Deep Kernel Bayesian Optimization for the design of stepped composite repairs under compression

Abstract

The structural integrity of thick fiber-reinforced polymer (FRP) laminates in naval applications relies on effective repair strategies. While stepped repairs provide aerodynamic and hydrodynamic continuity, optimizing their geometry involves a complex trade-off between strength recovery and material removal. High-fidelity Finite Element Method (FEM) simulations are essential to capture non-linear compressive failure modes but are computationally prohibitive for traditional iterative optimization. This study proposes a Deep Kernel Bayesian Optimization framework to accelerate the geometric design of stepped repairs. We employ a Deep Kernel Gaussian Process (DKGP) that couples a deep neural network feature extractor with a Gaussian Process to quantify epistemic uncertainty, guiding the search toward high-performance regions. To mitigate overfitting on sparse data, a novel progressive complexity strategy is introduced, dynamically adapting the neural architecture depth. Validated against parametric Cohesive Zone Modeling (CZM) simulations, the framework reduces computational cost by approximately 96% compared to Genetic Algorithms (GA) and 80% compared to static sampling. Crucially, the framework autonomously identified a strength-recovery limit (≈ 95% strength recovery) and learned to avoid premature adhesive debonding in complex off-axis ply configurations.