Optimizing Square Plates with Symmetrically Reinforced Circular Cutouts for Shear Buckling: A Bayesian Optimization Approach to Minimum Weight Design

Abstract

The present study focuses on utilizing the Bayesian Optimization Machine Learning algorithm for the weight optimization of a shear web of given size (a x b), material properties, boundary conditions, and loading conditions. The study is carried out in cooperation with GKN Fokker Aerostructures. The main objective of the research is to replace a pristine, unperforated web with a circularly perforated web where the circular cutout is reinforced such that the weight of the web is minimized w.r.t the pristine web while adhering to shear buckling criteria.

The Bayesian Optimization machine learning method is a Parametric Modelling approach which belongs to the search algorithm class whose purpose it is to find the optimum set of input parameters which maximize or minimize a predefined objective function. Bayesian Optimization attempts to model the objective function through a surrogate model. In the present study Gaussian Process-based surrogate models are used. Through the surrogate model the optimization algorithm can search the design space in a probabilistic manner in search of the global objective optimum.

Furthermore, a novel universal Bayesian Optimization convergence criteria was theorized in the present study. The convergence criteria is based on the decrease in change of uncertainty between subsequent evaluated sets of parameters by the optimizer. The performance of both the Bayesian Optimization algorithm and convergence criteria are verified on a three dimensional case study. The verification showed that the results of the optimization are within 3% of an apparent global minimum weight. The convergence criteria verification showed accurate convergence prediction which has as an implication that roughly 40% of the total optimization iterations could have been spared through the use of this criteria.