Hybrid Modeling And Optimization Based On Kriging And RBF

The design of complex products such as automobiles,aircraft,and ships often require expensive simulation calculations with long design cycles.Replacing real simulation models with surrogate models can greatly reduce the number of expensive function valuations while satisfying the accuracy,which just can solve the time and calculation costs brought by expensive simulation experiments.However,a single surrogate model cannot perform well on all problems and its scope of application is small.The establishment of a hybrid surrogate model is an improvement method.Noting that Kriging and RBF have good complementarities in performance,this paper focuses on the hybrid surrogate model of Kriging and RBF,and explores new methods from global modeling and global optimization of Kriging and RBF hybrid models,the main research contents are as follows:(1)A Kriging and RBF adaptive hybrid method based on cross validation hypercube(CVH)sampling was proposed to solve the problems of small applicability and insufficient accuracy of a single surrogate model.The accuracy of the surrogate model lacking adaptive sampling processes still has space for further improvement.In view of this,this paper proposed a Kriging and RBF adaptive hybrid modeling method(named AHM-CVH method)based on Cross-Validation Hypercube(CVH)strategy.In this method,Kriging and RBF are combined with weights to obtain a hybrid surrogate model,and then CVH strategy is implemented to explore new points for the hybrid model.The CVH adaptive sampling strategy generates a hypercube centered on the point with the largest CV error,then candidate points are randomly sampled in the hypercube.The candidate point furthest from the center and surrounding samples obtained by this method is the new adaptive sampling iteration point.The superiority of AHM-CVH method is verified by using eight benchmark functions and one engineering example.This method is superior to single Kriging or RBF model in performance,and has the characteristics of high accuracy and strong stability.(2)A global optimization algorithm based on an hybrid surrogate model of Kriging and RBF(GOA-HS)was studied,which improves the problem that a single surrogate model cannot balance global and local optimization due to insufficient accuracy.Single objective optimization can only obtain one optimized sampling point in one iteration process,so the adaptive iteration process may require a number of iterations to ultimately achieve the expected accuracy of the model,which will consume a lot of time and computational costs.Using multi-objective optimization can obtain a collection of many Pareto optimal solutions,thereby adding multiple optimized sampling points in one iteration process.To this end,a global optimization algorithm based on an adaptive hybrid surrogate model of Kriging and RBF(GOA-HS)is proposed in this paper.In each iteration process,a hybrid model based on Kriging and RBF is constructed by adaptively selecting weight coefficients.Next,the Pareto Front(referring to some optimized data points that may have optimal values)is generated by using dual objective optimization.One of the objectives in dual objective optimization is to minimize the product of the prediction function value and the distance parameter,and the other is to maximize the prediction variance of the model.After generating the Pareto frontier using dual objective optimization,the expected improvement(EI)method is used to further screen the points of the Pareto frontier,and generate multiple promising optimal sampling points,then add them to the model for updating and iteration until the expected accuracy is met.Fourteen standard numerical functions and the hydrogen fuel utilization in hydrogen fuel cell vehicle are tested to demonstrate the effectiveness and robustness of the GOA-HS method.