Stochastic Static Model Updating of Bridge Using Homotopy Method and Pre-Estimated Solution Domain

When implementing structural model updating, whether the model is stochastic or deterministic, the ill-posed issue is a challenging problem. To effectively address this problem, this paper proposes a new static stochastic model updating method, which combines the homotopy method with the pre-estimation technique of solution domains of the updating quantities. Firstly, considering the uncertain static measurement displacements, the solution domains of updating factors in structural models such as bridges are derived in terms of the sensitivity of static strain energy. Then the homotopy method is used to transfer the stochastic static model updating equation into a series of deterministic recursive equations about the expansion coefficients of updating factors. Within the pre-estimated solution domains, the expansion coefficients of the updating factors can be solved by the L-curve method and the convex optimization. When the measurement positions do not contain the loading points, a model expansion strategy is provided. Two numerical examples demonstrate that the proposed method can offer stable updating results, which coincide very well with those assumed real values, in the cases of high-dimension and limited measurement points. And when the displacements at the loading points are not directly measured, compared with the Bayesian method with the finite element samples, the proposed method has higher computational efficiency with the equivalent accuracy. When updating a practical continuous box-girder bridge, the proposed method can efficiently update a large finite element model, and the statistics of updating results agree very well with those of the static measurement data.