Journal of Applied Science and Engineering

Published by Tamkang University Press

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A Variable-Importance-Aware Universal Kriging Framework for Surrogate-Based Structural Optimization

 2026

 Volume 32

Muhammad Hassan Yaqoob and Huang Hai

Hangzhou International Innovation Institute, Regional Centre for Space Science and Technology Education in Asia and the Pacific,
School of Astronautics, Beihang University, Beijing, 100191, China

Received: March 1, 2026
Accepted: April 6, 2026
Publication Date: May 17, 2026

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Mass convergence history during Differential Evolution.

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Surrogate modelling is essential for simulation-based engineering optimization when high-fidelity simulations are computationally expensive. This paper presents Fuzzy-Based Weighted Universal Kriging (FBW-UK), a surrogate modelling framework designed to improve Kriging performance by explicitly incorporating variable importance information into the modelling pipeline. FBW-UK integrates three components: a data-driven fuzzy weighting mechanism based on Pearson-correlation importance scores, which amplifies influential variables and suppresses weakly informative ones through a sigmoidal membership function; a universal linear trend that captures global drift before Gaussian process regression; and an ARD Matérnkernel that provides per-dimension length-scale adaptation for residual modelling. The framework is validated on a CubeSat structural optimization problem using high-fidelity finite element simulations, with separate surrogates constructed for mass, stress, and deflection. Comparative results against Response Surface Methodology and Simple Kriging show that FBW-UKdelivers consistently better predictive performance across responses and evaluation metrics, with thelargest gains observed for the non-linear, constraint-critical stress response. The method also demonstrates stronger data efficiency, achieving competitive accuracy under limited-sample conditions and reducing the number of expensive simulations required for reliable surrogate construction. When integrated into a surrogate based optimization workflow, FBW-UK yields a lighter feasible structural design while satisfying stress and deflection constraints. The resulting optimum is physically interpretable, and the learned fuzzy weights align
with engineering intuition by identifying the most influential design variables. Overall, the study shows that importance-informed input-space rescaling can improve surrogate accuracy, robustness, and optimization effectiveness in computationally intensive engineering design.

Keywords: Fuzzy-Based Weighted Universal Kriging (FBW-UK); Surrogate modeling; Gaussian process regression; Structural optimization; CubeSat; Finite element analysis; Differential Evolution

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