Guided wave damage characterisation in beams utilising probabilistic optimisation

This paper introduces a probabilistic optimisation approach to the characterisation of damage in beams using guided waves. The proposed methodology not only determines the multivariate damage characteristics, but also quantifies the associated uncertainties of the predicted values, thus providing essential information for making decisions on necessary remedial work. The damage location, length and depth and the Young’s modulus of the material are treated as unknown model parameters. Characterisation is achieved by applying a two-stage optimisation process that uses simulated annealing to guarantee that the solution is close to the global optimum, followed by a standard simplex search method that maximises the probability density function of a damage scenario conditional on the measurement data. The proposed methodology is applied to characterise laminar damage and is verified through a comprehensive series of numerical case studies that use spectral finite element wave propagation modelling with the consideration of both measurement noise and material uncertainty. The methodology is accurate and robust, and successfully detects damage even when the fault is close to the end of the beam and its length and depth are small. The particularly valuable feature of the proposed methodology is its ability to quantify the uncertainties associated with the damage characterisation results. The effects of measurement noise level, damage location, length and depth on the uncertainties in damage detection results are studied and discussed in detail.