Predicting Open-Hole Laminates Failure Using Support Vector Machines With Classical and Quantum Kernels

Modeling open hole failure of composites is a complex task, consisting in a highly nonlinear response with interacting failure modes. Numerical modeling of this phenomenon has traditionally been based on the finite element method, but requires to tradeoff between high fidelity and computational cost. To mitigate this shortcoming, recent work has leveraged machine learning to predict the strength of open hole composite specimens. Here, we also propose using data-based models but to tackle open hole composite failure from a classification point of view. More specifically, we show how to train surrogate models to learn the ultimate failure envelope of an open hole composite plate under in-plane loading. To achieve this, we solve the classification problem via support vector machine (SVM) and test different classifiers by changing the SVM kernel function. The flexibility of kernel-based SVM also allows us to integrate the recently developed quantum kernels in our algorithm and compare them with the standard radial basis function (RBF) kernel. Finally, thanks to kernel-target alignment optimization, we tune the free parameters of all kernels to best separate safe and failure-inducing loading states. The results show classification accuracies higher than 90% for RBF, especially after alignment, followed closely by the quantum kernel classifiers.

High-Dimensional Bayesian Optimisation with Large-Scale Constraints -- An Application to Aeroelastic Tailoring

Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation methods, leading to a local solution in the design space while the global space is neglected. Bayesian Optimisation is a promising path towards sample-efficient, global optimisation based on probabilistic surrogate models. While Bayesian optimisation methods have demonstrated their strength for problems with a low number of design variables, the scalability to high-dimensional problems while incorporating large-scale constraints is still lacking. Especially in aeroelastic tailoring where directional stiffness properties are embodied into the structural design of aircraft, to control aeroelastic deformations and to increase the aerodynamic and structural performance, the safe operation of the system needs to be ensured by involving constraints resulting from different analysis disciplines. Hence, a global design space search becomes even more challenging. The present study attempts to tackle the problem by using high-dimensional Bayesian Optimisation in combination with a dimensionality reduction approach to solve the optimisation problem occurring in aeroelastic tailoring, presenting a novel approach for high-dimensional problems with large-scale constraints. Experiments on well-known benchmark cases with black-box constraints show that the proposed approach can incorporate large-scale constraints.