# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 5 Conclusions  
This study employs a regression/interpolation combination surrogate model for a multidisciplinary design optimization of a turbine blade, offering an efficient approach for optimizing the cooling turbine blade. The methodology integrates collaborative coupling feature parameterization modeling for the cooling turbine blade, simulation analyses focusing on aerodynamics and structural strength, and a regression/interpolation combination surrogate model. By optimizing the shape of the cooling turbine blade while considering various disciplinary constraints, the study achieves improved aerodynamic efficiency within the turbine stage. The main findings of this research are as follows:  
1. The optimized turbine blade exhibits enhanced aerodynamic performance while maintaining a relatively constant total expansion ratio and gas flow rate under strength constraints. Additionally, the 41-section efficiency improves by 0.69%.  
Figure 21: Static pressure distribution of the first-stage rotor blade at different blade height sections before and after optimization. (**a**) 10% span cross section; (**b**) 55% span cross section; (**c**) 90% span cross section.  
2. The increased chord length at the tip of the improved first-stage rotor blade effectively improves flow conditions in over 58% of the blade height region, leading to a reduction in low-speed flow area on the blade suction side.
3. The optimization of the first-stage rotor blade profile adjusts the load distribution on the blade surface, which helps eliminate flow separation at the trailing edge of the suction side near the blade tip, consequently reducing energy loss.  
These findings highlight the significant potential and prospects of the innovative regression/interpolation combination surrogate model in addressing challenging issues across various practical engineering applications. For future research, it is advisable to integrate additional disciplines such as vibration, heat transfer, and lifespan based on the insights gained from this study. This expansion will further enrich the multidisciplinary analysis model and fully exploit the advantages of the regression/interpolation combination surrogate model-based multidisciplinary design optimization approach for turbine blades in practical engineering applications.  
Conceptualization, W.W.; Data curation, E.K. and J.X.; Formal analysis, L.X.; Funding acquisition, C.Y.; Investigation, L.X. and J.X.; Methodology, W.W., L.X., and E.K.; Project administration, S.S. and C.Y.; Resources, W.W. and S.S.; Software, W.W., L.X., and J.X.; Supervision, S.S., C.W., and C.Y.; Validation, W.W., L.X., E.K., and C.W.; Visualization, C.W.; Writing--original draft, W.W.; Writing--review & editing, W.W. and E.K. All authors have read and agreed to the published version of the manuscript.  
This work was co-supported by the National Natural Science Foundation of China (Grant Nos. 52005421 and 12102375), the National Science and Technology Major Project (Grant Nos. J2019-1-0013-0013 and J2019-IV-0011-0079), the Independent Innovation Foundation of AECC (Grant No. ZZCX-2018-017), and the project funded by the China Postdoctoral Science Foundation (Grant No. 2021T140634).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.