Modeling the Effective Elastic Modulus and Thickness of Corrugated Boards Using Gaussian Process Regression and Expected Hypervolume Improvement

TL;DR

This paper develops a Gaussian Process Regression model with EHVI to accurately predict the effective elastic modulus and thickness of corrugated boards, aiding in their structural optimization.

Contribution

It introduces a novel application of GP with EHVI for modeling complex hypersurfaces of material properties in corrugated boards.

Findings

GP achieved MSE of 5.24 kPa^2 for elastic modulus

GP achieved MSE of 1 mm^2 for thickness

Enhanced modeling accuracy and adaptability for structural optimization

Abstract

This work aims to model the hypersurface of the effective elastic modulus, \( E_{z, \text{eff}} \), and thickness, \( th_{\text{eff}} \), in corrugated boards. A Latin Hypercube Sampling (LHS) is followed by Gaussian Process Regression (GP), enhanced by EHVI as a multi-objective acquisition function. Accurate modeling of \( E_{z, \text{eff}} \) and \( th_{\text{eff}} \) is critical for optimizing the mechanical properties of corrugated materials in engineering applications. LHS provides an efficient and straightforward approach for an initial sampling of the input space; GP is expected to be able to adapt to the complexity of the response surfaces by incorporating both prediction and uncertainty. Therefore, the next points being generated and evaluated are based on the complexity of the hypersurfaces, and some points, especially those with higher variance, are more exploited and carry more importance. The performance of GP with EHVI is measured by Mean Squared Error (MSE). Prediction of GP resulted in \( \text{MSE}(E_{z, \text{eff}}) = 5.24 \, \text{kPa}^2 \) and \( \text{MSE}(th_{\text{eff}}) = 1 \, \text{mm}^2 \). GP possesses then improved accuracy and adaptability for future applications in structural optimization.