Research On Variable-fidelity Efficient Global Optimization Method Based On Improved Co-Kriging Model

Efficient global optimization(EGO)approaches have attracted significant attention in simulation-based design optimization because they demonstrate outstanding performance in reducing computational costs.To further improve optimization efficiency,researchers propose the variable-fidelity EGO algorithms by applying variable-fidelity surrogate models to EGO approaches with attempt to fuse the advantages of both EGO algorithms and variable-fidelity surrogate models.The variable-fidelity surrogate models use a large number of low-cost low-fidelity(LF)sample points to obtain the model trend,and adopt a limited number of expensive high-fidelity(HF)sample points to facilitate the modeling accuracy of the surrogate models,thereby further reducing design costs.However,there are still deficiencies about the current studies on the variable-fidelity EGO algorithms:(1)The variable-fidelity EGO algorithms may lead to non-nested of HF / LF sample points when sequentially adding HF sample points,which will reduce the prediction accuracy of variable-fidelity surrogate models.Ultimately,it will affect the optimization accuracy and optimization efficiency of the optimization algorithm.(2)Existing variable-fidelity EGO algorithms are generally developed based on the expected improvement criterion and the lower confidence boundary criterion,and there is a lack of the variable-fidelity EGO algorithm based on the probability of improvement(PI)criterion.Therefore,the variable-fidelity surrogate model and variable-fidelity PI optimization method are mainly developed in this paper to deal with above-mentioned problems.The specific research work is as follows:Firstly,to ensure the prediction accuracy of Co-Kriging model under non-nested sampling data,in this paper,an improved Co-Kriging(ICK)surrogate model is proposed for variable-fidelity information fusion with both nested and non-nested sampling data.Specifically,a comprehensive Gaussian process(GP)Bayesian framework is developed by aggregating calibrated LF Kriging model and discrepancy stochastic GP model.The stochastic GP model enables the ICK model to consider the interpolation uncertainty from the LF surrogate model at HF samples,making it possible to estimate the model parameter separately under both nested and non-nested sampling data.The prediction accuracy and robustness of ICK model are compared with three typical Kriging based variable-fidelity surrogate models by using two numerical examples and two real-life cases.The influences of correlation coefficient,cost ratio and budget allocation ratio between LF and HF models are also investigated.Comparison results illustrate that the proposed ICK model is more accurate and robust than other variable-fidelity surrogate models for both numerical and complex engineering problems.Secondly,a variable-fidelity probability of improvement(VF-PI)method is developed in this work based on ICK model.An extended probability of improvement(EPI)function is developed to determine the location and fidelity level of the samples simultaneously.Moreover,to make the proposed approach can handle variable-fidelity optimization problems with constraints,the probability of satisfying the constraints is introduced and combined with the EPI function.The performance of the proposed VF-PI approach is demonstrated on eight analytical cases and two practical engineering examples.The comparisons between the proposed VF-PI approach and some existing approaches considering the computational efficiency and robustness are made.The merits of VF-PI approach are analyzed and summarized.Finally,the research contents and results of this paper are summarized,and the future research direction is prospected based on current research.