# A Novel Rolling Bearing Fault Diagnosis Method Based on MFO-Optimized VMD and DE-OSELM
Zhanfeng Sun  
2 Key Laboratory of Intelligent Operation and Maintenance Technology and Equipment for Urban Rail Transit of Zhejiang Province, Zhejiang Normal University, Jinhua 32100, China; [EMAIL_ADDRESS] (Z.S. ); sunji@[EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (L.Z. ); [EMAIL_ADDRESS] (M.H.) Zhanfeng Sun  
2 Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China; [EMAIL_ADDRESS]  
Zhanfeng Sun  
2 Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China; [EMAIL_ADDRESS]  
Zhanfeng Sun  
2 Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China; [EMAIL_ADDRESS]  
Zhanfeng Sun  
2 Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China; [EMAIL_ADDRESS]  
Zhanfeng Sun  
2 Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China; [EMAIL_ADDRESS]  
Zhanfeng Sun  
2 Key Laboratory of Intelligent Operation and Maintenance Technology and Equipment for Urban Rail Transit of Zhejiang Province, Zhejiang Normal University, Jinhua 32100, China; [EMAIL_ADDRESS] (Z.S. ); sunji@[EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (L.Z. ); [EMAIL_ADDRESS] (M.H.) Zhanfeng Sun  
2 Key Laboratory of Intelligent Operation and Maintenance Technology and Equipment for Urban Rail Transit of Zhejiang Province, Zhejiang Normal University, Jinhua 32100, China; [EMAIL_ADDRESS] (Z.S. ); sunji@[EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (L.Z. );et al. [18] introduced an adaptive signal analysis approach named VMD that deals with signal processing by formulating and resolving variational issues, providing strong resistance to noise. Owing to its ability to tackle modal mixing and endpoint effect effectively, VMD finds applications in multiple fields, including generator anomaly detection, structural health monitoring, and bearing fault diagnosis [19; 20; 21]. [PERSON] and colleagues [22] devised a diagnosis method for fault detection in rolling bearings using VMD and improved Kernel Extreme Learning Machine and demonstrated that VMD successfully addressed the mode mixing problem and boasted superior computational efficiency compared to EMD and LMD methods. However, VMD requires pre-set parameters, including the decomposition number (K) and penalty factor (\(\alpha\)), which significantly affect the final outcome. To identify the optimal parameter combination, several studies have proposed different methods. For instance, [PERSON] et al. [19] established a central frequency mode decomposition (CFMD), based on VMD, and the difficulty of the selection of initial parameters in the traditional VMD was relieved, provided that the range of bandwidth parameters was preset. [PERSON] et al. [23] compared the center frequency of modal components that were decomposed by different parameter combinations. However, this method had limited adaptability. [PERSON] et al. [24] implemented the Particle Swarm Optimization (PSO) algorithm to optimize VMD and demonstrated its ability to extract early fault features from bearing vibrations. Another study by [PERSON] et al. [25] suggested a parameter adaptive VMD strategy based on the grasshopper optimization algorithm (GOA) and validated its efficiency in analyzing the vibration signals of real rotating machinery. Moreover, [PERSON] et al. [26] adopted the grey wolf optimizer (GWO) algorithm, which was superior to the fixed-parameter VMD and maximum weighted kurtosis optimization VMD in terms of selecting the optimal parameter combination. These studies show that optimization algorithms with strong search abilities can achieve better adaptive selection of VMD parameters. Recently, the MFO algorithm [27] has achieved excellent performance in solving engineering optimization problems [28; 29]. [PERSON] et al. [30] compared MFO with other optimization algorithms, finding that MFO performed the best.