# Impulse Signal Detection for Bearing Fault Diagnosis via Residual-Variational Mode Decomposition  
[PERSON]  
1 College of Automation, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (B.L. ); [EMAIL_ADDRESS] (Y.W. )1  
[PERSON]  
1 College of Automation, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (B.L. ); [EMAIL_ADDRESS] (Y.W. )12  
[PERSON]  
1 College of Automation, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (B.L. ); [EMAIL_ADDRESS] (Y.W. )1  
[PERSON]  
1 College of Automation, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (B.L. ); [EMAIL_ADDRESS] (Y.W. )12  
Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote 2: [[https://www.mdpi.com/journals/pdf/12/1](https://www.mdpi.com/journals/pdf/12/1)]([https://www.mdpi.com/journals/pdf/12/1](https://www.mdpi.com/journals/pdf/12/1))  
worked better than the other two methods. [PERSON] et al. [21] analyzed the signal from wind turbines by combining VMD and blind-source separation to detect the bearing crack fault. [PERSON] et al. [22] introduced VMD to calculate the central frequency and combined it with data-driven time-frequency analysis to diagnose gear fault. Some other articles [23; 24; 25] also examined VMD in the fault diagnosis field. To sum up, VMD has been widely applied in the fault detection field. However, the above articles determined the number of modes and the balance parameter on the basis of experience. To solve this problem, [PERSON] et al. [26] applied a grasshopper optimization algorithm to determine the optimal parameters for VMD by maxing correlation coefficient kurtosis. [PERSON] et al. [27] proposed to optimize ensemble kurtosis (EK) and improved the frequency-band estimation process. In this method, the criterion EK may be partial to the kurtosis in the envelope spectrum due to the absence of a high-frequency part in it. VMD combined with an intelligent algorithm works well, but the computational complexity is high, given that VMD has to be executed for each agent. Some researchers proposed adaptive VMD from other perspectives, which can be parted into three aspects. First, the modal number is determined by the Fourier spectrum of a signal. [PERSON] et al. [28] proposed an independence-oriented VMD on the basis of the spectrum distribution to detect wheelset-bearing faults. Using this method, they determined a modal number using the number of the local maximum of the fast Fourier transform (FFT) spectrum. Thus, this method cannot work well when the signal's FFT spectrum is complex and often leads to over-decomposition. [PERSON] et al. [29] proposed an initial center frequency-guided VMD, in which the center frequency was determined by the energy fluctuation spectrum. This method may strike if the energy fluctuation function is interfaced with heavy noise. Second, the modal number is determined by the characteristics of each sub-modal. For example, [PERSON] et al. [30] proposed an adaptive VMD on the basis of the permutation entropy, the extreme value of spectrum, and kurtosis of each sub-modal, which is a complex method and has many parameters that need to be determined artificially. [PERSON] et al. [31] proposed a tentative VMD (TVMD) method to diagnose the bearing fault. The stop criterion was the order of difference for the two sub-modes which had the largest kurtosis and came from the two adjacent modal number decomposition results. In this method the criterion was kurtosis, which was vulnerable to random impulses. Finally, a coarse-to-fine process was proposed to determine parameters for VMD [32]. In this method, the modal number was set as one, and the noise sub-modal was subtracted in each iteration. The stop criterion was based on the theoretical frequency and the kurtosis of the sub-modal.