Probabilistic damage identification of FGM structures using model updating procedure based on expansion of incomplete FRF data

The spatial incompleteness and uncertainties of measured data are unavoidable factors that could significantly affect the reliability of damage detection results. It is therefore essential to utilize a method that can effectively deal with the spatial incomplete and contaminated data, and presents probabilistic damage identification results instead of deterministic results. In this regard, a probabilistic damage identification approach for functionally graded materials (FGM) structures using model updating procedure based on expansion of incomplete frequency response function (FRF) data with measurement noise is presented. The model updating procedure is formulated as an optimization scheme which is accomplished by minimizing a cost function based on the changes in expanded FRF data. To expand the incompletely measured FRFs, an iterative order reduction method is performed, which makes the identification resistant to the adverse effects of measurement noise. For the minimization process, we adopt a novel meta-heuristic algorithm called bald eagle search algorithm (BES), which has not yet been tested in the field of model updating. Based on the statistical distributions of the identified stiffness parameters in the damaged and undamaged states, the probability of damage existence (PDE) is established to describe the damage probability for each element. The performance of the proposed model updating procedure is verified using three FGM structures: a simple beam, a two-span beam and a cantilever plate. The statistical results indicate that under a high level of noise (15%), the proposed procedure can provide the prediction of damage localization with a high level of confidence and yield damage estimation results with acceptable errors.