The use of guided waves to identify damage has become a popular method due to its robustness and fast execution, as well as the advantage of being able to inspect large areas and detect minor structural defects. When a travelling wave on a plate interacts with a defect, it generates a scattered field that will depend on the defects geometry. By analysing the scattered field, one can thus characterize the type and size of the plate damage. A Bayesian framework based on a guided waves interaction model for damage identification of infinite plate for the first time is presented here. A semi-analytical approach based on the lowest order plate theories is adopted to obtain the scattering features for damage geometries with circular symmetry, resulting in an efficient inversion procedure. Subsequently, ultrasound experiments are performed on a large aluminium plate with a circular indentation to generate wave reflection and transmission coefficients. With the aid of signal processing techniques, the effectiveness and efficiency of the proposed approach are verified. A full finite element model is used to test the damage identification scheme. Finally, the scattering coefficients are reconstructed, reliably matching the experimental results. The framework supports digital twin technology of structural health monitoring.