## 4 Discussion and Conclusions  
This paper analyzes the aerodynamic performance of the blade profile with two-position local geometric deviations and explores the mechanism of the aerodynamic influence causing by the deviations. Through analyzing the factors which affect the aerodynamic performance on the coexisting condition, the coupled effect model was created to estimate the performance of the blade profile. Conclusions can be drawn as follows:  
Figure 8: Sample points and the leave-one-out test of the surrogate model. (**a**) Sample points when the deviations is in the \(-0.3\) position and \(-0.5\) position. (**b**) Using the leave-one-out method to verify the accuracy of the surrogate model.  
Figure 9: Model verification with the deviations in the \(-0.3\) position and \(-0.5\) position. (**a**) Comparison between the positive incidence range predicted by the GPR model on the coexisting condition and the sum of the positive incidence range on the separated condition. (**b**) Comparison between the positive incidence range predicted by the GPR model and the positive incidence range predicted by the coupled effect model on the coexisting condition.  
1. The aerodynamic performance influences of the blade local geometric deviations in different positions are not isolated from each other. In addition, there is a big difference in the incidence range between the sum of the separated condition and the coexisting condition. When solving the aerodynamic sensitivity of the blade profile, the impact of deviations in other positions should also be considered.
2. The coupled effect between deviations is related to the deviation heights, the thickness of the boundary layer and the distance between the deviations. When the upstream boundary layer thickens, the effect of the downstream deviation will be weakened.
3. By introducing the condition of a thick boundary layer and the assumption of exponential weakening effect, the coupled effect model was created to model the weakening effect of the downstream deviation. The accuracy of the model is proven by predicting the positive incidence range when the deviations are located on the suction surface. This model provides a new approach for the performance evaluation of the blade profile with multi-position deviations.  
Conceptualization, X.Y. and M.L.; methodology, X.Y. and M.L.; investigation, X.Y. and M.L.; writing--original draft preparation, M.L.; writing--review and editing, X.Y. and M.L.; supervision, B.L., X.Y. and G.A. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Natural Science Foundation of China (Grant Nos. 51806004, 51790511) and National Science and Technology Major Project (Grant No. 2017-II-0001-0013).  
Thanks to [PERSON] for providing the blade deviation generator. And thanks to [PERSON] and [PERSON] for their precious suggestions on the concept expression.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} \(Ma_{in}\) & Inlet Mach number \\ \(Re\) & Reynolds number \\ \(Tu\) & Turbulivity \\ \(\omega\) & Total pressure loss coeffcient \\ \(\alpha\) & Flow angle measured from axial \\ \(\theta\) & Momentum thickness of boundary layer \\ \(H\) & Shape factor \\ \(C_{f}\) & Blade surface friction coefficient \\ s & Surface distance from leading-edge \\ \(s_{0}\) & Total surface length \\ \end{tabular}