Stochastic static finite element model updating using the Bayesian method integrating homotopy surrogate model

The Bayesian model updating method usually involves tens of thousands of finite element model calculations, which will bring huge computational costs to large structures such as bridges. To reduce the computational costs, this paper develops a highly efficient Bayesian model updating method based on a new static homotopy surrogate model. The new surrogate model is established on the basis of the finite element model using the stochastic homotopy method, which is different from the existing surrogate models that depend on the selected samples. Then by using the hybrid Monte Carlo sampling algorithm integrating the homotopy surrogate model, the static Bayesian model updating of structure is implemented. The numerical example of a plate demonstrates that the established surrogate model has higher accuracy than the polynomial response surface model and Kriging model. Based on the uncertain static test data, the finite element model of a continuous concrete box-girder bridge is efficiently updated using the new method. And the statistics of the displacements in the updated bridge are in good agreement with that of the uncertain measurement data.