A global surrogate model for high-dimensional structural systems based on partial least squares and Kriging

Abstract

Surrogate model techniques have been widely used in uncertainty propagation (UP) of structural systems. However, establishing surrogate models for structural systems with high-dimensional input and output variables remains a challenging task. The computational burden of constructing surrogate model for such systems can be alleviated by simultaneously reducing the dimensionality of the high-dimensional input–output variables in advance. Partial least squares (PLS) technique can achieve this purpose by searching for the latent structures of the high-dimensional structural systems, i.e., the principal components (PCs) of the input and output variables and their functional relationships. Kriging is a surrogate model with analytical properties and good fitting effects for nonlinear functions, which has been widely used in UP and quantification of engineering structural systems. Therefore, this paper combines Kriging and PLS to develop a global surrogate model for high-dimensional structural systems, named as PLS-K. In the proposed method, PLS is employed to identify the input–output PCs, wherein Kriging model is used to establish the relationship between each pair of PCs. In this way, establishing Kriging model of the structural system with high-dimensional inputs and outputs is decomposed into a series of one-dimensional Kriging construction of input–output PCs, which can significantly alleviate the burden of surrogate model construction. In addition, in order to better incorporate Kriging model into PLS framework, the error-based weights updating (EBWU) procedure of PLS is analytically derived based on Kriging. Several examples demonstrate the efficiency and accuracy of the proposed method.