A new homotopy approach for stochastic static model updating with large uncertain measurement errors

Abstract

Large measurement errors are a major challenge in structural model updating. Based on the concept of homotopy, a new stochastic static model updating method is proposed to update structural models using uncertain static data with large measurement errors. First, considering the uncertainty of the static measurement, a stochastic model updating equation for element update factors is set up. To solve the stochastic model updating equation, a series of homotopy deformation equations are presented to establish the relationship between the deterministic update factors and the random update factors. Furthermore, the homotopy series expansions of the random update factors can be determined by solving the homotopy deformation equations. Since the measured degrees of freedom of updated structures are usually limited or unavailable, a static condensation technique is used for stochastic model updating. To address the ill-posed problems caused by incomplete measurement information and static measurement errors, the Tikhonov regularization method is used in the process of solving the homotopy deformation equations. Three numerical examples are given to demonstrate the validity of the proposed stochastic model updating method. The numerical results clearly show that unlike the second-order perturbation method, this new method can produce better accuracy in cases with large measurement errors. Compared with the Bayesian method with the Delayed Rejection Adaptive Metropolis sampling technique and even a fast Bayesian method, the proposed method utilizes much less computational time and provides an equivalent accuracy. Finally, static loading experiments on a two-span continuous concrete beam are implemented to validate the proposed model updating method.