**7. Conclusions**

Aiming at the non-stationary characteristics of the fault vibration signal of the check valve of a high-pressure diaphragm pump, a fault feature extraction method for the check valve based on LMD and wavelet packet analysis is proposed. Finally, the fault features were extracted by Hilbert envelope spectrum analysis. The following conclusions were obtained:

(1) The LMD method was used to decompose the original signal adaptively, which overcomes the problems of modal aliasing and endpoint effect caused by the EMD method, and there were fewer iterations. The component signal decomposed by this method only included five PF components and one residual signal component. In comparison, the EMD obtained more signal components (ten IMF components and one residual component). The results show that LMD can extract the time-frequency information of the signal more effectively and provide a guarantee for the screening of subsequent signal components.

(2) By calculating the K-L divergence value of each signal component and selecting the signal component whose K-L divergence value is less than the set threshold as the effective component signal, the problem of poor discrimination caused by the traditional kurtosis method can be avoided. Because the original signal contains more impact components, it is difficult to screen the signal. The experimental results in the signal screening link show that three signal components, PF1, PF2, and PF3, can be extracted as effective signals by using K-L divergence. If the kurtosis criterion is used for filtering, all signal component values are more significant than the set threshold and cannot be selected. At the same time, in the comparative experiment using EMD, four signal components were successfully selected as effective signals by using K-L divergence. When kurtosis was used as the screening criterion, it also showed the defect of poor discrimination.

(3) By further comparing and analyzing the envelope spectra after wavelet packet denoising based on different methods, it can be seen that the peak of characteristic frequency in the Hilbert envelope spectrum obtained by using the method proposed in this paper

is relatively apparent. The experimental results of envelope spectrum analysis show that six frequency components such as the fundamental frequency of check valve fault and the frequency from the second to sixth doubling frequency of the fundamental frequency can be extracted by using the method proposed in this paper. Although the above six frequency components were also extracted by the EMD wavelet packet joint denoising method, the overall amplitude was lower than that obtained by the method proposed in this paper. In addition, three frequency components such as 0.3125, 0.625 and 1.563 Hz cannot be found in the envelope spectrum of the signal denoised by wavelet packet alone. It is proved that the method proposed in this paper can extract the fault characteristics of the check valve more effectively.

As a large reciprocating industrial equipment, a high-pressure diaphragm pump can operate under complex working conditions such as high pressure, high temperature, high corrosion, and high concentration and is more widely used in the mining, metallurgy, petroleum, and chemical industries. This paper starts with the vibration signal analysis of the check valve, the core component of the high-pressure diaphragm pump, completes the fault feature extraction based on LMD and wavelet packet analysis, and provides a new idea for the research in this field. However, it may be affected by many uncertain factors and various fault forms under actual working conditions, so the proposed method may not be well applicable. Therefore, in future work, the research group will deeply summarize the latest theory and results of the time-frequency analysis method and further improve and perfect the proposed method to extract the operation state information of the check valve more effectively.

**Author Contributions:** Conceptualization, J.Y. and C.Z.; Data curation, J.Y.; Formal analysis, J.Y. and C.Z.; Funding acquisition, J.Y.; Methodology, J.Y.; Software, J.Y. and C.Z.; Validation, J.Y.; Writing—review and editing, C.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Scientific research fund project of Baoshan University (ZKMS202101), Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities' Association (grant NO. 2019FH001-121), collaborative education project of industry university cooperation of the Ministry of Education (202102049026), 10th batches of Baoshan young and middle-aged leaders training project in academic and technical (202109), and the PhD research startup foundation of Yunnan Normal University (No. 01000205020503131).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Conflicts of Interest:** The authors declare that they have no conflict of interest.
