## 2 Related Work  
The method of tool wear estimation can be divided into direct detection and indirect detection. Direct detection (e.g., optical measurement [9; 10; 11], scanning electron microscope (SEM) measurement [12], and atomic force microscope (AFM) measurement [13]) measures the tool surface state, the wear amount of the tool surface, and other parameters directly, to confirm the wear state of the diamond tool. However, its practical application is restrained by the cutting fluid, chip, lighting, and other conditions in the processing. Therefore, it can be applied to field monitoring, but online monitoring or in situ monitoring is difficult [3]. The optical measurement approach is more suitable for industrial applications, although the resolution range is limited to several hundred nanometers by optical diffraction [3]. On the other hand, the indirect detection approach judges the tool wear condition indirectly through the cutting force, surface roughness, vibration, acoustic emission, and other signals in the processing. This approach has lower accuracy, but the signals are easy to monitor online. Indirect detection can be divided into four main steps, namely, signal acquisition, signal processing, feature extraction, and state recognition. For example, in the aspect of signal acquisition, [PERSON] et al. [14; 15] detected acoustic emission signals and represented DTW with signals and cutting distance. [PERSON] et al. [16] used broadband acoustic emission sensors to measure the acoustic emission signals during the processing of nickel-phosphorus alloy by diamond tools. Cutting force signals contain characteristic information about tool wear and are often used to monitor DTW in ultra-precision diamond cutting [17]. [PERSON] et al. [16] measured the thrust variation during the processing of nickel-phosphorus alloy by force sensors, and further deduced DTW by identifying the \(1/\mathfrak{f}\mathfrak{g}\) noise in the power spectrum which varies with the degree of tool wear. [PERSON] et al. [17] confirmed the possibility of using a cutting force signal to monitor tool wear. [PERSON] et al. [18] analyzed the tool wear state by using cutting force characteristics such as phase-frequency characteristics and power amplitude-frequency characteristics of cutting force signals in the cutting process. [PERSON] et al. [19] proved through experiments that DTW would lead to an increase in cutting force. In signal processing and feature extraction, the wavelet transform technique can effectively detect transient features such as singularity or discontinuity, which greatly reduces the signal processing time [3]. In the state recognition, [PERSON] et al. [20] collected cutting force signals and vibration signals in ultra-precision machining, extracted wear-related signals by correlation analysis, and identified the wear state by self-organizing mapping (SOM). [PERSON] et al. [21] identified the state of the DTW by the cutting force signals and a fuzzy pattern recognition network. Due to the increase in machining data volume, deep learning algorithms have attracted more and more attention. [PERSON] et al. [4] performed time series images on the forces in three dimensions by time series imaging method and fed the three-channel images into a convolutional neural network for tool wear classification. Another way to obtain image-based datasets from time series is by imaging signals by time-frequency analysis techniques such as wavelet transform. Then, the resulting energy spectrum pictures are fed into the convolutional neural network. [PERSON] et al. [22] proposed a side-edge wear depth model based on feature fusion. They converted the signals of multiple sensors into multi-channel images, and then fed the multi-channel images into different convolutional neural networks to extract features in parallel from multi-source data and make tool-wear predictions. There are still some problems with DTW monitoring to be solved.