## 1 Introduction  
With the improvement of aero-engine performance, the compressor, one of the core aero-engine components, is facing higher design requirements. The blade is a basic part of the compressor, and its manufacturing quality affect the aero-engine production cost and performance directly. However, the manufacturing process is difficult when blades have complex three-dimensional shapes such as bending, twisting, and sweeping. Due to the cutting vibration, cutting heat, residual stress and other factors in the machining process, thin blades are easy to deform, which introduces geometric deviations inevitably. The manufacturing deviation is statistically uncertain, which leads to blade performance degradation. Therefore, it is important to consider the influence of manufacturing deviation in the blade design process and give a suitable manufacturing tolerance of the blade.  
The effect of manufacturing deviation on blade performance has been concerned for a long time. [PERSON] et al. [1; 2; 3] changed the blade coating thickness in each individual area to analyze the aerodynamic performance changes caused by the geometric deviations. [PERSON] [4; 5] and [PERSON] [6] started using the principal component analysis (PCA) method to analyze the measured rotor blade profile and created a reliable deviation statistics model. The statistical aerodynamic performance through adding modal deviations to the blade profile was analyzed. [PERSON] and [PERSON] [7; 8; 9] introduced a single-position deviation to the blade leading edge for investigating the influence of geometric deviations on the profile incidence range. [PERSON] et al. [10] developed a new robustness optimization method based on the Gaussian Random Field (GRF) to achieve a profile design with the robust aerodynamic performance. [PERSON] et al. [11] studied the mechanism of manufacture variations on transonic and supersonic blade aerodynamic performance. To quantify the blade aerodynamic performance with geometric deviations, the Monte Carlo method [12], adjoint method [13] and polynomial chaos method [14] have been applied by researchers. Currently, [PERSON] et al. [15] and [PERSON] et al. [8] have shown that the theoretical analysis should be combined with the manufacturing process to weaken the aerodynamic performance influence of the geometric deviation.  
From the discussion above, it can be seen that the influence mechanism and the sensitivity analysis of the blade deviations have been studied in detail. In addition, the robust optimization design of the blade profile with deviations has also been discussed. However, when considering the performance effect of the deviations, previous research mainly focused on a single-position or a single-modal deviation to analyze. However, the geometric deviation on the actual blade surface has a complex form. It still needs to consider whether the blade aerodynamic performance analysis based on a single-position deviation or a single-mode deviation is reliable for the actual blade with complex deviations. In addition, it also needs to consider the sensitivity analysis based on a single deviation is effective in predicting the actual blade aerodynamic performance or not. Hence, in this paper, the coupled effect mechanism of the two-position deviations on the blade performance was studied in detail by numerical simulation. By analyzing the aerodynamic influence pattern, a coupled effect model of the two-position geometric deviations was created. The accuracy of the model was verified by the DOE method and the surrogate model method. Through this study, the difference of the aerodynamic influence between the single deviation and the multiple deviations is further revealed. The mechanism of the coupled aerodynamic influence causing by the deviations is explored, and the coupled effect model for predicting the blade performance is proven to be reliable.