## 6 Discussions  
_Evaluation Results of BPNN Fusion Method on Variable Small-Sample Data_  
From an engineering perspective, the tradeoff between accuracy and modeling time must be considered. In order to obtain a modeling method combining RSM and BPNN, the two methods of RSM and BPNN will be compared and analyzed respectively, and the optimal method will be selected under different sample sizes according to specific experimental constraints and requirements to form the BPNN fusion method. The discussion provides a comparison of the predictive accuracy of the two algorithms based on 60 sets of data. However, in practical usage, the number of data samples often  
Figure 11: Comparison of grinding effects on workpieces under optimal and non-optimal robotic grinding parameters. varies significantly due to the scarcity of experimental materials. Therefore, this study designed experiments to measure method selection under different sample sizes. In the following, further investigation will be carried out by conducting training and fitting using 20-60 sets of data for 500 iterations each. The evaluation metrics, including \(R^{2}\), \(MSE\), \(RMSE\), and runtime, will be calculated and analyzed as assessment indicators of the results. Additionally, from the perspective of transferability in industrial applications, as shown in Figure 12, for both RSM and BPNN with 500 epochs, RSM required significantly less runtime compared to BPNN of the same data size. Since workers are often responsible for repetitive operations and may lack expertise in data processing, RSM can be directly embedded in the teach pendant used by workers as guidance, assisting them in modeling and predicting grinding process parameters. In contrast, BPNN requires preprocessing of data or complex hyperparameter selection, which entails a considerable amount of time for tuning until the model achieves satisfactory performance. Therefore, in terms of usability and transferability, RSM outperforms BPNN with 500 epochs. To address the issue of the BPNN's prolonged runtime, a training method of combining 10-iteration BPNN training with RSM is proposed, as indicated by the green line in Figure 12d. It can be clearly observed that, in terms of the \(R^{2}\), BPNN exhibited similar and satisfactory fitting performance for both 500 epochs and 10 epochs. The trends of \(MSE\) and \(RMSE\) were consistent, and the intersection with RSM also occurred at sample sizes between 30 and 40, indicating that reducing the number of training iterations from 500 epochs to 10 epochs still holds the aforementioned conclusion that the sample size  
Figure 12: (**a**). \(R^{2}\), (**b**). \(MSE\), (**c**). \(RMSE\) and (**d**). runtime comparison vs. sample size. threshold falls between 30 and 40. In terms of runtime, it can be observed that the runtime of BPNN is directly proportional to the number of epochs, with the training duration of 500 epochs being much longer than that of 10 epochs. Comparing the runtime of 10-epoch BPNN with RSM, the runtime of BPNN is still longer than that of RSM, but the individual runtime is consistently less than 1 s, indicating a faster response speed, which meets the requirements of practical industrial applications. In summary, RSM and 10-epoch BPNN were chosen to compose the proposed BPNN fusion method. Since the sample size threshold obtained in the above experiments is between 30 and 40, we choose to use RSM fitting when it is less than the threshold, and choose 10-epoch BPNN for training when it is greater than the threshold, and finally obtain the BPNN fusion method. As shown in the red line in Figure 12, BPNN avoids the shortcomings of RSM, which is not accurate enough when the data size is large, and BPNN, which has a large overfitting error when the data size is small. By shortening the number of iterations of BPNN, the runtime is reduced to a level suitable for industrial production scenarios.