A novel Bayesian approach for structural model updating utilizing statistical modal information from multiple setups

• A fast Bayesian methodology is presented for structural model updating.
• Model updating problem is formulated as one minimizing an objective function.
• Novel schemes are developed to obtain the optimal parameters and uncertainties.
• The method can incorporate local mode shapes of different setups automatically.
• Two examples demonstrated the accuracy and efficiency of the proposed method.

In this paper, a fast Bayesian methodology is presented for structural model updating utilizing modal information from multiple setups. A two-stage fast Bayesian spectral density approach formulated recently is firstly employed to identify the most probable modal properties as well as their uncertainties. The model updating problem is then formulated as one minimizing an objective function, which can incorporate statistical information about local mode shape components corresponding to different setups automatically, without prior assembling or processing. A fast analytic-iterative scheme is proposed to efficiently compute the optimal parameters so as to resolve the computational burden required for optimizing the objective function numerically. The posterior uncertainty of the model parameters can also be derived analytically and the computational difficulty in estimating the inverse of the high dimensional Hessian matrix required for specifying the covariance matrix is also properly tackled. The efficiency and accuracy of all these methodologies are verified by numerical examples.