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.

大的测量误差是结构模型更新的主要挑战。基于同伦的概念，提出了一种新的随机静态模型更新方法，用于利用测量误差较大的不确定静态数据更新结构模型。首先，考虑静态测量的不确定性，建立单元更新因子的随机模型更新方程。为求解随机模型更新方程，提出一系列同伦变形方程，建立确定性更新因子与随机更新因子之间的关系。此外，随机更新因子的同伦级数展开可以通过求解同伦变形方程来确定。由于更新结构的测量自由度通常是有限的或不可用的，静态压缩技术用于随机模型更新。针对测量信息不完整和静态测量误差导致的不适定问题，在求解同伦变形方程的过程中采用了Tikhonov正则化方法。给出了三个数值例子来证明所提出的随机模型更新方法的有效性。数值结果清楚地表明，与二阶微扰方法不同，这种新方法在测量误差较大的情况下可以产生更好的精度。与具有延迟拒绝自适应大都会采样技术的贝叶斯方法甚至快速贝叶斯方法相比，所提出的方法使用更少的计算时间并提供等效的精度。最后，