Bayesian Finite-Element Model Updating of Bridges Considering Boundary Condition Uncertainties

A Bayesian finite-element model updating method for updating the additional rotational and horizontal constraints of bridge boundary conditions using modal parameters is proposed. First, the spring constant is considered as an uncertain parameter in the stiffness matrix to show the effect of the boundary conditions in the model updating process. Moreover, the substructuring method is considered for solving eigenvalue problems. By reducing the size of the characteristic equations, the substructure approach overcomes the drawbacks and inefficiency of the model updating process caused by the abundance of the updated parameters in actual engineering applications. Bayesian model updating subsequently is used to quantify the uncertainties that exist in bridge model updating, including the uncertainties caused by boundary conditions. By introducing an adaptive transitional Markov chain Monte Carlo algorithm to obtain the posterior probability of parameters, the computational efficiency is improved. The posterior variance of the updating parameters clearly demonstrates the merit of the modified boundary conditions. Its application to a bridge structure demonstrates that the proposed method is efficient and applicable for engineering problems.