# Rotor Fault Diagnosis Method Based on VMD Symmetrical Polar Image and Fuzzy Neural Network
## 1 Introduction
From Table 1, we can know that compared with empirical mode decomposition (EMD) [10], local mean decomposition (LMD) [11], wavelet transform (WT) [12] and ensemble empirical mode decomposition (EEMD), VMD method could effectively avoid the mode mixing problem in the decomposition process, suppress disturbing components, and ensure the precision of subsequent signal feature extraction. At present, this method is widely applied to lots of fields, such as rotating machinery fault diagnosis and signal denoising. In view of the fact that vibration signals of rolling bearings are much contaminated by noise in the early failure period, [PERSON] et al. [13] proposed a denoising method based on VMD and singular value decomposition (SVD), and the experimental result shows that the proposed method can effectively retain the useful signals and denoise the bearing signals in extremely noisy backgrounds. [PERSON] et al. [14] combined the advantages of VMD, wavelet threshold denoising (WTD), and singular spectrum analysis (SSA), proposed a measured load signal denoising method and experimental results of synthetic signals demonstrate that the presented method outperforms the conventional digital signal denoising methods. [PERSON] et al. [15] applied VMD and soft wavelet-thresholding to denoise rotor vibration signals. Through noise reduction experiments of rotor vibration signals under different working conditions, the results show that the signal-to-noise ratio of the VMD method basically doubles the EMD one. [PERSON] et al. [16] proposed a novel denoising method that combines VMD and detrended fluctuation analysis (DFA). Through simulated and real signals analysis, the results show that the superior performance of this proposed filtering over EMD-based denoising and discrete wavelet threshold filtering. Unfortunately, from Table 1 we can also see that the selection of key parameters and the elimination of disturbing components in the process of VMD decomposition have always been the main factor that affects the decomposition precision and the efficiency of feature extraction. The pattern recognition method based on deep learning could automatically extract image features. But in order to obtain appropriate parameters, the deep network requires a large number of sample data to train the model. Insufficient, samples lead to overfitting of the model training, resulting in low generalization ability of the model and poor fault diagnosis precision. Even though, the present research on fault diagnosis methods of rotating machinery are still based on small samples. As a common intelligent information processing method, fuzzy neural network has strong self-learning and data direct processing ability, which can express the structure of the result clearly [17], making itself an effective method for small sample fault diagnosis. [PERSON] et al. [18] established a fault signal acquisition engine test stand and simulated six kinds of engine working conditions. WT method was used to extract signal features and compose state eigenvectors and the fuzzy neural network was used to realize the effective diagnosis of engine faults with small samples. [PERSON] et al. [19] proposed a fault diagnosis method for mine hoist braking system based on fuzzy neural networks, the experimental results show that the fuzzy neural network can diagnose faults accurately. [PERSON] et al. [20] applied fuzzy neural network to diagnose ventilator fault, through the example comparison of the fuzzy neural network and the BP neural network, the results illustrate that the fault diagnosis method of the fuzzy neural network can recognize the faults rapidly, accurately and steadily, which provides an efficient way for the diagnosis. Aiming at the non-stationary rotor fault vibration signal and it is hard to accurately extract image features by directly obtaining the symmetric polar image of the signal with environmental noise. In this paper, a novel method for fault feature extraction and pattern recognition is proposed.