## 2 Research and Progress of Surface Roughness Prediction in Metal Processing  
In recent years, experts and scholars have conducted experimental and predictive studies on the surface roughness of metal processing techniques such as milling, turning and grinding. The commonly used methods included empirical formula prediction, response surface regression analysis prediction, neural network prediction, genetic algorithms (GAs) and et al. [PERSON] et al. adopted artificial neural networks (ANNs) and developed a surface roughness prediction model for C26000 brass in dry cutting conditions on a CNC turning machine, which (with the interacting terms) took into account the interactions between the parameters and achieved an accuracy of 87.07%. Their study found feed speed as the most influential parameter, followed by grinding speed and the depth of cut [7]. [PERSON] et al. established a machined surface roughness prediction model using fuzzy neural networks based on the grinding wheel wear state and grinding parameters [8]. [PERSON] et al. combined ANNs with GAs for a post-grinding surface roughness prediction and optimization model [9]. [PERSON] et al. selected the working speed, cutting depth and feed speed as input parameters of the process and used an adaptive neuro-fuzzy inference system (ANFIS), neural network and regression analysis to develop prediction models for surface roughness and the metal removal rate during cylindrical grinding. Compared to neural networks and regression analyses, the surface roughness predictions based on ANFIS agreed well with the experimental results [10]. [PERSON] et al. developed a surface roughness prediction model for Ti-6 Al-4V abrasive belt grinding, based on the response surface methodology, and the average error between experimental measurements and model predictions was 6.08% [11]. [PERSON] et al. designed microgrinding tests for composites based on the response surface methodology, and their regression equation model (established by regression analysis and removing the insignificant terms) could relatively accurately reflect the effects of cutting depth, feed speed and spindle speed on surface roughness [12]. [PERSON] et al. conducted experimental research and estimations on the surface roughness of high-speed micro-end milling of titanium alloys using ANNs, group method data processing (GMDH) and multivariate regression analysis (MRA), and their observed results showed that the prediction accuracy of neural networks was higher than the other techniques [13]. [PERSON] et al. developed multivariate regression models (MRMs) and neural network prediction models under various cutting conditions from low-speed to high-speed steady machining, and their results showed that neural network models had higher prediction accuracy [14]. [PERSON] et al. applied empirical models and neural networks to predict the surface roughness for the cryogenic milling of titanium alloys, and the comparative analysis of their results revealed that the maximum relative error between experimental values and predictions by the neural network model was 3.64%, and the error variation was small. Compared with the empirical model, the neural network model had a higher prediction accuracy and generalization ability, which could better predict the effect of each parameter on surface roughness [15]. [PERSON] et al. developed two prediction models based on ANNs and MRMs for predicting the surface roughness of turning machining AISI 1040 steel. In both models, feed speed was identified as the most significant factor affecting surface roughness, followed by the depth of cut and line speed of cut. The results of their study showed that ANNs outperformed MRMs [16]. Therefore, ANNs have achieved certain research results in the prediction of surface roughness after machining. However, no research on the surface roughness prediction of the grind-hardening process or related results has been reported.