A new approach for stochastic model updating using the hybrid perturbation-Garlekin method

Abstract

Abstract Finite element (FE) model updating is used to modify the FE model with reliable measurement data to minimize the difference between simulated responses and measurement data. However, the measurement data are usually uncertain due to measurement errors, and the uncertain measurement data will inevitably lead to the uncertainty of the updated structural model. In this paper, a new approach for stochastic model updating is proposed based on the hybrid perturbation-Garlekin stochastic finite element method. First, a group of stochastic model updating equations is established that clearly describes the relationship between the update coefficients and the measurement errors. With the aid of a power series expansion, a high-order perturbation technique is used to solve the stochastic model updating equations combined with a regularization technique. Using different orders of perturbation terms of the update coefficient vector as basis vectors, a Garlekin projection scheme is provided to improve the accuracy of the update coefficient vector. Afterwards, the statistical characteristics of the update coefficients can be obtained. Three numerical examples are provided to illustrate the effectiveness of the proposed updating method. The numerical results show that compared with the Bayesian method, the proposed method requires much less computational cost to achieve an accurate result. Different from the low-order perturbation method, the newly presented method can address stochastic updating problems with large fluctuations in measurement errors. By using only the first several orders of modal data with an incomplete degree-of-freedom measurement, the statistics of frequencies and modal shapes of the updated modes obtained by the proposed method remain consistent with the measured results.