Structural damage assessment is prone to several unknowns related to boundary conditions and material properties. This study uses a Bayesian derivative method called Approximate Bayesian Computation (ABC) to address the challenge of damage identification, here rephrased as a structural anomaly detection. The main objective is to estimate the position and magnitude of the lumped masses attached to an aluminium beam. The method can estimate unknown parameters while considering the lack of knowledge on the structure-condition history. The presented method can provide the posterior probability density function (target PDF) of the position and magnitude of the attached mass without relying on prior knowledge of damping behaviour.