Abstract: To address the challenge that traditional damage monitoring methods based on the inverse Finite Element Method (iFEM) are difficult to achieving quantitative assessment, this paper proposes a probabilistic damage monitoring method for plate structures that combines iFEM with a Bayesian framework. This method uses the strain extrapolation capability of iFEM to reconstruct the extrapolated strain field near the damage under different damage hypotheses. By constructing a likelihood function between the extrapolated and measured strains, it achieves a posterior probability of the damage parameters, thereby achieving Bayesian damage monitoring without a healthy baseline. Simulation analyses were performed on rectangular plates and trapezoidal stiffened plates. The results show that the average errors of displacement and strain reconstruction using iFEM are below 1.0%, and the damage monitoring error is below 7.8%. The simulation results indicate that both the damage radius and the stiffness reduction factor influence the accuracy of damage monitoring.Furthermore, based on the variation of the strain field near damages of different sizes, the influence of mesh discretization on the accuracy of the method was investigated. A test platform for a trapezoidal stiffened plate was built to verify the effectiveness of the method under practical working. The damage monitoring error below 6.5%, achieving identification, localization, and probabilistic assessment of the damage.

Key words: structural health monitoring, inverse finite element method, Bayesian framework, damage monitoring, plate and shell structures