## 1 Introduction  
The important position of the tool in the cutting process has caused extensive research on the monitoring of tool wear states in the metal-cutting process [1, 2], which has a history of several decades. Among them, the complex profile of aeronautical structural parts makes the sensor signal in the processing process very non-stationary, which greatly increases the monitoring difficulty. Therefore, the monitoring system is required to have higher adaptability and robustness. As an important part of signal feature extraction, its main goal is to transform the sensor signal to achieve the dimensionality reduction and de-redundancy of the original data, and extracting from it has high sensitivity, robustness and reliability for monitoring targets, so as to improve the efficiency and accuracy of pattern recognition. According to the difference of transform domain, it can be divided into feature-extraction methods based on time domain [3, 4], frequency domain [4, 5] and time-frequency domain [4, 6, 7]. In the time domain, the most commonly used features are root mean square, mean, kurtosis, standard deviation, skewness, and crest factor. [PERSON] et al. [8] extracted four statistical features with tool wear sensitivity in the time domain: the mean to reflect the central tendency of the signal; the root mean square (RMS) to represent the average energy of the signal in a given time interval; kurtosis (Kur) to represent signal transients and stationarity; and margin (Mar) to represent the ratio of the square root amplitude to the peak value of the signal. While these features are easy to extract and use, important information about the frequency content of the milled signal cannot be obtained and is susceptible to environmental noise. At this time, there is great advantage in performing feature extraction on the signal in the frequency domain. In the frequency domain, Fourier transform technology has been widely used for tool wear monitoring, and most of the information about the frequency components of the signal is obtained through fast Fourier transform (FFT) [9]. [PERSON] et al. [10] presented fast Fourier transform (FFT) for frequency domain feature extraction. The features extracted from the frequency domain include peak amplitude spectrum (PAS) and peak power spectrum (PPS). During the entire milling process of cutting teeth from cutting in to cutting out, the change of signal energy can be seen from the time domain waveform of the signal, and the frequency component of the signal can be seen from the amplitude spectrum. The changes in the time domain and frequency domain can be observed in the time-frequency diagram of the signal at the same time. From the time-frequency diagram, it can be found that the frequency components of the signal have been changing with time. This time-frequency non-stationary characteristic cannot be represented by frequency domain features, so the method of time-frequency analysis can better reflect the characteristics of the signal. There are two main ideas for extracting the time-frequency features of a signal. One is to use multi-resolution analysis methods such as wavelet decomposition [11; 12], empirical mode decomposition [13] and variable mode decomposition [14; 15] to decompose the signal into components in different frequency bands and then select the components for monitoring. One or more components that are sensitive to the target are reconstructed, and then the time domain and frequency domain features are extracted respectively. [PERSON] et al. [14] used time-frequency domain methods such as variable-mode decomposition energy entropy, multi-scale power spectrum entropy, and multi-scale displacement entropy to process the processed signals collected by multiple sensors to obtain relevant feature data sets. [PERSON] et al. [15] proposed a method for identifying the wear state of milling cutters based on optimized variational modal decomposition (VMD).