## 6 Conclusions  
This paper expanded the application of 2-D CNN in the field of tool wear state identification. The raw signal was decomposed with constant power via DWFs. Then the frequency band with more impulsive components and higher signal-to-noise ratio was selected according to the kurtosis of the reconstructed sub-signal. Further, the 1-D spectrum was folded into 2-D spectral map. After converting the spectrum of the sample signal in different wear states into normalized 2-D maps, no significant difference characteristics could be found by visual observation. Therefore, the CNN model was trained to extract features from the 2-D map and achieve good classification accuracy. The deep convolutional neural network could adaptively extract implicit features from large input data. However, in the spindle vibration signal, the information on tool wear was interfered by other contents. The feature engineering based on DWFs constructed a better data set for CNN, and thus significantly improved the learning speed and recognition accuracy of CNN. In high-automation workshops that perform small-batch production, a milling tool often participates in the processing of different products. At this industrial site, the number of machined parts is not sufficient to accurately predict the remaining life of the milling tool. The experimental results show that the proposed method could indirectly monitor the wear state of the milling tool based on the spindle vibration signal. Even if the cutting conditions were unknown when acquiring signals, the wear state of the milling tool could still be accurately recognized. The 2-D CNN model constructed in this paper contained a total of 24,306 trainable parameters. After the CNN model was trained, the time cost of one sample was less than 0.005 s, while the data processing based on DWFs took about 0.13 s. Coupled with data acquisition and transmission time, the total time cost to perform a tool wear state recognition was less than 1.5 s, which basically met the requirements of online monitoring. Some conclusions could be drawn as follows:  
1. The impact of the cutting edge and the work piece was the main stimulus for the machine shaft vibration. As the sharpness of the cutting edge gradually decreased, the vibration mode of the spindle changed. The vibration acceleration data indirectly recorded the wear process of the tool. The 1-D CNN could extract implicit features from it, nevertheless, the test accuracy was only 75%. There were many interfering contents in the raw signal, and changes in cutting conditions interfered with the neural network, so proper feature engineering was indispensable. 2. Transforming the signal from the time domain to the frequency domain eliminated the interference of the initial phase on the neural network when the signal was acquired. Normalization could reduce the dependence of neural networks on signal strength, forcing them to mine features that were less relevant to cutting conditions. Using the normalized spectrum to train 1-D CNN, the test recognition accuracy reached 92%, which was obviously better than the temporal signal. 3. Folding the 1-D spectra into 2-D spectral maps gave full play to the more powerful learning ability of the 2-D CNN. The 1600-4800 Hz frequency band selected by the DWFs algorithm had a higher signal-to-noise ratio, which reduced the size of the input to CNN by half, and further improved the recognition accuracy of the neural network model, reaching 98.6%. The tool wear condition monitoring method proposed in this paper could also be used for other machining methods, such as drilling and turning. The method to identify the state of the monitoring signal using a 2-D CNN might also be extended to other fault diagnosis occasions, such as gear fault diagnosis based on vibration signals. **Author Contributions:** Conceptualization, X.C. and B.C. ; methodology, B.Y. ; software, X.C. ; validation, X.C. ; and B.C. ; formal analysis, B.Y. ; investigation, B.C. ; resources, B.Y. ; data curation, B.C.