# Multi-Objective Optimization of Cascade Blade Profile Based on Reinforcement Learning
## 7 Conclusions  
In this paper, a multi-objective optimization method based on reinforcement learning technique is proposed and applied in a hybrid optimization of the compressor cascade blade profile on the total pressure loss and the laminar flow area. Firstly, an ANN-based surrogate model is used as the environment in the DDPG network, feeding back the aerodynamic parameters corresponding to the deformed profiles with surrogate model trained with parameterized profiles and aerodynamic data calculated via CFD solver. Secondly, based on the reinforcement learning technique of DDPG, a multi-objective optimization method is proposed, where the profile geometry is taken as the State of the DDPG network, the modification of geometry is taken as the Action, and the DDPG network acts as an intelligent optimizer learning the design experience from the interaction with the environment. The optimizer can approach the good-performance profiles rapidly according to the learnt design experience.  
With the optimization on total pressure loss and laminar flow area, the cascade with modified blade profile has an improved performance and increased laminar flow area. The total pressure loss coefficient of the optimized profile is reduced by 3.59%, and the relative laminar flow area at the suction surface is 25.4% higher than the initial profile. The result shows that the DDPG-based method is one successful multi-objective optimization of cascade blade profile, with an improvement on using the accumulated calculation data to extract design experience and making design policies for guiding optimization. The cascade blade profile optimized in this case is the section profile at 40% span of one compressor rotor blade. This optimization method can be applied to profiles at different spans of the rotor. With multiple profiles at various spans considered, this method can be extended to 3D shape optimization method and be applied to 3D rotor blades.  
Conceptualization, S.Q.; methodology, S.Q. and S.W.; software, S.Q. and C.W.; validation S.Q.; formal analysis, S.Q. and L.W.; investigation, S.Q., L.W. and C.W.; resources, Y.Z.; writing-original draft preparation, S.Q.; writing-review and editing, S.W.; visualization, S.Q. and S.W.; supervision, G.S.; project administration, G.S.; funding acquisition, G.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by AECC Commercial Aircraft Engine in the project of Laminar Flow Design and Turbulent Drag Reduction of Compressor Blade Profile and Experimental Verification.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} DDPG & Deep Deterministic Policy Gradient \\ RL & Reinforcement Learning \\ DRL & Deep Reinforcement Learning \\ DQN & Deep Q-learning \\ CFD & Computational Fluid Dynamics \\ PCA & Principal Component Analysis \\ ANN & Artificial Neural Network \\ LHS & Latin Hypercube Sampling \\ MSE & mean square error \\ SS & suction surface \\ PS & pressure surface \\ IF & intermittency factor \\ \end{tabular}