Performance Analysis of Radial Basis Function Metamodels for Predictive Modelling of Laminated Composites.

Kanak Kalita,Xiao-Zhi Gao,Manickam Ramachandran,S Madhu,Shankar Chakraborty

doi:10.3390/ma14123306

Abstract

High-fidelity structural analysis using numerical techniques, such as finite element method (FEM), has become an essential step in design of laminated composite structures. Despite its high accuracy, the computational intensiveness of FEM is its serious drawback. Once trained properly, the metamodels developed with even a small training set of FEM data can be employed to replace the original FEM model. In this paper, an attempt is put forward to investigate the utility of radial basis function (RBF) metamodels in the predictive modelling of laminated composites. The effectiveness of various RBF basis functions is assessed. The role of problem dimensionality on the RBF metamodels is studied while considering a low-dimensional (2-variable) and a high-dimensional (16-variable) problem. The effect of uniformity of training sample points on the performance of RBF metamodels is also explored while considering three different sampling methods, i.e., random sampling, Latin hypercube sampling and Hammersley sampling. It is observed that relying only on the performance metrics, such as cross-validation error that essentially reuses training samples to assess the performance of the metamodels, may lead to ill-informed decisions. The performance of metamodels should also be assessed based on independent test data. It is further revealed that uniformity in training samples would lead towards better trained metamodels.

Highlights

Composites are one the most widely used materials of the 21st century
The prime objective of this paper is to comprehensively investigate the viability of radial basis function (RBF) metamodels as a reliable surrogate for high-fidelity analysis of laminated composite structures
Figure22depicts depicts estimated while randomly dividing the training dataset the best values of trials of

Summary

Introduction

Composites are one the most widely used materials of the 21st century. Laminated composite structures have become an inevitable component of modern structural, marine and aerospace applications. Accurate estimation of the static and dynamic performance of such structures is an important task. With modern computing facilities and a plethora of highly accurate numerical strategies and mathematical theories, composite structures are being extensively analyzed in silico. Despite the high accuracy of numerical approaches, such as the finite element method (FEM), their time-intensiveness often hinders their widespread applications, especially when multiple re-runs are required (e.g., for different sets of ply angles or global optimization tasks). In this regard, metamodels can provide a remarkable saving in computational effort and cost. The accuracy of a metamodel usually depends on various factors, like type, size and complexity of the problem, training data characteristics, the algorithm used, etc

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