Research On Sequential Design Optimization Methods Based On Variable-Fidelity Metamodel

Variable-fidelity metamodeling approach constructs the metamodel by fusing the information of models with different fidelity level,effectively balancing the contradiction between the metamodeling cost and accuracy,which has received more and more attention in engineering design optimization.The sequential design optimization approach based on the variable-fidelity metamodel can can take advantage of high reliability of high-fidelity model and low cost of low-fidelity model,and has great potential in the engineering design optimization.At present,there are some deficiencies in the research of design optimization approach based on variable-fidelity metamodel.The current variable-fidelity metamodeling approach does not make full use of the information provided by high/low fidelity sample points to construct highly accurate variable variable-fidelity metamodel.The influence of uncertainty of metamodel on the accuracy of multi-objective design optimization methods and the difference of calculation cost of high-fidelity and low-fidelity model are not considered enough,which hinders the application of this kind of approach in practical engineering problems.In the current sequential design optimization methods based on variable complexity approximation model,there is a lack of theoretical research on the mapping of low-fidelity model information to high-fidelity space.Aiming at the above problems,this subject studies variable-fidelity metamodeling and sequential design optimization approaches based on variable-fidelity sampling,aiming to improve the predication performance of variable-fidelity metamodels and design optimization efficiency.The main research content includes the following aspects:(1)Aiming at the problem that the variable-fidelity metamodeling approach based on the addition scaling function ignores the influence of the roughness of the scaling function on the metamodel accuracy,a low-fidelity scaling factor selection method is proposed to improve the prediction performance of variable-fidelity metamodel.Through several numerical examples and prediction of the maximum deformation of the micro air vehicle fuselage,the proposed approach is compared with the current variable-fidelity metamodeling approaches,the effectiveness of the proposed variablefidelity metamodeling approach is illustrated.(2)In order to reduce the computational cost of multi-objective design optimization,an online variable-fidelity metamodel assisted multi-objective genetic algorithm is proposed.Firstly,the influence of the prediction uncertainty of the variable-fidelity metamodel on the dominance relationship between the dominated solutions and the non-dominated solutions in the multi-objective genetic algorithm is studied.Then,a sequential updating strategy of the variable-fidelity metamodel is proposed,which selects the high-fidelity and low-fidelity sample points to update the metamodel according to the changing state of the dominance relationship.Finally,the applicability and efficiency of the proposed approach are verified by several numerical examples,the multi-objective design optimization of the torque arm and the multiobjective design optimization of the adapter.(3)In order to select the high-fidelity and low-fidelity sample points in the optimization process based on the variable-fidelity metamodel to sequential update the model,the importance of high-fidelity and low-fidelity samples in variable-fidelity design optimization is quantified on the basis of in-depth study of the EGO algorithm.Then the acquisition function of variable-fidelity design optimization without constraints is proposed considering the cost difference between high-fidelity and lowfidelity models.The location and fidelity level of the next sample point can be determined by optimizing the acquisition function.Then,the constraint handling method based on metamodel uncertainty unknown constraints in the design optimization problems is proposed to ensure the feasibility of the optimization solution.Finally,the proposed approach is verified by a series of numerical examples,the design optimization of the micro air vehicles and the design optimization of the long base.