Taguchi-based design of experiments in training POD-RBF surrogate model for inverse material modelling using nanoindentation

Abstract

This paper investigates the use of a surrogate model based on Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) for calibrating the nanoindentation-based loading of an elastic–plastic material. Using Taguchi design of experiments and Analysis of Variance (ANOVA), the total number of finite element-based training points is reduced for input parameters that exhibited lower significance. It is found that ANOVA-based sensitivity information can be used to reduce the number of training points without significantly affecting model accuracy. It is also observed that RBFs capable of conforming nonlinearly perform better when the spatial distance between training points increases. Furthermore, for some RBFs the performance is further tuned by choice of the shape parameters. Finally, it is demonstrated that the surrogate model’s performance remains stable under the effect of random noise. Thereby, this study provides a general framework for solving a nanoindentation-based material modelling inverse problem using the POD–RBF technique.