**5. Conclusions**

Investigating the problem of a check valve's fault state being difficult to classify, this paper proposed a diagnosis method based on multi-domain features and KELM. It adopted the method to analyze bearing test fault data and check valve fault data. The conclusions are as follows:


The accuracy of KELM is affected by the kernel parameters and penalty coefficients. Achieving fast and accurate parameters for different objects is the focus of future research. Application of the theory in practice would be the ultimate end of this research, and online fault diagnosis and big data analysis also need to be considered next.

Though the proposed method achieves better diagnosis results and provides superior accuracy for feature extraction and better robustness in fault diagnosis, the stability of the multi-feature method with coarse-grained data could be further improved. Therefore, it needs more time for training and classification. Next, we will develop a fast training algorithm to facilitate model training.

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

**Funding:** This research was supported by the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (no. ICT2022B06), the PhD research startup foundation of Yunnan Normal University (no. 01000205020503131), and the Fundamental Research Program of Yunnan Province (no. 202101AU070061), Project of Educational Commission of Yunnan Province of China.

**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 no conflict of interest.
