Improved Hierarchical Kriging Model And Its Application In Simulation Model Validation

Numerical simulations has become an indispensable method to reduce the simulation cost and improve the design efficiency in the design of engineering products.By integrating the simulation models of different fidelity,the multi-fidelity(MF)surrogate modelling technique can make full use of the adavantage of different simulation models and shows great potential.Within a limited design cost,how to fuse the data from simulation models of different fidelity is the core problem in the multi-fidelity surrogate model based engineering design.Meanwhile,the MF model has prediction uncertainty,and if the influence of the prediction uncertainty is ignored in optimization problems,the optimal solution may become infesible,and further lead to the failure of the design.Therefore,uncertainty quantification is an important guarantee for the successful application of MF surrogate models into the design of engineering products.What’s more,simulation model validation is an important process in the design of engineering products,and it needs to run simulation for multiple times to make a judgement about the validity of the simulation model,resulting in the increase of the validation cost.Conducting research on how to combine the MF surrogate modelling technique with the simulation model validation methods is of great significance to reduce the validation cost and improve the design efficiency.Therefore,this thesis conducts research on three aspects: the sequential MF surrogate modelling method,uncertainty quantification method,and the MF model based simulation model validation model.The specific research contents are as follows:(1)Sequential multi-fidelity surrogate modelling method: The correction method of low-fidelity(LF)model response in hierarchical kriging is inaccurate,and it cannot accurately represent the relationship between LF and high-fidelity(HF)responses.Thus,an improved hierarchical kriging(IHK)model is proposed to improve the fusion method of HF and LF data and the global performance of the existing MF model.Based on it,a sequential MF surrogate modelling method based on adaptive hybrid leave-one-out error criterion is also proposed.The sequential MF surrogate modelling method makes full use of the difference information between HF and LF models,and solves the following two problems:how to effectively integrate the data of HF and LF sample points and how to allocate the distribution of sample points reasonably.Through two numerical examples,an aerodynamic modelling problem of the DLR-F6 wing body,and the design of the lattice structure of the automobile A pillar,the effectiveness of the proposed method is demonstrated by comparing with existing surrogate modelling methods.(2)Uncertainty quantification of MF model: To select a reasonable metric to estimate the uncertainty of a MF model,this paper firstly compares the performance of four uncertainty quantification metrics that do not rely on additional test points.Based on the analysis results,a MF model uncertainty quantization method based on ensemble weighted average is proposes.By properly weighting the estimated uncertainty quantization results from different metrics,the true error of the MF model can be estimated more accurately,and the poor performance of a single uncertainty quantification metric in some specific problems can be avoided.In addition,when using the MF model to replace the constraint function in the optimization problem without considering its uncertainty,the optimal solution may be infeasible.Therefore,to reasonable quantify the uncertainty of MF model,a conservative MF surrogate modeling method based on the confidence level is proposed.From the test results of problems with different characteristics,it can be seen that the the conservative degree of the MF model can be increased by adding a reasonable conservative level to the estimated response of the MF model,resulting in the increased feasibility of the optimal solution.(3)Simulation model validation method based on MF surrogate model: In order to reduce the simulation cost of existing simulation model validation methods,a simualtion model validation method based on IHK surrogate model is proposed in this paper,which transforms the two-level nested optimization problem in typical simulation model validation method into a single-layer optimization problem,and reduces the complexity of the optimization problem.At the same time,by constructing an IHK model ahead to quickly predict the closeness between the simulation model and experimental results under different uncertain parameters allocations as well as the reliability of the simulation model,the desired simulation cost can be reduced and the design efficiency can be improved.In addition,to prevent the prediction uncertainty of the MF surrogate model affecting the simulation model validation results,a simulation model validation method based on MF surrogate model considering the prediction uncertainty is proposed,which combines the conservative MF surrogate modelling method and the simulation model validation method.The proposed method can ensure the simulation model satisfies the design requirement after model validation.