The decomposition number K and penalty factor α in the variational mode decomposition (VMD) algorithm have a great influence on the decomposition effect and the accuracy of subsequent fault diagnosis. Therefore, a gear fault diagnosis method based on genetic mutation particle swarm optimization VMD and probabilistic neural network (GMPSO-VMD-PNN) algorithm is proposed in this paper. Firstly, the GMPSO algorithm is used to optimize the [K , α] parameter combination in the VMD algorithm, and the optimal [K , α] parameter combination of each gear fault vibration signal to be decomposed is selected. Then, the gear fault vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, and the sample entropy value of each IMFs is extracted to form the feature vector of subsequent fault diagnosis. Finally, the characteristic vector of gear fault vibration signal is input into PNN model, and gear fault is accurately classified. By comparing with fixed parameter VMD algorithm, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm, the superiority of this method in gear fault diagnosis is verified. Therefore, the GMPSO-VMD-PNN algorithm proposed in this paper has certain application value for gear fault diagnosis.

The vibration signal of an early rolling bearing is nonstationary and nonlinear, and the fault signal is weak and difficult to extract. To address this problem, this paper proposes a genetic mutation particle swarm optimization variational mode decomposition (GMPSO-VMD) algorithm and applies it to rolling bearing vibration signal fault feature extraction. Firstly, the minimum envelope entropy is used as the objective function of the GMPSO to find the optimal parameter combination of the VMD algorithm. Then, the optimized VMD algorithm is used to decompose the vibration signal of the rolling bearing and several intrinsic mode functions (IMFs) are obtained. The envelope spectrum analysis of GMPSO-VMD decomposed rolling bearing fault signal IMF1 was carried out. Moreover, the feature frequency of the four fault states of the rolling bearing are extracted accurately. Finally, the GMPSO-VMD algorithm is utilized to analyze the simulation signal and rolling bearing fault vibration signal. The effectiveness of the GMPSO-VMD algorithm is verified by comparing it with the fixed parameter VMD (FP-VMD) algorithm, complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm and empirical mode decomposition (EMD) algorithm.

A gear fault diagnosis method based on kurtosis criterion variational mode decomposition (VMD) and self-organizing map (SOM) neural network is proposed. Firstly, the VMD algorithm is used to decompose the gear vibration signal, and the instantaneous frequency mean is calculated as the evaluation index, and the characteristic curve is drawn to screen out the most relevant intrinsic mode functions (IMFs) of the original vibration signal. Then, the number of VMD decompositions is determined, and the kurtosis value of IMFs are extracted to form the feature vectors. Then, the kurtosis value feature vectors of IMFs are normalized to form the kurtosis value normalized vectors. Finally, the normalized vectors of kurtosis value are input into SOM neural network to realize gear fault diagnosis. When the number of training times of SOM neural network is 100, the gear fault category is accurately classified by SOM neural network. The results show that when the training times of SOM neural network is 100 times, the gear fault diagnosis method, based on the kurtosis criterion VMD and SOM neural network is 100%, which indicates that the new method has a good effect on gear fault diagnosis. Appl. Sci. 2019, 9, 5424 2 of 25 the decomposed mode is fixed. It is better to use different wavelet bases for the analysis of different signals to achieve the best processing effect. EMD and LMD are prone to endpoint effect and mode mixing during the decomposition process. Therefore, Dragomiretskiy [9] proposed a variational mode decomposition to solve the problems caused by EMD and LMD in the decomposition process. Wang [10] used variational mode decomposition (VMD) to extract various fault features of the gearbox under strong noise environment, and compared with the ensemble empirical mode decomposition (EEMD) decomposition results, it shows that the algorithm can effectively improve the signal-to-noise ratio of the signal. Li [11] proposed a fault diagnosis method based on VMD and generalized composite multi-scale dynamic entropy (GCMSDE) to identify different health conditions of planetary gearboxes. Feng [12] uses VMD to decompose the planetary gearbox vibration signal into several intrinsic mode functions (IMFs), and performs Fourier transform on the amplitude envelope and instantaneous frequency of the sensitive IMFs to obtain the amplitude and frequency demodulation spectrum. The planetary gearbox faults have been detected based on demodulation and have been successfully identified on all three gears (sun gear, planetary gear, and ring gear). Wang [13] used the improved VMD algorithm to diagnose the gearbox and compared it with EEMD to verify the effectiveness of the proposed method. Si [14] proposes an improved VMD linked wavelet denoising method, which can suppress high frequency narrowband noise and normal noise in electromagnetic acoustic transducer (EMAT) signal, and this method can retain defect information.In recent years, researchers have studied a large number of fault classification algorithms. Among them, the gear fault...