## 7 Conclusions  
This study designs an BPNN model to predict the surface quality of smart manufacturing. The proposed method first normalizes the data and performs polynomial feature transformation. Then, ANOVA is employed to analyze and select significant features. Subsequently, both RSM and BPNN models are used for prediction and evaluation. By reducing the iteration times for training BPNN and evaluating sample sizes, the BPNN model is constructed. Finally, reverse computation and parameter optimization of the established model are performed, and validation experiments on real machines are carried out. The results demonstrate that the proposed BPNN model exhibits excellent predictive performance for the surface roughness of aerospace aluminum alloy workpieces. The main contributions and conclusions of this study are as follows:  
1. During the selection of polynomial features after dimensional expansion, ANOVA is adopted to evaluate the significance of process features. Features with \(p\)-values exceeding the significance threshold are eliminated, resulting in polynomial interaction features based on four experimental process parameters: grinding force, feed speed, wheel speed, and sandpaper grit size. 2. Based on the RSM and BPNN prediction models, an BPNN fusion model is designed. This model combines the reliability of RSM for small sample sizes and the accuracy of BPNN for large sample sizes under varying sample sizes. Taking into account the training time and fitting efficiency, this model is better suited to handle data modeling for single-piece and small-batch workpieces under varying experimental conditions, meeting industrial requirements for efficient model establishment. 3. After performing reverse computation and parameter optimization on the model, the optimized parameters are used to calculate the selected feature results for real-machine validation. The experiments validate the applicability of this method in predicting the surface roughness of single-piece and small-batch workpieces in industrial robotic grinding applications. However, the exploration and application of algorithms in this study are relatively straightforward, leaving room for improvement in the use of more advanced algorithms. Future research could introduce more sophisticated machine learning algorithms and compare their effectiveness. Future studies may also expand the inputs and outputs of the model. For instance, grinding depth could be added as an input variable, while material removal rate and robotic processing time could be considered to be output variables to construct a multi-objective optimization model, thereby addressing the diverse requirements of different industrial applications. Additionally, future research should consider training and validating the model with larger datasets, incorporating data augmentation or transfer learning for small-sample training to enhance the robustness and generalizability of the model. The following supporting information can be downloaded at: www.mdpi.com/xxx/s1. Conceptualization, Y.X., K.W. and Y.P. ; Data curation, Y.X. and Y.M. ; Formal analysis, K.W. and Y.Q. ; Funding acquisition, K.W. and Y.P. ; Investigation, Y.X. and Y.M. ; Methodology, Y.X. ; Resources, K.W. and Y.P. ; Validation, Y.X. and Y.M. ; Writing--original draft, Y.X. ; Writing--review and editing, Y.Q. and Y.P. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key R&D Program of China under Grant 2022 YFB4701200, Beijing Natural Science Foundation under Grant 3232018, the Science, Technology and Innovation Commission of Shenzhen Municipality under Grant SGDX2020530110804030, JCYJ20220818100417038, and JCYJ 20220531102009022, the National Key Laboratory of Aerospace Institutions under Grant 2024 ASM-KFZY01. Not applicable. The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest.