{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:28:59Z","timestamp":1768350539318,"version":"3.49.0"},"reference-count":79,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T00:00:00Z","timestamp":1559433600000},"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":["51605068"],"award-info":[{"award-number":["51605068"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771087"],"award-info":[{"award-number":["61771087"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51879027"],"award-info":[{"award-number":["51879027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51579024"],"award-info":[{"award-number":["51579024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The bearing system of an alternating current (AC) motor is a nonlinear dynamics system. The working state of rolling bearings directly determines whether the machine is in reliable operation. Therefore, it is very meaningful to study the fault diagnosis and prediction of rolling bearings. In this paper, a new fault diagnosis method based on variational mode decomposition (VMD), Hilbert transform (HT), and broad learning model (BLM), called VHBLFD is proposed for rolling bearings. In the VHBLFD method, the VMD is used to decompose the vibration signals to obtain intrinsic mode functions (IMFs). The HT is used to process the IMFs to obtain Hilbert envelope spectra, which are transformed into the mapped features and the enhancement nodes of BLM according to the complexity of the modeling tasks, and the nonlinear transformation mean according to the characteristics of input data. The BLM is used to classify faults of the rolling bearings of the AC motor. Next, the pseudo-inverse operation is used to obtain the fault diagnosis results. Finally, the VHBLFD is validated by actual vibration data. The experiment results show that the BLM can quickly and accurately be trained. The VHBLFD method can achieve higher identification accuracy for multi-states of rolling bearings and takes on fast operation speed and strong generalization ability.<\/jats:p>","DOI":"10.3390\/sym11060747","type":"journal-article","created":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T02:08:40Z","timestamp":1559527720000},"page":"747","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Study on a Novel Fault Diagnosis Method Based on VMD and BLM"],"prefix":"10.3390","volume":"11","author":[{"given":"Jianjie","family":"Zheng","sequence":"first","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Yu","family":"Yuan","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Li","family":"Zou","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Wu","family":"Deng","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"},{"name":"The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China"},{"name":"Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031, China"}]},{"given":"Chen","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Huimin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"},{"name":"The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China"},{"name":"Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.ymssp.2016.08.003","article-title":"Rotating machine fault diagnosis through enhancement stochastic resonance by full-wave signal construction","volume":"85","author":"Lu","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/j.measurement.2006.10.010","article-title":"A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM","volume":"40","author":"Yang","year":"2007","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35042","DOI":"10.1109\/ACCESS.2018.2834540","article-title":"A novel fault diagnosis method based on integrating empirical wavelet transform and fuzzy entropy for motor bearing","volume":"6","author":"Deng","year":"2018","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"45934","DOI":"10.1109\/ACCESS.2018.2865780","article-title":"Ensemble data reduction techniques and Multi-RSMOTE via fuzzy integral for bug report classification","volume":"6","author":"Guo","year":"2018","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5201","DOI":"10.1007\/s12206-018-1018-7","article-title":"Rolling bearing fault diagnosis based on mean multigranulation decision-theoretic rough set and non-naive Bayesian classifier","volume":"32","author":"Yu","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1049\/iet-sen.2018.0006","article-title":"Feature extraction based on information gain and sequential pattern for English question classification","volume":"12","author":"Liu","year":"2018","journal-title":"IET Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2445","DOI":"10.1007\/s00500-017-2940-9","article-title":"A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm","volume":"23","author":"Deng","year":"2019","journal-title":"Soft Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.ymssp.2019.01.008","article-title":"Integrated GNSS\/IMU hub motion estimator for offshore wind turbine blade installation","volume":"123","author":"Ren","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.apm.2019.02.004","article-title":"Chaos-induced and Mutation-driven algorithm for constrained engineering design problems","volume":"71","author":"Chen","year":"2019","journal-title":"Appl. Math. Model."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.jsv.2017.11.007","article-title":"Condition monitoring and fault diagnosis of motor bearings using undersampled vibration signals from a wireless sensor network","volume":"414","author":"Lu","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"015507","DOI":"10.1088\/2053-1591\/aae46b","article-title":"Microwave heating-assisted pyrolysis of mercury from sludge","volume":"6","author":"Xie","year":"2019","journal-title":"Mater. Res. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"20281","DOI":"10.1109\/ACCESS.2019.2897580","article-title":"An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem","volume":"7","author":"Deng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jsv.2018.05.020","article-title":"Planetary gearbox fault diagnosis based on data-driven valued characteristic multigranulation model with incomplete diagnostic information","volume":"429","author":"Yu","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1177\/1077546314548909","article-title":"A normalized Hilbert-Huang transform technique for bearing fault detection","volume":"22","author":"Osman","year":"2014","journal-title":"J. Vib. Control"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1007\/s10033-017-0190-5","article-title":"Motor fault diagnosis based on short-time Fourier transform and convolutional neural network","volume":"30","author":"Wang","year":"2017","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1177\/1077546314532671","article-title":"The changes of complexity in the performance degradation process of rolling element bearing","volume":"22","author":"Pan","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, T., Hu, Z., Jia, Y., Wu, J., and Zhou, Y. (2018). Forecasting crude oil prices using ensemble empirical mode decomposition and sparse Bayesian learning. Energies, 11.","DOI":"10.3390\/en11071882"},{"key":"ref_18","unstructured":"Ren, Z., Skjetne, R., and Gao, Z. (2019). A crane overload protection controller for blade lifting operation based on model predictive control. Energies, 12."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, G., Chen, B., Jiang, S., Fu, H., Wang, L., and Jiang, W. (2019). Double entropy joint distribution function and its application in calculation of design wave height. Entropy, 21.","DOI":"10.3390\/e21010064"},{"key":"ref_20","unstructured":"Zhao, H.M., Sun, M., Deng, W., and Yang, X.H. (2017). A new feature extraction method based on EEMD and multi-scale fuzzy entropy for motor bearing. Entropy, 19."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, R., Guo, S.K., Wang, X.Z., and Zhang, T.L. (2019). Fusion of multi-RSMOTE with fuzzy integral to classify bug reports with an imbalanced distribution. IEEE Trans. Fuzzy Syst.","DOI":"10.1109\/TFUZZ.2019.2899809"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhao, H.M., Yao, R., Xu, L., Yuan, Y., Li, G.Y., and Deng, W. (2018). Study on a novel fault damage degree identification method using high-order differential mathematical morphology gradient spectrum entropy. Entropy, 20.","DOI":"10.3390\/e20090682"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.energy.2017.11.028","article-title":"The heat and mass transfer characteristics of superheated steam coupled with non-condensing gases in horizontal wells with multi-point injection technique","volume":"143","author":"Sun","year":"2018","journal-title":"Energy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1142\/S0218194019500074","article-title":"Identify severity bug report with distribution imbalance by CR-SMOTE and ELM","volume":"29","author":"Guo","year":"2019","journal-title":"Int. J. Softw. Eng. Knowl. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhou, Y.R., Li, T.Y., Shi, J.Y., and Qian, Z.J. (2019). A CEEMDAN and XGBOOST\u2013based approach to forecast crude oil prices. Complexity.","DOI":"10.1155\/2019\/4392785"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.asoc.2017.06.004","article-title":"Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment","volume":"59","author":"Deng","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Guo, J.H., Mu, Y., Xiong, M.D., Liu, Y.Q., and Gu, J.X. (2019). Activity feature solving based on TF-IDF for activity recognition in smart homes. Complexity.","DOI":"10.1155\/2019\/5245373"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fu, H., Li, Z., Liu, Z., and Wang, Z. (2018). Research on big data digging of hot topics about recycled water use on micro-blog based on particle swarm optimization. Sustainability, 10.","DOI":"10.3390\/su10072488"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.3233\/JIFS-169548","article-title":"Multivariable LS-SVM with moving window over time slices for the prediction of bearing performance degradation","volume":"34","author":"Tang","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1007\/s00500-015-1841-z","article-title":"Ensemble Bayesian networks evolved with speciation for high-performance prediction in data mining","volume":"21","author":"Kim","year":"2017","journal-title":"Soft Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4387","DOI":"10.1007\/s00500-016-2071-8","article-title":"A novel collaborative optimization algorithm in solving complex optimization problems","volume":"21","author":"Deng","year":"2017","journal-title":"Soft Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1177\/1077546313483653","article-title":"Performance degradation assessment of rolling bearing based on bispectrum and support vector data description","volume":"20","author":"Wang","year":"2014","journal-title":"J. Vib. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s12206-017-1205-y","article-title":"Fault diagnosis of planetary gearbox with incomplete information using assignment reduction and flexible naive Bayesian classifier","volume":"32","author":"Yu","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"96","DOI":"10.3901\/CJME.2014.1103.166","article-title":"Feature extraction and recognition for rolling element bearing fault utilizing short-time Fourier transform and non-negative matrix factorization","volume":"28","author":"Gao","year":"2015","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.ymssp.2015.03.030","article-title":"Weak fault signature extraction of rotating machinery using flexible analytic wavelet transform","volume":"64","author":"Zhang","year":"2015","journal-title":"Mech. Syst. Signal. Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1051\/meca\/2015067","article-title":"Bearing fault diagnosis using Hilbert-Huang transform (HHT) and support vector machine (SVM)","volume":"17","author":"Kabla","year":"2016","journal-title":"Mech. Ind."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.ymssp.2017.11.004","article-title":"Integrated ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection","volume":"104","author":"Yuan","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compchemeng.2018.03.022","article-title":"Fault detection and diagnosis using empirical mode decomposition based principal component analysis","volume":"115","author":"Du","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"238","DOI":"10.2174\/2213275911205030238","article-title":"A multi-layer KMC-RS-SVM classifier and DGA for fault diagnosis of power transformer","volume":"5","author":"Fei","year":"2012","journal-title":"Recent Pat. Comput. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kang, L., Zhao, L., Yao, S., and Duan, C.X. (2019). A new architecture of super-hydrophilic \u03b2-SiAlON\/graphene oxide ceramic membrane for enhanced anti-fouling and separation of water\/oil emulsion. Ceram. Int.","DOI":"10.1016\/j.ceramint.2019.05.195"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1016\/j.ymssp.2016.09.024","article-title":"Adaptive sparsest narrow-band decomposition method and its applications to rolling element bearing fault diagnosis","volume":"85","author":"Cheng","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"17834","DOI":"10.1109\/ACCESS.2019.2893277","article-title":"Rolling bearing performance degradation assessment based on convolutional sparse combination learning","volume":"7","author":"Huang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.ymssp.2018.05.015","article-title":"Rolling bearing fault diagnosis and performance degradation assessment under variable operation conditions based on nuisance attribute projection","volume":"114","author":"Huang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4113","DOI":"10.1016\/j.eswa.2013.12.026","article-title":"An approach to fault diagnosis of reciprocating compressor valves using Teager-Kaiser energy operator and deep belief networks","volume":"41","author":"AlThobiani","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/j.measurement.2016.07.054","article-title":"Hierarchical adaptive deep convolution neural network and its application to bearing fault diagnosis","volume":"93","author":"Guo","year":"2016","journal-title":"Measurement"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"15066","DOI":"10.1109\/ACCESS.2017.2728010","article-title":"Stacked sparse autoencoder-based deep network for fault diagnosis of rotating machinery","volume":"5","author":"Qi","year":"2017","journal-title":"IEEE Access"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.isatra.2017.03.017","article-title":"Rolling bearing fault diagnosis using adaptive deep belief network with dual-tree complex wavelet packet","volume":"69","author":"Shao","year":"2017","journal-title":"ISA Trans."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Li, S.B., Liu, G.K., Tang, X.H., Lu, J., and Hu, J. (2017). An ensemble deep convolutional neural network model with improved d-s evidence fusion for bearing fault diagnosis. Sensors, 17.","DOI":"10.3390\/s17081729"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/j.ymssp.2017.08.002","article-title":"Rolling bearing fault feature learning using improved convolutional deep belief network with compressed sensing","volume":"100","author":"Shao","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3261","DOI":"10.1109\/TII.2018.2819674","article-title":"Sparse deep stacking network for fault diagnosis of motor","volume":"14","author":"Sun","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.ymssp.2017.06.022","article-title":"A deep convolutional neural network with new training methods for bearing fault diagnosis under noisy environment and different working load","volume":"100","author":"Zhang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2727","DOI":"10.1109\/TIE.2017.2745473","article-title":"Electric locomotive bearing fault diagnosis using a novel convolutional deep belief network","volume":"65","author":"Shao","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.neucom.2018.05.024","article-title":"An intelligent diagnosis scheme based on generative adversarial learning deep neural networks and its application to planetary gearbox fault pattern recognition","volume":"310","author":"Wang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.ymssp.2018.04.038","article-title":"A data indicator-based deep belief networks to detect multiple faults in axial piston pumps","volume":"112","author":"Wang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.neucom.2018.07.034","article-title":"Unsupervised fault diagnosis of rolling bearings using a deep neural network based on generative adversarial networks","volume":"315","author":"Liu","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"125005","DOI":"10.1088\/1361-6501\/aae27a","article-title":"A novel deep fuzzy clustering neural network model and its application in rolling bearing fault recognition","volume":"29","author":"Zhao","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1109\/TIE.2018.2798633","article-title":"An imbalance modified deep neural network with dynamical incremental learning for chemical fault diagnosis","volume":"66","author":"Hu","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/j.ymssp.2016.08.042","article-title":"Independence-oriented VMD to identify fault feature for wheel set bearing fault diagnosis of high speed locomotive","volume":"85","author":"Li","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jsv.2018.07.039","article-title":"Initial center frequency-guided VMD for fault diagnosis of rotating machines","volume":"435","author":"Jiang","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.ymssp.2019.02.056","article-title":"Periodic impulses extraction based on improved adaptive VMD and sparse code shrinkage denoising and its application in rotating machinery fault diagnosis","volume":"126","author":"Li","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"31501","DOI":"10.1109\/ACCESS.2019.2903204","article-title":"Early fault diagnosis for planetary gearbox based on adaptive parameter optimized VMD and singular kurtosis difference spectrum","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1854021","DOI":"10.1142\/S0218001418540216","article-title":"Real-time calibration and registration method for indoor scene with joint depth and color camera","volume":"32","author":"Zhang","year":"2018","journal-title":"J. Pattern Recognit. Artif. Intell."},{"key":"ref_63","unstructured":"Guo, S.K., Liu, Y.Q., Chen, R., Sun, X., and Wang, X.X. (2018). Using an improved SMOTE algorithm to deal imbalanced activity classes in smart home. Neural Process. Lett."},{"key":"ref_64","unstructured":"Wen, J., Zhong, Z.F., Zhang, Z., Fei, L.K., Lai, Z.H., and Chen, R.Z. (2018). Adaptive locality preserving regression. IEEE Trsns. Circ. Syst. Vid."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Liu, Y.Q., Wang, X.X., Zhai, Z.G., Chen, R., Zhang, B., and Jiang, Y. (2019). Timely daily activity recognition from headmost sensor events. ISA Trans.","DOI":"10.1016\/j.isatra.2019.04.026"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1186\/s13640-017-0227-9","article-title":"A fast framework construction and visualization method for particle-based fluid","volume":"2017","author":"Zhang","year":"2017","journal-title":"EUPASIP J. Image Video Process."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1080\/19475705.2018.1482963","article-title":"Landslide susceptibility assessment in the nantian area of china: A comparison of frequency ratio model and support vector machine","volume":"9","author":"Huang","year":"2018","journal-title":"Geomat. Nat. Haz. Risk"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jallcom.2018.11.375","article-title":"Temperature dependent photoluminescence of surfactant assisted electrochemically synthesized ZnSe nanostructures","volume":"781","author":"Zhang","year":"2019","journal-title":"J. Alloy Compd."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Liu, G., Chen, B., Gao, Z., Fu, H., Jiang, S., Wang, L., and Yi, K. (2019). Calculation of joint return period for connected edge data. Water, 11.","DOI":"10.3390\/w11020300"},{"key":"ref_70","unstructured":"Zhou, J., Du, Z., Yang, Z., and Xu, Z. (2019). Dynamic parameters optimization of straddle-type monorail vehicles based multiobjective collaborative optimization algorithm. Vehicle Syst. Dyn."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/TBCAS.2018.2843286","article-title":"Analysis and simulation of capacitor-less ReRAM-based stochastic neurons for the in-memory spiking neural network","volume":"12","author":"Lin","year":"2018","journal-title":"IEEE Trans. Biomed Circ. Syst."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1109\/TCSVT.2018.2799214","article-title":"Robust sparse linear discriminant analysis","volume":"29","author":"Wen","year":"2019","journal-title":"IEEE Trans. Circ. Syst. Vid."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/j.enconman.2019.05.057","article-title":"An opposition-based sine cosine approach with local search for parameter estimation of photovoltaic models","volume":"195","author":"Chen","year":"2019","journal-title":"Energ. Convers. Manage."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"35182","DOI":"10.1109\/ACCESS.2018.2847732","article-title":"Multi-objective optimum design of high-speed backplane connector using particle swarm optimization","volume":"6","author":"Yu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.apm.2018.07.044","article-title":"An improved grasshopper optimization algorithm with application to financial stress prediction","volume":"64","author":"Luo","year":"2018","journal-title":"Appl. Math. Model."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"39515","DOI":"10.1109\/ACCESS.2019.2906935","article-title":"Study on Threshold selection methods in calculation of ocean environmental design parameters","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE ACCESS"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1162\/neco.2006.18.7.1527","article-title":"A fast learning algorithm for deep belief nets","volume":"18","author":"Hinton","year":"2006","journal-title":"Neural Comput."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/TNNLS.2017.2716952","article-title":"Broad learning system: An effective and efficient incremental learning system without the need for deep architecture","volume":"29","author":"Chen","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_79","unstructured":"(2017, July 13). Bearing Data Center. Available online: http:\/\/csegroups.case.edu\/bearingdatacenter\/home."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/747\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:55:37Z","timestamp":1760187337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,2]]},"references-count":79,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["sym11060747"],"URL":"https:\/\/doi.org\/10.3390\/sym11060747","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,2]]}}}