A likelihood-free Bayesian approach for characterisation of multiple delaminations in laminated composite beams

Abstract

This paper presents a probabilistic model-based optimisation framework for localising and characterising multiple delaminations in laminated composite beams using ultrasonic guided waves (GW). A likelihood-free Bayesian method, approximate Bayesian computation by subset simulation (ABC-SS), is implemented to determine the number of delaminations and identify the unknown damage characteristics and their associated uncertainties. The ABC algorithm provides a practical way to approximate the posterior distributions of uncertain damage parameters and select the most plausible damage model for determining the number of delaminations through direct comparison of the experimentally measured and numerically simulated GW signals without assuming any likelihood functions. To overcome the expensive computational cost of traditional finite element simulations, a higher-order laminated model (HOLM) is employed to model the GW propagation behaviour in the delaminated composite beams with satisfactory accuracy and acceptable computational efficiency. Benefiting from the accurate simulation, the dataset comparison utilises the original time-domain GW signals, thereby preventing the loss of any key information from the signals for damage identification. A comprehensive series of numerical case studies are used to demonstrate the accuracy, robustness and feasibility of HOLM simulation and the proposed multiple-delamination identification framework. The practicability and accuracy of the proposed ABC framework are further validated using two experimental datasets.