Abstract
The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements.
Highlights
The surrogate model [1,2,3,4,5], called a “response surface model”, a “meta model”, an “approximate model” or a “simulator”, has been applied to different engineering design fields
When the cumulative contribution rate is greater than 80%, we believe that the PC can reflect the characteristic of the original variable to a certain extent, and the corresponding parameter h is the final selected principal component number: Step 4: Determine a new conversion matrix according to the known sample data and using the formula zi = ui1x1 + ui2x2 + . . . + uidxd(i = 1, . . . , h) to calculate the value of the h PCs; the n*h transformation matrix is obtained
The following two conclusions can be drawn from the figure: (a) It can be seen from the figure that, as the number of sample points increases, the time required for HDKM-PCDR and Kriging to build a model gradually increases
Summary
The surrogate model [1,2,3,4,5], called a “response surface model”, a “meta model”, an “approximate model” or a “simulator”, has been applied to different engineering design fields. A new method based on principal component analysis (PCA) [23] has been proposed to approximate high-dimensional proxy models It seeks the best linear combination coefficient that can be provided with the smallest error without using any integral. How to improve modeling efficiency as much as possible while reducing the loss in accuracy requires further study For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed. A high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed Through this method, the PCDR strategy can convert high-dimensional correlation parameters in the Kriging model into low-dimensional ones, which are used to reconstruct new correlation functions.
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