# An Automatic Fault Diagnosis Method for the Reciprocating Compressor Based on HMT and ANN
## 5 Conclusions  
In this paper, a novel fault diagnosis approach for RC based on \(p\)-\(V\) diagrams and image processing technologies was proposed. The raw pressure data in a working cycle of the compressor were employed to plot a \(p\)-\(V\) diagram, then the \(p\)-\(V\) diagram were decomposed into four sectionalized curves according to the working processes happened in the cylinder. Afterwards, HMT was used to extract the comprehensive gradients of compression and expansion curves, and VPT was applied to extract the vertical projection features of the discharge curve. Finally, all the features were feed to the ANN classifier to obtain the predicted class. To validate the performance of the proposed method, a seeded fault testing was conducted on a RC test rig to collect real running data. Seven faulty cases and the healthy case were seeded in the test rig. The impacts of different faults on \(p\)-\(V\) diagrams were discussed, and the results showed that the gradients of the compression and expansion curves and the fluctuation of the discharge curve are sensitive in the faulty cases, according to the analysis of the experimental results shown in Figure 7.  
Finally, the proposed method was adopted on the data from the seeded fault testing. The experimental results showed that the new method is steady during training, and has a good performance in classification, with an accuracy of 97.9%. Conceptualization, Q.L. and X.Y. ; methodology, Q.L. and X.Y. ; software, Q.L. ; validation, Q.L. and H.M.; formal analysis, Q.L. and L.C. ; investigation, Q.L. ; resources, X.Y. and L.C. ; data curation, Q.L. ; writing--original draft preparation, Q.L. ; writing--review and editing, Q.L., X.Y., L.C. and Y.S. ; visualization, Q.L. ; supervision, X.Y., L.C. and Y.L. ; project administration, X.Y. ; funding acquisition, X.Y. and Y.L. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China [grant numbers 52076166] and Open Foundation of State Key Laboratory of Compressor Technology (Compressor Technology Laboratory of Anhui Province), No. SKL-YSJ202111. The authors  
[PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON] Fault detection in reciprocating compressor valves under varying load conditions. _Mech. Syst. Signal Process._**2016**, _70_-71, 104-119. [CrossRef]
* _[PERSON] et al. (2017)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Single and combined fault diagnosis of reciprocating compressor valves using a hybrid deep belief network. _Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci._**2017**, _232_, 3767-3780. [CrossRef]
* _[PERSON] et al. (2019)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] An Intelligent Fault Diagnosis Method for Reciprocating Compressors Based on LMD and SDAE. _Sensors_**2019**, _19_, 1041. [CrossRef] [PubMed]
* _[PERSON] et al. (2019)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A new method for nondestructive fault diagnosis of reciprocating compressor by means of strain-based p-V diagram. _Mech. Syst. Signal Process._**2019**, _133_, 106268. [CrossRef]
* _[PERSON] et al. (2011)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] A recognition and novelty detection approach based on Curvelet transform, nonlinear PCA and SVM with application to indicator diagram diagnosis. _Expert Syst. Appl._**2011**, _38_, 12721-12729. [CrossRef]
* _[PERSON] et al. (2010)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Fault Diagnosis for Reciprocating Air Compressor Valve Using P-V Indicator Diagram and SVM. In Proceedings of the 2010 Third International Symposium on Information Science and Engineering, Shanghai, China, 24-26 December 2010; pp. 255-258. [CrossRef]
* _[PERSON] et al. (2013)_ [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Detecting broken reciprocating compressor valves in the PV diagram. In Proceedings of the 2013 IEEE/ ASME International Conference on Advanced Intelligent Mechatronics (AIM), Wollongong, Australia, 16 September 2013; pp.