Bayesian model updating based on modal flexibility for structural health monitoring

A Bayesian probabilistic model updating method based on modal flexibility for structural health monitoring is presented. Firstly, the flexibility matrices are constructed by using a sequence of identified modal data sets including modal frequencies and mode shapes. Then flexibility vectors are obtained by using vectorization of the lower triangular portion of the flexibility matrices and their covariance matrix is also calculated. The obtained flexibility vector data sets and their covariance matrix are incorporated into a formula of Bayesian updating and the most probable values of model stiffness parameters are obtained by maximizing the posterior PDF of the model parameters. The associated uncertainties are also quantified by calculating the covariance matrix of model parameters at the most probable values. By comparing the updated PDFs of stiffness parameters of the structure before and after possible damage, the probability of damage in each sub-structure can be estimated. The proposed method is illustrated with a numerical example.