**6. Experimental Analysis**

The field data of the high-pressure diaphragm pump check valve obtained by the data acquisition system of a slurry transmission pipeline in Western China were used in the experiment. The diaphragm pump used in the slurry transmission pipeline pump station was of the TZPM series, and the data acquisition card used was the PXIe-3342 eight-channel acquisition card. Through the acceleration sensor arranged outside the diaphragm pump, the vibration signal was collected and transmitted to the computer. Then, the collected data of the check valve in the wear fault state were analyzed to extract its fault characteristics. The Schematic diagram of high-pressure diaphragm pump and fault check valve is shown in Figure 4 [22]. The vibration signal acquisition system diagram of check valve is shown in Figure 5 [22].

**Figure 4.** Schematic diagram of high-pressure diaphragm pump and fault check valve. (**a**) High pressure diaphragm pump; and (**b**) fault check valve.

**Figure 5.** Vibration signal acquisition system diagram of check valve.

In the check valve, wear breakdown caused by coarse particles stuck in the valve is very common. The check valve of the high-pressure diaphragm pump has a conevalve-type structure, and the main components are the valve body, valve core, and spring. Among them, the "valve core spring" constitutes a low-damping oscillation system, and its frequency is:

$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m\_s}}\tag{20}$$

where *k* is the stiffness value of the spring; and *m*s is the equivalent mass value. Set the spring stiffness as follows according to the activity of the plunger of the pump

$$k = 4\pi^2 (2f)^2 m\_s \tag{21}$$

where *f* is the frequency of normal operation of the high-pressure diaphragm pump. Its normal operating frequency is 0.5~0.517 Hz, and the frequency of the spring valve core system *fp* = 2*f*, namely, 1~1.034 Hz. The check valve will show the corresponding fault fundamental frequency and double frequency when it fails.

The check valves of the high-pressure diaphragm pump are matched by the feed valve and discharge valve in pairs. Therefore, the normal operation vibration signal and fault vibration signal of a group of feed and discharge check valves were randomly selected as a group of experimental data for analysis. The fault data of the check valve used in the experiment were the data when a wear breakdown fault occurred. The sampling frequency of this experiment was 2560 Hz, and the sampling data length was 10,240. After A/D conversion, the collected vibration acceleration signal was input into the computer through the controller.

Next, the normal operation and fault operation data of 10,240 check valves were taken for analysis. Figure 6 is the time-domain waveform diagram of the normal operation of the check valve. Figures 7 and 8 are the time-domain diagram and frequency-domain diagram when the check valve fails, respectively. Through comparative analysis of Figures 6 and 7, it can be seen that when the check valve was in normal operation, the vibration signal contains prominent impact components, and the amplitude was relatively more apparent. It can be seen from Figure 8 that the operating frequency was mainly within 200 Hz, but it was impossible to conclude whether it had a fault. To further analyze the signal, LMD decomposition was carried out first. As shown in Figure 9, the original signal was decomposed into several PF components and a residual component. To compare the decomposition effect, empirical mode decomposition (EMD) was used to decompose the signal. The results are shown in Figure 10. After EMD decomposition, more component signals were obtained, and there was a certain degree of modal aliasing. Through comparison, it can be seen that the effect of signal decomposition using the LMD method was better, as it reduced the phenomenon of mode aliasing to a grea<sup>t</sup> extent. Therefore, the obtained signal component contained more information. At the same time, LMD had fewer iterations. Next, we calculated the K-L divergence of all component signals decomposed by LMD, EMD, and the original signal. The results are shown in Tables 1 and 2.

**Figure 6.** Time-domain waveform of check valve in normal operation.

**Figure 7.** Time-domain waveform of check valve fault operation.

**Figure 8.** Frequency-domain waveform of check valve fault operation.

**Figure 9.** LMD decomposition results.

As shown in Table 1, the K-L divergence values of PF1, PF2, and PF3 were relatively small and less than the set threshold. Because the discrimination of K-L divergence was relatively obvious, it can be seen that their correlation with the original signal was relatively high. From the calculation results of kurtosis values, the kurtosis values of PF1 to PF5 were all greater than 3. Although it can be seen that the above component signals contained more impact components, this led to some difficulties in the signal screening. Therefore, the filtered PF1, PF2, and PF3 components were reconstructed according to the K-L divergence value. It can be seen from Table 2 that the K-L divergence values of IMF2, IMF 3, IMF4, and IMF 5 were less than the set threshold, which shows that their correlation with the original signal is relatively high. At the same time, by analyzing the calculation results of the kurtosis values from IMF 1 to IMF 10, it can be seen that the kurtosis values of other IMF components were greater than 3, except IMF 6, IMF 9, and IMF 10, which also made it difficult to screen effective signals. Similarly, the above component signal was selected for

reconstruction according to the K-L divergence value calculation result. Although the above filtered signal components were highly correlated with the original signal, they contained a large number of fault signal features, and a large number of noise interference components. Therefore, to reduce the impact of noise on fault feature extraction, it was necessary to denoise the reconstructed signal by using the wavelet packet. In this experiment, the sym5 wavelet was used to decompose and reconstruct the reconstructed signal. The reconstructed signal waveform is shown in Figure 11, and the signal time-domain waveform after noise reduction is shown in Figures 12 and 13.


**Figure 10.** EMD decomposition results.

**Table 1.** K-L divergence and kurtosis of PF component.


**Table 2.** K-L divergence and kurtosis of IMF component.


**Figure 11.** Time-domain waveform reconstruction.

**Figure 12.** Time-domain waveform of signal based on LMD wavelet packet denoising.

**Figure 13.** Time-domain waveform of signal based on EMD wavelet packet denoising.

Next, the signals based on LMD wavelet packet denoising, EMD wavelet packet denoising, and wavelet packet direct denoising were demodulated by the Hilbert envelope to compare and analyze the experimental results. The results are shown in Figures 14–16. It is evident from Figure 14 that there was a fundamental frequency (0.3125 Hz) and a second to sixth doubling frequency of the fundamental frequency components (0.625, 0.9375, 1.25,

1.563 and 1.875 Hz) in the envelope spectrum of the signal after noise reduction based on the LMD wavelet packet, which has become the dominant frequency of the vibration signal, indicating that a fault occurred at this time. As shown in Figure 15, fundamental frequency (0.3125 Hz) and other doubling frequency components appeared in the envelope spectrum of the signal denoised based on the EMD wavelet packet. Still, the overall amplitude was less than the result seen in Figure 14. As shown in Figure 16, frequency components such as fundamental frequency (0.3125 Hz) and the second doubling frequency (0.625 Hz) cannot be found in the envelope spectrum of the signal after wavelet packet noise reduction. Therefore, using the proposed method for fault feature extraction can achieve better results.

**Figure 14.** Signal envelope spectrum based on LMD wavelet packet denoising.

**Figure 15.** Signal envelope spectrum based on EMD wavelet packet denoising.

The above qualitative analysis shows that the proposed method has better fault feature extraction advantages than the other two methods. Firstly, the fault signal of the check valve was decomposed by the time-frequency analysis method, and the complete timefrequency distribution information of the signal was obtained. Compared with EMD, LMD suppresses the endpoint effect brought about by EMD, eliminates the problems of over envelope, under envelope, and mode aliasing caused by EMD, and the decomposed signal can retain the information of the original signal. Secondly, this research introduces K-L divergence as the screening criterion in the signal screening link. Through the calculation

and comparative analysis of the K-L divergence value of each signal component, it can be seen that the discrimination of K-L divergence was relatively more significant, which is helpful to better select the signal component. Then, the subsequent reconstructed signal was denoised by a wavelet packet to filter out the noise interference. Finally, through the Hilbert envelope spectrum analysis, it can be seen that the characteristic frequency in the Hilbert envelope spectrum obtained by the proposed method was relatively apparent. Meanwhile, six frequency components such as the fundamental frequency of the fault and the second to sixth doubling frequency of the fundamental frequency can be extracted.

**Figure 16.** Signal envelope spectrum based on wavelet packet denoising.
