# Rotor Fault Diagnosis Method Based on VMD Symmetrical Polar Image and Fuzzy Neural Network
## 1 Introduction  
Rotating machinery is widely used in many industries such as aerospace and railway transportation. Rotor is an important component of rotating machinery equipment. Due to the increase in equipment complexity and precision, and the continuity of work tasks, local faults will inevitably occur on the rotor. According to statistical results, rotor local faults account for more than 50% of the causes leading to the failure of rotating machinery [1]. If the rotor faults cannot be detected in time, the working performance of the whole equipment will be affected, and huge economic losses will be caused in serious cases. Therefore, rotor fault diagnosis has always been a hot spot in the field of fault diagnosis [2]. Generally, the extraction of rotor fault features is mainly based on the time domain, frequency domain or time-frequency domain of the signal. In recent years, image processing has been widely used to diagnose rotor faults. Method of amplitude standardization based on signal sampling length can be used to transform the rotor vibration signal into a two-dimensional gray image, in which the texture feature, the feature frequency, and the brightness of the gray image are used to establish the characteristic matrix of the image. Thereby different degrees of unbalanced faults can be recognized [3]. [PERSON] et al. [4] used the nonlinear chirp mode decomposition method to decompose the gas turbine rotor vibration signal into components, then the instantaneous frequency of each frequency component wasobtained, and the fault diagnosis of the rotor was carried out by the convolutional neural network (CNN). [PERSON] et al. [5] proposed a rotor fault diagnosis approach that transformed multiple rotor vibration signals into symmetrized dot pattern (SDP) image, and identified the SDP graphical feature characteristic of different states using a CNN. [PERSON] et al. [6] expressed the time-frequency image of the rotor vibration signal as a texture feature tensor for the pattern recognition of rotor fault states with the linear support higher-tensor machine (SHTM). The experimental results showed that the method of classifying time-frequency texture feature tensor can achieve ideal diagnosis precision. The core of the fault diagnosis method based on image processing technology is to generate a simple and intuitive image, which can take abundant characteristic information of the rotor fault signals. Among image generation methods, the symmetrical polar coordinate method transforms the signal into a polar coordinate and expresses it in the form of a two-dimensional snowflake image, which is directly obtained from the time-domain signal and without the need for frequency analysis. This method is simple to calculate and it is an ideal image generation method. However, due to the diversity of working conditions and the complexity of the mechanical system, the rotor vibration signal shows obvious signs of non-linear and non-stationary [7]. In addition, due to the influence of environmental noise, acquisition devices and other factors, the collected rotor vibration signals contain various disturbing signals [8]. It is difficult to ensure the precision of image feature acquisition by directly obtaining the symmetric polar image of this signal. Therefore, in order to strengthen the fault characteristic components, it is necessary to eliminate the disturbing signals before generating snowflake images. Variational modal decomposition (VMD) [9] method is an adaptive and nonrecursive signal decomposition method. VMD method decomposes the non-linear and non-stationary signal into a series of intrinsic modal functions (IMFs) with limited bandwidth by solving the optimal solution of the variational problem. Table 1 lists the shortcomings of common signal decomposition methods.