Research On Data Dimensionality Reduction And Sampling Strategy For High-dimensional Kriging Modeling

The Kriging surrogate model has achieved good approximation results in solving low-dimensional engineering design problems,but it is not effective for high-dimensional complex problems.In the Kriging approximation modeling process,the computation of Kriging model is greatly increased because of the sample data,which leads to inefficiency,low accuracy and even failure of the modeling process.Therefore,the research on the efficiency and accuracy of high-dimensional Kriging modeling process is conducive to more efficient and accurate simulation of actual high-dimensional complex problems.First,this paper studies the efficiency of high-dimensional Kriging modeling.Combining the Kriging model with multi-dimensional scaling,an effective Kriging modeling method based on multi-dimensional scaling is proposed to avoid the "curse of dimensionality" in the process of high-dimensional modeling.The core of this method is to complete the conversion of high-dimensional design data to low-dimensional design data according to the principle that the relative distance between sample points before and after dimensionality reduction remains unchanged.Therefore,the high-dimensional Kriging modeling problem is transformed into a low-dimensional Kriging modeling problem to improve the modeling efficiency.The application of this method can more efficiently establish a global approximate Kriging model for complex high-dimensional engineering design problems.Second,this paper studies the accuracy of high-dimensional Kriging modeling.Valuable sample points are very important to improve the modeling accuracy.To this end,this paper proposes a high-precision Kriging modeling method based on hybrid sampling criteria.Maximize the mean squared error function as the first sampling criterion.In order to avoid the situation that the correlation matrix is ill-conditioned because the distance between sample points is too close,this paper takes the correlation between the sample points as one of the sampling conditions.The second sampling criterion is constructed by combining the mean square error function and the correlation function using multiplication and division.Candidate points obtained by optimizing the two fill sampling criteria are screened to determine the final sample points for Kriging modeling.The application of this method can establish a global approximate Kriging model with higher accuracy for complex engineering design problems.Eventually,the method proposed in this paper is tested by using the benchmark function and applied to the simulation example.The modeling method proposed in this paper and other modeling methods are tested for the same 3high-dimensional benchmark functions,and the test results show that,the method has good modeling efficiency under the condition of meeting certain accuracy requirements,and then it is applied to the simulation example of aircraft longitudinal flight control.In addition,the test results of 16 benchmark functions and 2 cases indicate that the method can improve the accuracy and stability of the Kriging,and it is applied to the house heating simulation case.In conclusion,the research in this paper has certain theoretical and practical significance for the approximate modeling of solving complex problems in the field of engineering design.