TY - JOUR

T1 - Globally supported surrogate model based on support vector regression for nonlinear structural engineering applications

AU - Funk, Steffen

AU - Airoud Basmaji, Ammar

AU - Nackenhorst, Udo

N1 - Funding Information: The support of the German Research Foundation (DFG) during the priority program IRTG 2657 (grant ID: 433082294) is gratefully acknowledged . In addition, this work was supported by the compute cluster, which is funded by the Leibniz University of Hannover, the Lower Saxony Ministry of Science and Culture (MWK) and the German Research Foundation (DFG). On behalf of all authors, the corresponding author states that there is no conflict of interest.

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Elasto-plasticity

KW - Global surrogate modelling

KW - Kernel function

KW - Nonlinear finite element method

KW - Support vector regression (SVR)

UR - http://www.scopus.com/inward/record.url?scp=85141002153&partnerID=8YFLogxK

U2 - 10.1007/s00419-022-02301-3

DO - 10.1007/s00419-022-02301-3

M3 - Article

AN - SCOPUS:85141002153

VL - 93

SP - 825

EP - 839

JO - Archive of applied mechanics

JF - Archive of applied mechanics

SN - 0939-1533

IS - 2

ER -