Globally supported surrogate model based on support vector regression for nonlinear structural engineering applications

Abstract

This work presents a global surrogate modelling of mechanical systems with elasto-plastic material behaviour based on support vector regression (SVR). In general, the main challenge in surrogate modelling is to construct an approximation model with the ability to capture the non-smooth behaviour of the system under interest. This paper investigates the ability of the SVR to deal with discontinuous and high non-smooth outputs. Two different kernel functions, namely the Gaussian and Matèrn 5/2 kernel functions, are examined and compared through one-dimensional, purely phenomenological elasto-plastic case. Thereafter, an essential part of this paper is addressed towards the application of the SVR for the two-dimensional elasto-plastic case preceded by a finite element method. In this study, the SVR computational cost is reduced by using anisotropic training grid where the number of points are only increased in the direction of the most important input parameters. Finally, the SVR accuracy is improved by smoothing the response surface based on the linear regression. The SVR is constructed using an in-house MATLAB code, while Abaqus is used as a finite element solver.