**4. Conclusions**

In this paper, a fault state detection and evaluation method based on SDE is proposed, which can track the degradation state of bearing and check valve and detect the operation state of mechanical parts at the current time. Through the analysis of the IMS bearing data in the laboratory environment and the check valve data in the industrial environment, the effectiveness of the proposed method is proved. By comparing the proposed SDE with single features, fusion feature and traditional entropy feature, the following conclusions can be drawn.

(1) In the condition monitoring of check valve and bearing, the MEI scores of SDE features are 0.4382 and 0.4717, respectively, and these two scores are much higher than those of single features, fusion features, and traditional entropy features. The results show that sliding window down-sampling improves the trend of degradation features, TANSIG mapping enhances the performance of SDE features to characterize degradation states, and the introduction of LOWESS improves the anti-interference performance of features. The SDE feature and its state warning line can effectively track the operation state of the check valve and determine the fault warning point earlier.

(2) The reason why the MEI scores of the 44 degradation features of the check valve is smaller than that of the 44 degradation features of the bearing is that the vibration signal of check valve in industrial environment is affected by factors such as slurry erosion and multi-part vibration. Even so, the proposed smooth SDE feature can still detect the degradation state of the check valve effectively.

(3) A new method for fault detection of mechanical parts is proposed in this paper, which can not only guide the formulation of maintenance and replacement plan, but also improve the operation safety of diaphragm pump and other equipment. Next, we will study the fault trend prediction methods and early fault diagnosis techniques.

**Author Contributions:** Conceptualization, C.Z. and Y.J.; methodology, C.Z.; software, Y.J.; validation, H.B., Y.Y. and L.X.; formal analysis, C.Z.; investigation, C.Z.; resources, Y.Y.; data curation, C.Z.; writing—original draft preparation, H.B.; writing—review and editing, C.Z.; visualization, C.Z.; supervision, H.B. and Y.Y.; project administration, Y.Y.; funding acquisition, Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China Program (No.61663017 and No. 41971392), PhD research startup foundation of Yunnan Normal University (No.01000205020503131) and Yunnan Province Ten-thousand Talents Program.

**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.

**Acknowledgments:** This work was supported by the National Natural Science Foundation of China (No.61663017 and No. 41971392) and Yunnan Province Ten-thousand Talents Program. The author sincerely thanks the team for their guidance, and thanks the Case West Reserve University and Yunnan Dahongshan pipeline company for their bearing datasets and check valve datasets. The author sincerely expresses thanks to the reviewers for taking the time to review the paper in a busy schedule.

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