## 4 Noise Control
### Optimization of Structural Parameters  
In view of the above research, in order to reduce the \"buzz-saw\" noise, on the one hand, based on the flow characteristics and previous studies, the flow separation is reduced by increasing the blade outlet angle [20] and increasing the impeller outlet radius. On the other hand, by increasing the width of the diffuser and the outlet area of the first stage volute, the interference between the rotating flow and the volute tongue is reduced. The schematic of the optimized parameters is shown in Figure 17.  
The aerodynamic optimization platform established in Reference [21] is adopted for the parameter selection of the air compressor structure improvement in this paper. The optimization platform integrates geometric parameterization, a surrogate model, sensitivity analysis, and a multi-objective genetic algorithm. Among these, the sensitivity analysis mainly adopts the optimal prediction meta-model (MOP), and the optimization process adopts the multi-objective genetic optimization algorithm based on the MOP surrogate model. Based on the optimal design variable subset of each target parameter, different surrogate models are established by the polynomial method, moving least squares method, and Kriging method, respectively. A set of competitive metamodels for each target parameter is formed. The evaluation is performed using a model-independent cross-validation method proposed by [PERSON] and [PERSON] [22], called the coefficient of prognosis (_CoP_), expressed as follows:  
\[CoP=(\frac{\mathrm{E}\big{[}Y_{\text{test}}\cdot\hat{Y}_{\text{test}}\big{]}}{ \sigma_{Y_{\text{test}}}\cdot\hat{\sigma}_{Y_{\text{test}}}})^{2} \tag{2}\]  
where the value of the _CoP_ is obtained based on the test sample point data of cross-validation. The prediction error is used to evaluate the prediction quality of the model. Both regression models and interpolation models are applicable. According to the size of the _CoP_ of the meta-model, the optimal prediction meta-model of each target parameter is determined, that is, the MOP surrogate model. The sensitivity of the design parameters  
Figure 17: Schematic of the optimized parameters. (**a**) Blade outlet angle. (**b**) Other optimized parameters. of the optimal prediction metamodel for target parameters is quantified by using the _CoP_ value of the optimal prediction metamodel together with the total effect sensitivity index. That is, the variance contribution of a single design parameter is the product of the _CoP_ value and the overall effect sensitivity index, as follows:  
\[CoP(X_{i})=\text{ CoP}\cdot S_{\text{T}}^{\text{MOP}}(X_{i}) \tag{3}\]  
\[S_{\text{T}}^{\text{MOP}}(X_{i})=1-V(Y|X_{\sim i})/V(Y) \tag{4}\]  
where \(Y\) is the output variable of the model, \(X_{i}\) is the input variable of the model, \(V(Y)\) is the variance of \(Y\) caused by all input variables, and \(V(Y|X_{\sim i})\) is the variance of \(Y\) caused by all input variables except \(X_{i}\). Three target parameters are defined for the optimization object of this study, which are the total pressure loss coefficient, the average absolute airflow angle of the impeller outlet section, and the pressure range of the impeller outlet section. The ranges and changes of structural parameters before and after improvement are shown in Table 6.  
Figures 18 and 19 are B-B static entropy contours of the first and second stage impellers of the improved air compressor at 90% and 50% blade height. Since the blade tip clearance height is the same, the flow separation phenomenon in the blade tip clearance is not significantly improved, but the flow separation phenomenon at the leading edge and the trailing edge is significantly improved. Figure 20 is a pressure contour of the first and second stage diffusers and solutes at 50% of the width of the diffuser after the improvement. After the improvement, the pressure unevenness at the inlet of the diffuser has been significantly improved, and the static pressure gradient at the volu