## 4 Conclusions  
In this paper, the multi-condition aerodynamic optimisation of the centrifugal impeller is studied, and the optimisation algorithm DNSGA is proposed and verified on the test function. An automatic optimisation method is studied and designed, combining the DNSGA with MDOF surface parameterisation and CFD flow-field analysis. The method is successfully applied to the aerodynamic optimisation of the FC centrifugal impeller. The main conclusions are as follows:  
1. Compared with other classical multi-objective evolutionary algorithms, DNSGA performs well in population diversity and convergence, especially concerning greater improvement in diversity. This optimisation algorithm improves the traditional method of NSGA-II for selecting the value of the objective function by improving the division of non-dominated ranking and spatial density ranking on decision variables. This provides a new scientific method for the application and research of the multi-objective evolutionary algorithm.
2. The optimised geometric deformation of the blade increases the back-bend angle of the blade, the positive angle of attack at the inlet, and the relative Mach number in the blade channel. These changes reduce the diffuser angle and reverse the pressure gradient, reducing the separation loss and improving the flow at the downstream outlet. Under multi-working conditions, the aerodynamic performance curve moved upward as a whole, and the flow condition was significantly improved. The isentropic efficiency under the rated conditions increased by 1.2%, the flow increased by 9.1%, the pressure ratio increased by 0.24%, and the comprehensive margin increased by 10%. The isentropic efficiency under common working conditions increased by 1.29%, the flow increased by 8.8%, the pressure ratio increased by 0.74%, and the comprehensive margin increased by 6.2%. Moreover, it is verified that the aerodynamic optimisation of the FC impeller can improve the efficiency of rated and common working conditions simultaneously. The centrifugal impeller design optimisation system presented in this paper provides technical support and a new method for scientific research to study the aerodynamic optimisation of centrifugal impellers for vehicle-mounted FCs.
3. The parametric method used in this paper is based on the Bezier surface blade optimization method. The limitation of this method is that the change of one variable control point on the Bezier surface will cause the change of the entire surface and cannot achieve the local optimization of the blade geometry, so as not to get the best  
Figure 19: Comparison of the entropy contour of B2B surface at 80% height before and after optimisation (common operating condition).  
blade geometry. In order to overcome this drawback, we will introduce a more flexible B-spline surface parameterization method or Free-Form deformation method, which can do to control the local surface variation and thus may obtain a blade geometry with better aerodynamic performance.  
Conceptualization, J.L., W.L., P.F.; data curation, J.L., W.L., K.H. and P.F.; formal analysis, J.L., P.F. and M.L.; funding acquisition, W.L. and K.H.; investigation, J.L. and P.F.; methodology, J.L., P.F.; project administration, W.L. and K.H.; resources, J.L. and P.F.; software, J.L. and P.F.; supervision, J.L. and Y.W.; validation, J.L.; writing--original draft, J.L. and P.F.; writing--review and editing, J.L. and W.L. All authors have read and agreed to the published version of the manuscript.  
The authors would like to acknowledge the financial support from the National Key Research and Development Program of China (Project No. 2020 YFB1709101), this support is gratefully acknowledged.  
Not applicable.  
The data are contained within the article.