RESEARCH PAPER
AHC-SCLS-Driven Cluster Quality Improvement of Hierarchical Sample Entropy for Rotating Machinery Fault Feature Extraction
1
School of Mechanical and Automotive Engineering, Xiamen University of Technology, China
2
School of Mechanical Engineering, Dongguan University of Technology, China
Submission date: 2025-12-02
Final revision date: 2026-01-30
Acceptance date: 2026-02-09
Online publication date: 2026-02-10
Corresponding author
Jiesi Luo
School of Mechanical and Automotive Engineering, Xiamen University of Technology, 361024, Xiamen, China
School of Mechanical and Automotive Engineering, Xiamen University of Technology, 361024, Xiamen, China
KEYWORDS
Fault diagnosisLaplacian scoreHierarchical sample entropyAgglomerative hierarchical clusteringSilhouette coefficient
TOPICS
ABSTRACT
To address insufficient fault discriminability from excessive feature redundancy in rotating machinery analysis, an AHC-SCLS-driven clustering quality enhancement method for hierarchical sample entropy (HSE) is proposed. Hierarchical entropy decomposition first decouples multi-scale entropy features across frequency bands. Agglomerative hierarchical clustering (AHC) then constructs a hierarchical feature tree and reduces dimensionality via redundant attribute merging. A dual-criterion SCLS framework is integrated, where the average Silhouette Coefficient (SC) selects optimal cluster number and the Laplacian Score (LS) screens the most discriminative feature per cluster to form a refined subset. Experiments on the Ottawa University bearing and laboratory gearbox datasets validate the superiority of AHC-SCLS-optimized features. The PSO-SVM classifier achieves 99.29% accuracy on both datasets, other classifiers maintain 95.04%–97.87% accuracy, and the method outperforms mRMR, PCA and other traditional approaches across all classifiers.
REFERENCES (29)
1.
Song Y, Cao J, Hu Y. In-process feature extraction of milling chatter based on second-order synchroextracting transform and fast kurtogram. Mechanical Systems and Signal Processing. 2024;208:111018. https://doi.org/10.1016/j.ymss....
2.
Pincus SM. Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences. 1991;88(6):2297–2301. https://doi.org/10.1073/pnas.8....
3.
Richman JS, Moorman JR. Physiological time series analysis using approximate entropy and sample entropy. American Journal of Physiology, Heart and Circulatory Physiology. 2000;278(6):H2039–H2049. https://doi.org/10.1152/ajphea....
4.
Cao Y, Tung WW, Gao JB, Protopopescu VA, Hively LM. Detecting dynamical changes in time series using the permutation entropy. Physical Review E. 2004;70(4):046217. https://doi.org/10.1103/PhysRe....
5.
Wang Z, Zhang M, Chen H, Li J, Li G, Zhao J, Yao L, Zhang J, Chu F. A generalized fault diagnosis framework for rotating machinery based on phase entropy. Reliability Engineering & System Safety. 2025;256:110745. 10.1016/j.ress.2024.110745.
6.
Wang Z, Liu Y, Bai R, Chen H, Li J, Chen X, Yao L, Zhao J, Chu F. Multi-modal multi-scale multi-level fusion quadrant entropy for mechanical fault diagnosis. Expert Systems with Applications. 2025;281:127715. https://doi.org/10.1016/j.eswa....
7.
Shen C, Jiang P, Luo J, Lin G, Zhang S. Optimal weighted multi-scale entropy-energy ratio feature for machine fault diagnosis. Measurement. 2025;242:115782. https://doi.org/10.1016/j.meas....
8.
Wang Z, Liang P, Bai R, Liu Y, Zhao J, Yao L, Zhang J, Chu F. Few-shot fault diagnosis for machinery using multi-scale perception multi-level feature fusion image quadrant entropy. Advanced Engineering Informatics. 2025;63:102972. https://doi.org/10.1016/j.aei.....
9.
Lu N, Zhou TX, Wei JF, Yuan WL, Li RQ, Li ML. Application of a whale optimized variational mode decomposition method based on envelope sample entropy in the fault diagnosis of rotating machinery. Measurement Science and Technology. 2021;33(1):015014. 10.1088/1361-6501/ac3470.
10.
Wang Z, Yao L, Cai Y. Rolling bearing fault diagnosis using generalized refined composite multiscale sample entropy and optimized support vector machine. Measurement. 2020;156:107574. https://doi.org/10.1016/j.meas....
11.
Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of complex physiologic time series. Physical Review Letters. 2002;89(6):068102. https://doi.org/10.1103/PhysRe....
12.
Jiang Y, Peng CK, Xu Y. Hierarchical entropy analysis for biological signals. Journal of Computational and Applied Mathematics. 2011;236(5):728–742. https://doi.org/10.1016/j.cam.....
13.
Zhou X, Yuan R, Lv Y, Li B, Fu S, Li H. Hierarchical multiscale fluctuation-based symbolic fuzzy entropy: A novel tensor health indicator for mechanical fault diagnosis. IEEE Sensors Journal. 2025;25(3):5013–5029. https://doi.org/10.1109/JSEN.2....
14.
Su Z, Tang B, Liu Z, Qin Y. Multi-fault diagnosis for rotating machinery based on orthogonal supervised linear local tangent space alignment and least square support vector machine. Neurocomputing. 2015;157:208–222. https://doi.org/10.1016/j.neuc....
15.
Zhao K, Xiao J, Li C, Xu Z, Yue M. Fault diagnosis of rolling bearing using CNN and PCA fractal based feature extraction. Measurement. 2023;223:113754. https://doi.org/10.1016/j.meas....
16.
Huang J, Yan X. Related and independent variable fault detection based on KPCA and SVDD. Journal of Process Control. 2016;39:88–99. https://doi.org/10.1016/j.jpro....
17.
Rousseeuw PJ. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987;20:53–65. https://doi.org/10.1016/0377-0....
18.
Duda RO, Hart PE, Stork DG. Pattern Classification. 2nd ed. New York: Wiley; 2012.
19.
Zhao S, Liang X, Wang L, Zhang H, Li G, Chen J. A fault diagnosis method for analog circuits based on EEMD–PSO–SVM. Heliyon. 2024;10(18):e21601. 10.1016/j.heliyon.2024.e38064.
20.
Li Z, Wang Q, Xiong J, Cen J, Dai Q, Liang Q, Lu T. A building electrical system fault diagnosis method based on random forest optimized by improved sparrow search algorithm. Measurement Science and Technology. 2024;35(5):055110. 10.1088/1361-6501/ad2255.
21.
Li M., Yan C., Liu W., Liu X., Zhang M., Xue J., Fault diagnosis model of rolling bearing based on parameter adaptive AVMD algorithm, Applied Intelligence, 2023;53(3):3150–3165, doi:10.17531/ein/163547.
22.
Zhao Y, Yang X, Huang J, Gao J, Cui J. Improved weighted extreme learning machine with adaptive cost-sensitive strategy for imbalanced fault diagnosis of rotating machinery. Mechanical Systems and Signal Processing. 2024;217:111526. https://doi.org/10.1016/j.ymss....
23.
Melnik R., Koziak S., Dižo J., Kuźmierowski T., Piotrowska E., Feasibility study of a rail vehicle damper fault detection by artificial neural networks. Eksploatacja i Niezawodność – Maintenance and Reliability. 2023;25(1). doi:10.17531/ein.2023.1.5.
24.
Peng H, Long F, Ding C. Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2005;27(8):1226–1238. https://doi.org/10.1109/tpami.....
25.
Miller GR. Beyond ANOVA – Basics of Applied Statistics. Boca Raton: Chapman & Hall/CRC; 1997.
26.
Patange A, Soman R, Pardeshi S, Kuntoglu M, Ostachowicz W. Milling cutter fault diagnosis using unsupervised learning on small data: A robust and autonomous framework. Eksploatacja i Niezawodność – Maintenance and Reliability. 2024;26(1),doi:10.17531/ein/178274.
27.
Niu M, Jiang H, Wu Z, Shao H. An enhanced sparse autoencoder for machinery interpretable fault diagnosis. Measurement Science and Technology. 2024;35(5):055108. 10.1088/1361-6501/ad24ba.
28.
Sehri M, Dumond P. University of Ottawa constant and variable speed electric motor vibration and acoustic fault signature dataset. Data in Brief. 2024;53:110144. https://doi.org/10.1016/j.dib.....
29.
Luo J, Chen Y, Huang Q, Zhang X, Li H, Wei Z, Deng L. Joint application of VMD and IWOA–PNN for gearbox fault classification via current signal. IEEE Sensors Journal. 2023;23:13155–13164. https://doi.org/10.1109/JSEN.2....
Share
RELATED ARTICLE
| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
