{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:24:05Z","timestamp":1775694245190,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"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":["61973041"],"award-info":[{"award-number":["61973041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFB1705403"],"award-info":[{"award-number":["2019YFB1705403"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Due to the symmetry of the rolling bearing structure and the rotating operation mode, it will cause the coupling modulation phenomenon when it is damaged in multiple places at the same time, which makes it difficult to accurately identify all kinds of faults. For such problems, a compound fault diagnosis method based on adaptive chirp mode decomposition (ACMD), Gini index fusion and long short-term memory (LSTM) neural network optimized by Aquila Optimizer (AO) is proposed. Firstly, a series of IMF components are obtained by decomposing the vibration signal by means of ACMD, and the required components are selected by using the correlation coefficient method. Then, the Gini index of the square envelope (GISE) and the Gini index of the square envelope spectrum (GISES) of each component are calculated, respectively, and they are fused to construct a highly dimensional feature matrix. Then, with the aim of solving the problem of difficult selection of LSTM hyperparameters, the AO-LSTM model is constructed. Finally, the feature matrix is divided into a training set and a test set. The training set is input into the model for training, and then the training network is used to predict the test set, and outputs diagnostic results. The simulation and experimental results show that the proposed method can achieve higher accuracy and stronger robustness, compared with the existing intelligent diagnosis methods for bearing compound faults.<\/jats:p>","DOI":"10.3390\/sym13122386","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T08:17:58Z","timestamp":1639124278000},"page":"2386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Compound Fault Diagnosis of Rolling Bearing Based on ACMD, Gini Index Fusion and AO-LSTM"],"prefix":"10.3390","volume":"13","author":[{"given":"Jie","family":"Ma","sequence":"first","affiliation":[{"name":"Mechanical Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7453-4724","authenticated-orcid":false,"given":"Xinyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Mechanical Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, Y., Yan, X.S., Zhang, C.N., and Wen, L. (2019). An ensemble convolutional neural networks for bearing fault diagnosis using multi-sensor data. Sensors, 19.","DOI":"10.3390\/s19235300"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ma, J.P., Zhuo, S., Li, C.W., Zhan, L.W., and Zhang, G.Z. (2021). An enhanced intrinsic time-scale decomposition method based on adaptive l\u00e9vy noise and its application in bearing fault diagnosis. Symmetry, 13.","DOI":"10.3390\/sym13040617"},{"key":"ref_3","first-page":"1143","article-title":"Review of multiple fault diagnosis methods","volume":"32","author":"Zhang","year":"2015","journal-title":"Control Theory Appl."},{"key":"ref_4","first-page":"174","article-title":"Compound faults diagnosis method of rolling bearing based on sparse representation of cascaded over complete dictionary","volume":"40","author":"Zheng","year":"2021","journal-title":"J. Vib. Shock"},{"key":"ref_5","first-page":"146","article-title":"A method of compound fault signal separation based on EVMD-LNMF","volume":"38","author":"Wang","year":"2019","journal-title":"J. Vib. Shock"},{"key":"ref_6","first-page":"140","article-title":"An improved deconvolution algorithm and its application in compound fault diagnosis of rolling bearing","volume":"39","author":"Qi","year":"2020","journal-title":"J. Vibration. Shock"},{"key":"ref_7","first-page":"442","article-title":"Research on composite fault diagnosis method based on the second generation wavelet","volume":"20","author":"Cui","year":"2009","journal-title":"China Mech. Eng."},{"key":"ref_8","first-page":"45","article-title":"Helicopter rolling bearing hybrid faults diagnosis using minimum entropy deconvolution and Teager energy operator","volume":"36","author":"Chen","year":"2017","journal-title":"J. Vib. Shock"},{"key":"ref_9","first-page":"297","article-title":"Compound fault diagnosis of wind turbine rolling bearing based on MK-MOMEDA and Teager energy operator","volume":"42","author":"Qi","year":"2021","journal-title":"Acta Energ. Sol."},{"key":"ref_10","first-page":"1950","article-title":"Separation of composite rolling bearings fault features with strong noise interference","volume":"49","author":"Wan","year":"2018","journal-title":"J. Cent. South Univ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.jsv.2018.10.010","article-title":"Detection of rub-impact fault for rotor-stator systems: A novel method based on adaptive chirp mode decomposition","volume":"440","author":"Chen","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2548","DOI":"10.1109\/TIE.2017.2739689","article-title":"Improvement of kurtosis-guided-grams via Gini index for bearing fault feature identification","volume":"65","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Ind. Electr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"125001","DOI":"10.1088\/1361-6501\/aa8a57","article-title":"Health assessment of rotating machinery using a rotary encoder","volume":"28","author":"Miao","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.isatra.2020.01.019","article-title":"Rolling element bearing fault identification using a novel three-step adaptive and automated filtration scheme based on Gini index","volume":"101","author":"Albezzawy","year":"2020","journal-title":"ISA Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108514","DOI":"10.1016\/j.measurement.2020.108514","article-title":"An adaptive variational mode decomposition based on sailfish optimization algorithm and Gini index for fault identification in rolling bearings","volume":"173","author":"Nassef","year":"2021","journal-title":"Measurement"},{"key":"ref_16","first-page":"134","article-title":"Adaptive fault diagnosis algorithm for rolling bearings based on one-dimensional convolutional neural network","volume":"39","author":"Qu","year":"2018","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_17","first-page":"1134","article-title":"Fault identification of rolling bearing based on RS-LSTM","volume":"13","author":"Chen","year":"2018","journal-title":"China Sci. Paper"},{"key":"ref_18","unstructured":"Chen, Y.Q. (2013). Intelligence Diagnosis System Research of Rolling Bearing Composite Faults. [Master\u2019s Thesis, Yanshan University]."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, Y.Y., Jia, Y.X., Wu, W.Y., Cheng, Z.H., Su, X.B., and Lin, A.Q. (2020). A diagnosis method for the compound fault of gearboxes based on multi-feature and BP-AdaBoost. Symmetry, 12.","DOI":"10.3390\/sym12030461"},{"key":"ref_20","first-page":"139","article-title":"An approach of intelligent compound fault diagnosis of rolling bearing based on MWT and CNN","volume":"40","author":"Han","year":"2016","journal-title":"J. Mech. Transm."},{"key":"ref_21","first-page":"34","article-title":"Bearing compound fault diagnosis based on HHT algorithm and convolution neural network","volume":"36","author":"Shi","year":"2020","journal-title":"Trans. Chin. Soc. Agric. Eng."},{"key":"ref_22","first-page":"1","article-title":"Deep learning approach and its application in fault diagnosis and prognosis","volume":"56","author":"Yu","year":"2020","journal-title":"Comput. Eng. Appl."},{"key":"ref_23","first-page":"126","article-title":"Application of improved CNN-LSTM model in fault diagnosis of rolling bearings","volume":"30","author":"Cao","year":"2021","journal-title":"Comput. Syst. App."},{"key":"ref_24","first-page":"68","article-title":"Combined MCKD-Teager energy operator with LSTM for rolling bearing fault diagnosis","volume":"53","author":"Zhang","year":"2021","journal-title":"J. Harbin Inst. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107250","DOI":"10.1016\/j.cie.2021.107250","article-title":"Aquila Optimizer: A novel meta-heuristic optimization algorithm","volume":"157","author":"Abualigah","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"108333","DOI":"10.1016\/j.ymssp.2021.108333","article-title":"Practical framework of Gini index in the application of machinery fault feature extraction","volume":"165","author":"Miao","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"171559","DOI":"10.1109\/ACCESS.2019.2954091","article-title":"Rolling bearing initial fault detection using long short-term memory recurrent network","volume":"7","author":"Shi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_28","first-page":"16","article-title":"A method fault diagnosis of rolling bearing of wind turbines based on long short-term memory neural network","volume":"25","author":"Zhang","year":"2017","journal-title":"Comput. Meas. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TR.2018.2882682","article-title":"A hybrid prognostics approach for estimating remaining useful life of rolling element bearings","volume":"69","author":"Wang","year":"2020","journal-title":"IEEE Trans. Reliab."},{"key":"ref_30","first-page":"1","article-title":"XJTU-SY bolling element bearing accelerated life test datasets: A tutorial","volume":"55","author":"Lei","year":"2019","journal-title":"J. Mech. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2386\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:44:50Z","timestamp":1760168690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2386"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,10]]},"references-count":30,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122386"],"URL":"https:\/\/doi.org\/10.3390\/sym13122386","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,10]]}}}