Multi-fidelity methods for health monitoring of aerospace structures

In engineering applications, common problems rely on optimization: improving system or structure design, health monitoring with damage assessment and control problems. Modern approaches solve these problems using computer simulations to find the best design among all the possibilities or to find the right damage parameters configuration. High-fidelity simulations, like the finite element in structural design or CFD codes for fluid dynamics, have high computational cost that can be computationally untractable. To accelerate the optimization process two main approaches can be used to reduce the overall execution cost: use a small number of model evaluations and use cheaper, but with reduced accuracy, numerical models. In this work of thesis we combine these two techniques: we employ a surrogate based optimization which is built along the optimization process by choosing the most informative sample reduces the number of function evaluations. Furthermore, the other main feature consists in using different simulation fidelity levels; the lower and cheaper ones purpose is to extensively explore the design space, the highest is used to improve the overall accuracy of the surrogate model in specific points. More in detail is used a Bayesian Multi-fidelity framework where the surrogate is modeled with a Gaussian Process, it merges and fuses the fidelities sampling in the design space using the acquisition functions: these indicate the next point to sample with the relative fidelity to maximize information gain. In this work of thesis we use and compare 3 different acquisition functions: Probability of Improvement, Expected Improvement and Max value Entropy Search; then we apply them on a damage identification problem in a composite specimen. We consider a composite carbon fiber specimen with a modeled cut in the fiber direction that means discontinuity in the stress transmission; composites dam- ages are critical because often difficult to spot but they reduce greatly the structural strength hence the monitoring is crucial to ensure the health of the structure. The problem uses the strain reference field of a damage configuration and the algorithm actively builds a surrogate model, that minimizes the Root Mean Square Error between the reference and the surrogate strain fields, to find the cut geometrical properties. We observe major reduction in cost, and number of evaluations, comparing to the singlefidelity counterpart.