{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T20:41:26Z","timestamp":1778272886459,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T00:00:00Z","timestamp":1629158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52075117"],"award-info":[{"award-number":["52075117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Research Project","award":["JSZL2020203B004"],"award-info":[{"award-number":["JSZL2020203B004"]}]},{"name":"Key Laboratory Opening Funding of Harbin Institute of Technology","award":["HIT.KLOF.2016.077"],"award-info":[{"award-number":["HIT.KLOF.2016.077"]}]},{"name":"Key Laboratory Opening Funding of Harbin Institute of Technology","award":["HIT.KLOF.2017.076"],"award-info":[{"award-number":["HIT.KLOF.2017.076"]}]},{"name":"Key Laboratory Opening Funding of Harbin Institute of Technology","award":["HIT.KLOF. 2018.074"],"award-info":[{"award-number":["HIT.KLOF. 2018.074"]}]},{"name":"Key Laboratory Opening Funding of Harbin Institute of Technology","award":["HIT.KLOF. 2018.076"],"award-info":[{"award-number":["HIT.KLOF. 2018.076"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The health status of the momentum wheel is vital for a satellite. Recently, research on anomaly detection for satellites has become more and more extensive. Previous research mostly required simulation models for key components. However, the physical models are difficult to construct, and the simulation data does not match the telemetry data in engineering applications. To overcome the above problem, this paper proposes a new anomaly detection framework based on real telemetry data. First, the time-domain and frequency-domain features of the preprocessed telemetry signal are calculated, and the effective features are selected through evaluation. Second, a new Huffman-multi-scale entropy (HMSE) system is proposed, which can effectively improve the discrimination between different data types. Third, this paper adopts a multi-class SVM model based on the directed acyclic graph (DAG) principle and proposes an improved adaptive particle swarm optimization (APSO) method to train the SVM model. The proposed method is applied to anomaly detection for satellite momentum wheel voltage telemetry data. The recognition accuracy and detection rate of the method proposed in this paper can reach 99.60% and 99.87%. Compared with other methods, the proposed method can effectively improve the recognition accuracy and detection rate, and it can also effectively reduce the false alarm rate and the missed alarm rate.<\/jats:p>","DOI":"10.3390\/e23081062","type":"journal-article","created":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T21:27:40Z","timestamp":1629235660000},"page":"1062","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Novel Framework for Anomaly Detection for Satellite Momentum Wheel Based on Optimized SVM and Huffman-Multi-Scale Entropy"],"prefix":"10.3390","volume":"23","author":[{"given":"Yuqing","family":"Li","sequence":"first","affiliation":[{"name":"Deep Space Exploration Research Center, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingjia","family":"Lei","sequence":"additional","affiliation":[{"name":"Deep Space Exploration Research Center, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengpeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Naval Research Academy, Beijing 100061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rixin","family":"Wang","sequence":"additional","affiliation":[{"name":"Deep Space Exploration Research Center, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minqiang","family":"Xu","sequence":"additional","affiliation":[{"name":"Deep Space Exploration Research Center, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.isatra.2020.12.048","article-title":"Fixed-time attitude coordination control for spacecraft with external disturbance","volume":"114","author":"Zhuang","year":"2021","journal-title":"ISA Trans."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1007\/s12206-021-0406-6","article-title":"Vibration mechanism and improved phenomenological model of the planetary gearbox with broken ring gear fault","volume":"35","author":"Luo","year":"2021","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1049\/rsn2.12092","article-title":"Fault detection approach applied to inertial navigation system\/air data system integrated navigation system with time-offset","volume":"15","author":"Li","year":"2021","journal-title":"IET Radar Sonar Navig."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, W., and Zhou, J. (2019). Fault Diagnosis for Rolling Element Bearings Based on Feature Space Reconstruction and Multiscale Permutation Entropy. Entropy, 21.","DOI":"10.3390\/e21050519"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5419","DOI":"10.1109\/TII.2020.3022369","article-title":"Multiscale Diversity Entropy: A Novel Dynamical Measure for Fault Diagnosis of Rotating Machinery","volume":"17","author":"Wang","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wodecki, J. (2021). Time-Varying Spectral Kurtosis: Generalization of Spectral Kurtosis for Local Damage Detection in Rotating Machines under Time-Varying Operating Conditions. Sensors, 21.","DOI":"10.3390\/s21113590"},{"key":"ref_7","first-page":"1471","article-title":"EMD and GNN-AdaBoost fault diagnosis for urban rail train rolling bearings","volume":"12","author":"Cai","year":"2019","journal-title":"Discret. Contin. Dyn. Syst. S"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"93155","DOI":"10.1109\/ACCESS.2020.2990528","article-title":"Bearing Fault Detection and Diagnosis Using Case Western Reserve University Dataset with Deep Learning Approaches: A Review","volume":"8","author":"Neupane","year":"2020","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.ast.2019.06.013","article-title":"Observer-based fault tolerant control and experimental verification for rigid spacecraft","volume":"92","author":"Hu","year":"2019","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"106674","DOI":"10.1016\/j.ast.2021.106674","article-title":"Design and experimental validation of a disturbing force application unit for simulating spacecraft separation","volume":"113","author":"Hou","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"275002","DOI":"10.1088\/1361-6463\/abf44c","article-title":"Surface electrostatic discharge of charged typical space materials induced by strong electromagnetic interference","volume":"54","author":"Song","year":"2021","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1016\/j.asr.2021.01.047","article-title":"Spacecraft survivability in the natural debris environment near the stable Earth-Moon Lagrange points","volume":"67","author":"Boone","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1029\/2020EA001235","article-title":"ICESat-2\/ATLAS Onboard Flight Science Receiver Algorithms: Purpose, Process, and Performance","volume":"8","author":"McGarry","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1109\/TEC.2020.3032532","article-title":"Induction Machine Fault Detection and Classification Using Non-Parametric, Statistical-Frequency Features and Shallow Neural Networks","volume":"36","author":"Kumar","year":"2020","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tao, L., Yang, X., Zhou, Y., and Yang, L. (2021). A Novel Transformers Fault Diagnosis Method Based on Probabilistic Neural Network and Bio-Inspired Optimizer. Sensors, 21.","DOI":"10.3390\/s21113623"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1007\/s43236-020-00057-z","article-title":"Two-level fault diagnosis RBF networks for auto-transformer rectifier units using multi-source features","volume":"20","author":"Lin","year":"2020","journal-title":"J. Power Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2757","DOI":"10.1016\/j.cja.2020.06.024","article-title":"A fault diagnosis model based on weighted extension neural network for turbo-generator sets on small samples with noise","volume":"33","author":"Wang","year":"2020","journal-title":"Chin. J. Aeronaut."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6288","DOI":"10.1109\/TPEL.2020.3034190","article-title":"An Adaptive Multisensor Fault Diagnosis Method for High-Speed Train Traction Converters","volume":"36","author":"Dong","year":"2021","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109330","DOI":"10.1016\/j.measurement.2021.109330","article-title":"Deep learning through LSTM classification and regression for transmission line fault detection, diagnosis and location in large-scale multi-machine power systems","volume":"177","author":"Belagoune","year":"2021","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Oh, S., Han, S., and Jeong, J. (2021). Multi-Scale Convolutional Recurrent Neural Network for Bearing Fault Detection in Noisy Manufacturing Environments. Appl. Sci., 11.","DOI":"10.3390\/app11093963"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108806","DOI":"10.1016\/j.petrol.2021.108806","article-title":"An evolutional SVM method based on incremental algorithm and simulated indicator diagrams for fault diagnosis in sucker rod pumping systems","volume":"203","author":"Lv","year":"2021","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6248","DOI":"10.1109\/TIE.2020.2994868","article-title":"Fault Diagnosis of an Autonomous Vehicle with an Improved SVM Algorithm Subject to Unbalanced Datasets","volume":"68","author":"Shi","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109022","DOI":"10.1016\/j.measurement.2021.109022","article-title":"Rolling bearing fault diagnosis with combined convolutional neural networks and support vector machine","volume":"177","author":"Han","year":"2021","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"106779","DOI":"10.1016\/j.ijepes.2021.106779","article-title":"A novel data-driven method for maintenance prioritization of circuit breakers based on the ranking SVM","volume":"129","author":"Lu","year":"2021","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6675078","DOI":"10.1155\/2021\/6675078","article-title":"A New Support Vector Regression Model for Equipment Health Diagnosis with Small Sample Data Missing and Its Application","volume":"2021","author":"Liu","year":"2021","journal-title":"Shock. Vib."},{"key":"ref_26","first-page":"1","article-title":"An efficient approach for damage identification based on improved machine learning using PSO-SVM","volume":"20","author":"Khatir","year":"2021","journal-title":"Eng. Comput."},{"key":"ref_27","first-page":"60","article-title":"Sparse representation theory for support vector machine kernel function selection and its application in high-speed bearing fault diagnosis","volume":"4","author":"Wang","year":"2021","journal-title":"ISA Trans."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1109\/TIE.2019.2898619","article-title":"Intelligent fault identification based on multisource domain generalization towards actual diagnosis scenario","volume":"67","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4032628","DOI":"10.1155\/2020\/4032628","article-title":"Fault Diagnosis of Rolling-Element Bearing Using Multiscale Pattern Gradient Spectrum Entropy Coupled with Laplacian Score","volume":"2020","author":"Yan","year":"2020","journal-title":"Complexity"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1002\/cpe.5691","article-title":"Weighted ReliefF with threshold constraints of feature selection for imbalanced data classification","volume":"32","author":"Song","year":"2020","journal-title":"Concurr. Comput. Pract. Exp."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/S0076-6879(04)84011-4","article-title":"Sample entropy","volume":"384","author":"Richman","year":"2004","journal-title":"Methods Enzymol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"068102","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale Entropy Analysis of Complex Physiologic Time Series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/JRPROC.1952.273898","article-title":"A Method for the construction of minimum-redundancy codes","volume":"40","author":"Huffman","year":"1952","journal-title":"Proc. IRE"},{"key":"ref_34","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, WA, Australia."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1062\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:45:34Z","timestamp":1760165134000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,17]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23081062"],"URL":"https:\/\/doi.org\/10.3390\/e23081062","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,17]]}}}