Bayesian structural damage identification using fraction function regularisation model based on natural frequency and mode shape curvature

The existing models based on Bayesian inference and L1 regularisation provide a feasible scheme to the uncertainty problem in structural damage identification. However, L1 regularisation cannot accurately describe the sparsity of damage due to excessive punishment of large damage parameters, and the mode shape data used by such models are insensitive to the damage. This compromises the accuracy of damage identification. Compared with L1 regularisation, the fraction function regularisation avoids excessive punishment for larger elements in the damage parameters, resulting in a more accurate sparse solution. The mode shape curvature is more sensitive to damage because it can be viewed as the differential form of the mode shape. Inspired by this, a fraction function regularisation model based on natural frequency and mode shape curvature data is proposed in this paper to further improve the accuracy of Bayesian damage identification. In addition, an improved cuckoo search algorithm is proposed to solve the model by introducing a ranking-based mutation strategy. The results obtained from both the numerical investigation and the experimental study consistently indicate that the proposed method can provide accurate and reliable identification results.