Research On Key Technologies Of Kriging-based Multi-fidelity Optimization

In solving the computationally expensive black-box optimization problems,the surrogate-based multi-fidelity optimization(SBMFO)methods can effectively reduce the amount of computation cost.However,the existing SBMFO methods still have the following shortcomings: the adaptability of single surrogarte calibrated multi-fidelity methods is poor,the optimization efficiency of existing SBMFO methods needs to be improved,the influence of model uncertainty is not considered in most existing methods,and the available design experience and knowledge in specific engineering problems are not comobined with the optimization.Based on the Kriging model,this thesis investigates some key technologies involved in the above shortcomings and the main research achievements and innovations of this work are given as follows:(1)A hybrid surrogate model based multi-fidelity optimization method is proposed to improve the adaptability of single surrogarte calibrated multi-fidelity methods.This method integrates three kinds of common surrogate models including Kriging model.According to the characteristics and prediction accuracy of different surrogate models,a hybrid calibration surrogate model is constructed to calibrate the low-fidelity model when approximating the high-fidelity model.The modeling accuracy and stability of the proposed method are verified by mathematical test problems.In addition,a multi-fidelity optimization method is proposed based on the hybrid calibration surrogate model.The test results show that the optimization efficiency is improved compared with single surrogate calibration based methods.Finally,the proposed method is verified through a multi-fidelity engineering design problem,and it is found that the proposed method can get better results with less calculation,which provides a new reference method for multi-fidelity design optimization.(2)A multi-fidelity optimization method based on space division and correlation analysis is proposed in this thesis to improve the efficiency of existing SBMFO methods,.According to the multi-fidelity sample data,the design space is divided into four categories: overlapped subspace,high-fidelity subspace,merged subspace and global space.Then different optimization strategies are utilized to perform the optimization in these four spaces alternately.In subspace optimizations,high or low fidelity Kriging model is selected adaptively according to the correlation analysis results between the high and low fidelity surrogate models.The test results of mathematical problems show that the performance of this method is better than some existing SBMFO methods.Finally,the proposed method is applied to design the platform of a floating offshore wind turbine,and the results show that the proposed method obtained the best result with the least calculation,which verifies the efficiency of the proposed method.(3)Considering that most of the existing SBMFO methods do not take the model uncertainty into consideration,a multi-fidelity optimization method under uncertainty is proposed.Based on the uncertainty analysis of different fidelity surrogate models,the information fusion of multi-fidelity data is carried out by using the optimal estimation idea of Kalman filter,and the multi-fidelity surrogate model with high accuracy and uncertainty information is obtained.Then a multi-fidelity optimization method is proposed by using the above multi-fidelity model,which considering the influence of model uncertainty during the optimization.The proposed method is compared with the single fidelity optimization method,the additional bridge function based optimization method and the Co-Kriging based optimization method through mathematical test problems,which shows the advantages of this method.Finally,the method is applied to optimize the shell structure of an autonomous underwater vehicle,and the better design result is obtained with less calculation,which verifies the applicability of the method.(4)Since most of the existing SBMFO method fails to combine the available design experience and knowledge with the optimization method in specific engineering problems,this paper investigated how to combine the existing knowledge with the optimization design method.By using the blended-wing-body underwater glider(BWBUG)shape design problem as an example,a multi-fidelity shape optimization method based on double-stage surrogate model is proposed.In this method,the structure of the surrogate model is simplified by combining the characteristics of BWBUG shapes and the existing knowledge.Then,a large number of low-fidelity two-dimensional airfoils and a small number of high-fidelity three-dimensional shape calculations are used to perform the shape design optimization.Compared with high-fidelity and low-fidelity shape optimization methods,the efficiency of the proposed method is verified.The proposed method provides an efficient method for the shape optimization of new BWBUGs,and this method can be widely used in similar optimization problems.