An efficient Bayesian method with intrusive homotopy surrogate model for stochastic model updating

Abstract

This paper proposes a new stochastic model updating method based on the homotopy surrogate model (HSM) and Bayesian sampling. As a novel intrusive surrogate model, the HSM is established by the homotopy stochastic finite element (FE) method. Then combining the advanced delayed‐rejection adaptive Metropolis–Hastings sampling technology with HSM, the structural FE model can be updated by uncertain measurement modal data. The numerical results show that the updating effectiveness of the proposed method is better than that of the Bayesian methods with the non‐intrusive surrogate models, such as stochastic response surface model and Kriging model. Compared to the Bayesian method with the intrusive second‐order perturbation model, the updating results of the proposed method are more accurate, especially when the fluctuation of the uncertain measured data is large and the stiffness of the structure significantly changes. The model updating results of a cable‐stayed bridge show that the statistic modal properties of the updated bridge model have a very good agreement with the uncertain measurement modal data.