# A Novel Rolling Bearing Fault Diagnosis Method Based on MFO-Optimized VMD and DE-OSELM
However, the original MFO algorithm searches in the region around its unique flame, hence increasing the risk of falling into the local optimum and slow convergence speed. Therefore, the original MFO algorithm requires improvement. Although VMD can effectively solve the modal problem, there will still be false intrinsic modal functions (IMF) in the decomposed IMF, which will affect the accuracy of the fault classification of rolling bearings [31]. Therefore, it is necessary to screen the decomposed IMF. In addition to feature extraction, the swift and accurate identification of fault types is pivotal for fault diagnosis. ELM replaces the gradient descent algorithm with a random assignment method and enhances the generalization ability of traditional classification networks, making it effective for fault diagnosis [32]. [PERSON] et al. [33] proposed a fault diagnosis model based on multiscale weighted permutation entropy (MWPE) and ELM, which demonstrated superior recognition accuracy and speed compared to using various multiscale feature extraction methods with BPNNs and SVMs. Similarly, [PERSON] et al. [34] achieved the diagnosis of slipper abrasion faults using ELM and demonstrated that the classification performance of ELM is superior to BP and SVM. [PERSON] et al. [35] proposed OSELM to resolve the long training time issue of ELM when the training data were large. This algorithm obviates the need to retrain historical data to facilitate rapid diagnosis. [PERSON] et al. 's use of VMD and OSELM for real-time detection and classification of power quality events provided high classification accuracy and robustness [36]. However, the randomly generated input weight and hidden layer bias in the OSELM algorithm have been found to limit its prediction accuracy and robustness. Hence, this paper introduces the ensemble DE-OSELM method, which was proposed by [PERSON] et al. [37], to realize fault classification and diagnosis. This paper presents a novel approach for detecting rolling bearings faults, utilizing optimized VMD and DE-OSELM. Firstly, the method adopts a dynamic adaptive weight factor and a crossover operator. Compared with the original MFO algorithm and other intelligent optimization algorithms, the improved MFO algorithm has higher global optimization ability and search accuracy, and it solves the problem of sub-optimal performance and limited convergence accuracy of multi-objective optimization algorithm. Secondly, the improved MFO is used to optimize VMD and overcome the susceptibility of VMD parameters to artificial settings, thus facilitating the adaptive selection of these parameters. Thirdly, since the vibration characteristics of the signal cannot be fully interpreted by a single index, this method introduces a new evaluation index, the effective weighted correlation sparsity index, to strip false modal components and filter the IMF recovered through VMD decomposition. The energy features of the effective IMFs are subsequently extracted as feature vectors. Finally, in order to improve the classification accuracy, the energy eigenmatrix is normalized and subjected to DE-OSELM training to identify the fault type.