| Variable selection can screen out the active variables which have a great impact on the outputs from a large number of input variables,which helps to improve the accuracy of the model and enhances the interpretability of the model.In the era of big data,the industrial field has an increasingly urgent demand for a variety of experiments.Although physical experiments have good repeatability and randomness,there are systematic errors.Thus it becomes feasible to use computer experiments to fit the data obtained from physical experiments.In this dissertation,we study the basic theory of Kriging variable selection.Based on the penalized blind Kriging method,four step-by-step penalized blind Kriging methods are proposed to further improve time efficiency,and the Oracle properties of the third method are proved.The GR,BP and PBK methods are compared by numerical simulation and example analysis,the results show that the second method and the third method have more advantages than other methods in identification,prediction accuracy and time efficiency.Method 1 has obvious advantages in prediction accuracy and time efficiency.However,there is an over-fitting phenomenon in its identification.Method 4 is a refitting method to improve the prediction accuracy of PBK method,so its performance in time efficiency is poor.In the Gaussian process part of the Kriging model,the solution optimization of correlation parameters is easy to fall into local solutions.Therefore,we penalize the correlation parameters in the Gaussian process of the Kriging model at the first,and then select the BIC or LRT method for variable selection.Through numerical simulation and example analysis,OK,UK,PBK,PLK,PBLK,the method proposed by Youngsaeng and Jeong-soo are compared with the variable selection methods proposed by this dissertation,and it is found that our methods have more advantages in identification and prediction accuracy when the real function is nonlinear function or the linear function with large sample,while our method is comparable with other methods when the real function is linear function with small sample. |
