## 6 Conclusions  
This study has presented a fault diagnosis method of a reciprocating compressor based on RSSD-RCMDE to process the nonlinear, non-stationary, and multi-coupling vibration signals. ASO is involved in the optimization of the high-quality factor and low-quality factor of RSSD for the vibration signals of a reciprocating compressor in three working conditions: normal valve, valve wear, and spring failure. GA is employed to optimize the signal length, embedding dimension, and time delay in RCMDE, and the RCMDE value of the low-resonance component after the decomposition of RSSD in each working condition is calculated. Finally, the entropy value is substituted into PSO-SVM for pattern recognition. In this paper, only the single-fault identification of the reciprocating compressor is discussed, and the compound fault is not taken on board. In the future, the proposed method can be improved and applied to compound the fault identification of reciprocating compressors. The following conclusions are drawn in this paper:  
1. ASO is used to optimize RSSD, and the kurtosis value of the low-resonance component is taken as the optimization objective function, which can effectively improve the fault signal decomposition ability of the RSSD method based on resonance. The feasibility and effectiveness of the proposed method in the fault signal processing of the reciprocating compressor are experimentally verified.
2. GA is employed to optimize the three parameters of RCMDE: the signal length, embedding dimension, and time delay. The optimized RCMDE is applied to pattern recognition, which can effectively improve the accuracy of the results.
3. The fault modes of reciprocating compressors can be effectively identified by the fault diagnosis method based on the proposed RSSD-RCMDE model.  
The working state of reciprocating compressors under actual working conditions is more complex, and actual engineering data should be used for verification in the future work. The proposed method is only applicable to the fault diagnosis of reciprocating compressors; therefore, further research should be conducted to clarify its application in other engineering equipment.  
Conceptualization, F.L. and X.D.; methodology, X.D.; validation, X.D., Q.L. and S.C.; formal analysis, W.H. and S.Z.; investigation, F.L. and X.D.; resources, S.Z.; data curation, X.H.; writing--original draft preparation, W.H.; writing--review and editing, F.L. and X.D.; visualization, X.D. and Q.L.; supervision, S.C.; project administration, F.L.; funding acquisition, F.L. and Q.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the project of the National Natural Science Foundation of China (Grant Number 52206041), Natural Science Research Project of Universities in the Jiangsu Province (Grant Number 19 KJA430004), and the Jiangsu Province Graduate Research and Practice Innovation Program (Grant Number SJCX24_1664).  
The data used to support the findings of this study are currently under embargo while the research findings are commercialized. Requests for data, [6/12 months] after publication of this article, will be considered by the corresponding author.  
The authors have no conflicts of interest to declare, have all read and approved the manuscript, and agree with its submission. There are no other persons who satisfy the criteria for authorship.