# Optimization Design of Centrifugal Fan Blades Based on Bezier Curve Method
## 5 Conclusions  
Fitting the blade profile with fourth-order Bezier curves, a surrogate mapping between the design parameters and the optimization objectives was established with a radial basis neural network model, and multi-objective optimization was carried out using a multi-objective genetic algorithm. The following conclusions were reached:  
1. The fourth-order Bezier curve method achieved a fitting accuracy of 99.6% when reproducing the original blade shape, which met the required precision for blade profile fitting.
2. Based on the blade profile display results, the fourth-order Bezier curve method offered more flexible control over the curvature at different chord lengths. The optimized blade curvature increased from the inlet to a peak and then decreases towards the outlet, resulting in a more pronounced profile at the inlet and a smoother profile at the outlet.
3. The optimal Latin hypercube summation method was used to construct the samples, and significance analysis was conducted on the design parameters. It can be seen form the result that \(\beta_{2}\) and \(r_{2}\) had a greater influence on static pressure, while \(\beta_{1}\) and \(\beta_{3}\) had a greater impact on static pressure efficiency. The optimization results were consistent with the significance analysis, indicating that there were interactions among the design parameters and that the overall model was extremely significantly correlated.
4. The radial basis neural network accurately and effectively captured the mapping relationship between the design parameters and the target outcomes. Compared with numerical results, the prediction error of the surrogate model did not exceed 1%, which met the accuracy requirements.  
Figure 19: Vortex structures and vorticity of fans.  
After optimization, the fan's static pressure at the design operating condition increased by 12.7 Pa, and the static pressure efficiency increased by 3.2%, leading to improved fan performance. The optimized fan's high-efficiency point shifted toward the low-flow region, with notable improvements in both efficiency and static pressure under low-flow conditions. This broadened the high-efficiency operating range, making the fan better suited to various application scenarios.
* 6. After optimization, the streamlines aligned more closely with the blade profile. The impact at the blade inlet and the separation on the suction side were improved, resulting in reduced flow loss. At the same time, the vortical structures and vortex intensity within the channel were significantly diminished, effectively suppressing complex flow phenomena.  
Methodology, K.L. and T.H.; software, J.W. and D.Z.; validation, H.H., D.G. and L.J.; writing--original draft preparation, J.W.; writing--review and editing, K.L., M.L. and T.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52376005; the National Natural Science Foundation of China, grant number 52378094; the Henan Provincial Science and Technology Research Project, grant number 222102220033, the Henan Provincial Science and Technology Research Project, grant number 242102220004; and the Luoyang Science and Technology Research Project, grant number 2302035A.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.  
Authors [PERSON], [PERSON] and [PERSON] were employed by the company Zhejiang Yiliida Ventilator Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.