)/h. According to Step 5, the corresponding entropy weight can be attached under different pressure stages in a corresponding flow rate. The final relevant coefficient in the corresponding flow rate can be calculated by Step 6. The average value can be acquired by repeating Step 5 and Step 6. The calculation results are enumerated in Table 2.  
For the above calculating consequence, the value closer to 1 means the relevance is more intense. On the contrary, when the value is closer to 0, it depicts a weaker relevance. By ranking the feature target in the principle of small to large, the recommended ordering of vibration feature target in different flow rate is as follows:  
1. 40 m\({}^{3}\)/h: variance > absolute mean > root mean square > standard deviation > skewness > mean > kurtosis factor > maximum > margin factor> peak > impulse factor> minimum > crest factor > kurtosis > shape factor. 2. 50 m\({}^{3}\)/h: kurtosis factor > variance > root mean square > standard deviation > absolute mean > maximum > peak > skewness > minimum > margin factor > impulse factor > crest factor > kurtosis > mean >shape factor. 3. 60 m\({}^{3}\)/h: kurtosis factor > kurtosis > shape factor > skewness > mean > variance > margin factor > impulse factor > crest factor > minimum > maximum > peak > standard deviation > root mean square > absolute mean. 4. Average: kurtosis factor > variance > absolute mean > root mean square > standard deviation > skewness > maximum > peak > mean > kurtosis > minimum > shape factor > margin factor > impulse factor > crest factor. From the calculated results, the relevance coefficient might have diversity under different operating conditions. However, the relevance coefficient of the kurtosis factor, variance, absolute mean and root mean square above all along which recommend applying priority. The shape factor, margin factor, impulse factor, and peak factor always below 0.5 means that the low sensitive with NPSH. This explains why the summary feature targets from the literature [21; 23] have good effects in detecting and monitoring the cavitation in terms of mathematics. From the physical concept, such as the kurtosis factor, it is a quantity indicating how sharply a probability distribution increases and decreases around the distribution mean. As one sort of dimensionless coefficient, it has great sensitivity to the impulse signal and is nearly independent of the rotation speed, size, and load with machine. The numerical value uncovers the fact that this feature target has an intensity relation with NPSH which can put the vibration signal induced by the bubble burst into the range of the impulse signal. Thus, this feature target is especially appropriate to establish the relation between the vibration and