# Bearing Fault Diagnosis Method Based on Improved VMD and Parallel Hybrid Neural Network
## 1 Introduction  
Rotating machinery is widely used in industrial production. As a key component of rotating machinery, the failure of the rolling bearing will directly affect the normal operation of the whole equipment. But it is often in a continuous load working state, which is prone to failure [1]. The failure of the rolling bearing will cause the stopping of large machinery and cause great losses, which will put the staff at risk. Therefore, the research on fault diagnosis of the rolling bearing has great practical value. A bearing vibration signal is non-stationary and non-linear, and there are many interference factors in the working environment, so it is difficult to analyze the signal [2]. For the traditional signal decomposition method, high-frequency noise will destroy the local characteristics of the signal, resulting in different frequency components mixed with the same intrinsic mode function, affecting the accuracy and aggravating mode aliasing. For the method of neural networks, noise may be mistaken for effective features by neural networks, resulting in the model overfitting the noise rather than the real signal mode, which then results in the deviation of feature learning. Traditional signal analysis methods include time domain analysis and frequency domain analysis. The time domain analysis method directly extracts various statistical indicators of the analysis signal. The frequency domainanalysis method converts the signal to the frequency domain through the Fourier transform and uses the fault frequency for the analysis. These traditional analysis methods are still very useful for some simple signal analysis tasks, but with the continuous breakthrough of signal analysis technology, time-frequency analysis, a new signal analysis method, has entered people's vision [3]. Common time-frequency analysis methods include wavelet transform (WT), short-time Fourier transform (STFT), empirical mode decomposition (EMD), and local mean decomposition (LMD). The principle of wavelet transformation is based on the multi-scale decomposition and reconstruction of signals, using a group of special functions called wavelet basis functions to represent the signal and extracting the time-domain and frequency-domain information of the signal by decomposing and reconstructing the signal at different scales. However, it is difficult to select the wavelet basis function. Selecting an inappropriate wavelet basis function may lead to inaccurate analysis results or the inability to meet specific needs. The requirement for the length of the data is high, and the boundary effect may occur at the boundary of the signal. [PERSON], K et al. [4] proposed an empirical wavelet transformation and Capon time-frequency analysis method for a denoising analysis of EMG and EEG signals. Using adaptive spectrum segmentation and filter design in the empirical wavelet transform, the shortcomings of the fixed basis function of the traditional wavelet transform are overcome, while the Capon time-frequency analysis method has significant advantages in improving the resolution and eliminating interference, and the combination of the two has achieved a good denoising effect. The STFT is a mathematical tool for joint analysis of signals in the time and frequency domains. It analyzes the frequency components while preserving the time locality by dividing the signal into frames and windows and performing the Fourier transform segment by segment. However, Fourier transform has the problem that time and frequency resolution cannot be obtained at the same time, and compared with wavelet transform, it uses a fixed-length window throughout the whole analysis process, which cannot adapt to the signal characteristics. EMD decomposes the signal to acquire a series of intrinsic mode functions (IMFs) which represent the time-varying characteristics of different scales in the signal. [PERSON] et al.