Research On Sequential Robust Optimization Design Method Based On Multi-Fidelity Surrogate Model

In the process of robust optimization(RO)design of modern engineering products,numerical simulations become a necessary means of evaluating the performance of products.High-fidelity(HF)design requirements usually bring computational expensive simulations.At the same time,the objective functions and constraints are highly nonlinear and implicit,which brings the challenge of solving difficulties and low design efficiency.The multifidelity(MF)surrogate modeling approaches,which can integrate the data from both the low-fidelity(LF)and high-fidelity models,have been introduced to mimic the computational expensive objective functions and constraints,bringing a way to solve these issues.While,to facilitate the usage of robust optimization based on the MF surrogate models,there are still some challenges: The existing MF surrogate modeling approaches cannot effectively handle the situations,in which multiple non-hierarchical LF models with different degrees of correlation between the HF model in the subregion of the design space;the existing MF surrogate model assisted RO approaches may yield an inferior or even infeasible solution since they generally treat the MF surrogate model as the real HF model and ignore the interpolation uncertainties from the MF surrogates;and currently the MF surrogate model and the RO approaches are combined statically,which may lead to a conservative solution when the HF samples are limited.To address these dilemmas,this work focuses on the sequential RO approach based on MF surrogate model and their engineering applications,with the goal of improving the prediction performance of the MF surrogates and the accuracy of RO design.The main contents of this thesis are summarized as follows:(1)A MF surrogate modeling approach based on a discrepancy smoothing strategy is proposed.When adopting different methods to simplify HF models to obtain LF models,the fidelity levels of the LF models often vary over the design space.This results in nonhierarchical LF models with different degrees of correlation between the HF model in the subregion of the design space.To address the issue that existing MF surrogate modeling approaches cannot effectively handle multiple non-hierarchical LF models,a multi-fidelity surrogate modeling approach based on a comprehensive Gaussian process(GP)Bayesian framework,termed as NHLF-Cokriging,is proposed.In the proposed NHLF-Cokriging model,all the non-hierarchical LF models are taken as the trend functions and ensembled by allocating different scale factors.Then,the other GP model is constructed as the discrepancy function to calibrate the ensembled term.Specifically,to make the discrepancy GP model easy to be fitted,an optimization problem whose objective is to minimize the second derivative of the prediction values of the discrepancy GP model is defined to obtain optimal scale factors.Several numerical examples are tested.The comparison results illustrate the advantages of the proposed method regarding the prediction performances.(2)A RO method that considers the effect of uncertainties from the design variables,input parameters,and the MF surrogate model is proposed.The MF surrogate model constructed under limited samples inevitably has interpolation uncertainties.Ignoring the uncertainties from the MF surrogate model may yield an inferior or even infeasible solution.To address this issue,the compound effect of these three uncertainties is quantified.Then the relationship between these three uncertainties and the compound effect is expounded.On this basis,a RO method that considers these three uncertainties,termed as NHLFCokriging-RO,is developed.The testing results on numerical cases show that the proposed method can ensure the robustness of the optima.(3)A sequential RO method based on the expectation improvement of the MF surrogate model is proposed.Currently,the MF surrogate model and the RO approaches are combined statically,the useful information obtained in the process of RO is not fully explored to guide the searching stage,which may lead to a conservative solution when the HF samples are limited.To address this issue,the dynamic updating methods based on robustness expectation improvement and probability of feasibility are proposed for the objective functions and constraints separately.On this basis,a sequential RO method by combining these two strategies is proposed.The testing results on numerical cases show the superiority of the method in optimizing quality and solving efficiency.(4)The applications of the proposed approaches on properties prediction and robust optimization design of typical underwater structure are carried out.For the requirements of fast prediction and robust performance improvement for underwater structure with computational expensive simulations/experiments,high nonlinear and implicit objective functions/constraints,the proposed methods are applied to the remaining speed prediction of underwater structure breaking the ice and RO design of metamaterial vibration isolator with honeycomb structure.The engineering effectiveness and feasibility of the proposed methods are verified.