## 4 Model Prediction Results and Analysis  
### Ga-Gbrt Model  
From the perspective of artificial intelligence, the task of predicting surface roughness can be transformed into a supervised regression problem. The input variables are the cutting parameters (cutting speed \(v\), feed rate \(f\), and depth of cut \(ap\)), and each sample obtains the corresponding target value (surface roughness \(Ra\)). The surface roughness regression problem that is based on GBRT is addressed by taking the following steps:Despite the capability of the GBRT method to automatically identify nonlinear interactions through decision tree learning and its success is referred to in many studies, it remains constrained by a number of drawbacks. Firstly, the GBRT method is incapable of explicit regularization. The regularization effect can be achieved by means of the learning rate, the number of iterations, and the maximum depth parameter. The interaction of these parameters in regularization is lacking in clarity. Secondly, the step size of the learning rate parameter is viewed as implicit regularization. Besides, in order to avoid over-fitting, there is a potential need for a smaller step size. However, a small learning rate parameter means that the computational cost of the application is high. Thirdly, regression tree learning is treated as a black box. In this paper, attempts are made to optimize the model parameters in the training set data by using genetic algorithm to improve the generalization ability of the GBRT model while achieving a higher test accuracy. Figure 5 presents the schematic diagram of the GA-GBRT prediction model. According to the prediction accuracy of GBRT, the appropriate initial parameters (lifting iteration number \(M\), maximum depth \(D\) of individual regression estimation, and learning rate \(V\)) are determined by a combination of genetic algorithm and k-degree cross-verification. The performance evaluation index is the goodness of fit \(R^{2}\) between the predicted value \(y_{i}\) of GBRT and the observed value \(y_{i}\). As indicated by Figure 6, the k-fold cross-validation strategy is adopted to construct and validate the model. In this paper, in order to prevent the over-fitting of the prediction algorithm, the k value is set to 5, which is effective in reducing the running time for the computer. The training data of 50 groups were split into five groups on a random  
Out of the collected data, 50 groups were selected as the training group, and 10 of which were taken as the test group. The use of the GA-GBRT prediction module is illustrated in Figure 5. The main steps were as follows:  
Step 1: The turning experimental data was collected, and the training group data was used to train the key parameters of the GBRT model. Step 2: Parameter coding and population initialization: A chromosome sequence was generated on a random basis for increasing the number of iterations \(M\), the maximum depth \(D\) of the individual regression estimator, and the learning rate \(V\). The initial population was set to 30 and the maximum evolutionary algebra was set to 50. Step 3: The fitness value of the goodness of fit of each individual was calculated. Step 4: If the number of cycles failed to reach the maximum number of iterations, the population was selected, crossed, and mutated to produce a new generation of populations, and the GBRT model training continued. Step 5: Steps 3 and 4 repeat themselves until the maximum evolution algebra was reached or the maximum number of iterations was exceeded to obtain the optimal model parameters. The GBRT-GA algorithm relies on the use of different combinations of three main parameters (\(M\), \(D\), \(V\)). At the time of the 20 th generation, the maximum value is obtained, the fitness value of the best  
Figure 5: GA-GBRT model development flow chart. Figure 6: K-fold cross-verification flow chart. individual \(R^{2}=0.968\), the optimal parameters are found (\(M=82\), \(D=1\), \(V=0.14\)), and the number of iterations is lower than the default value of 100.