This paper studies the finite element (FE) model updating of an 18-story experimental structure. FE model updating requires solving optimization problems that are generally non-convex and have unknown number of local optima. For such problems, neither randomized local optimization algorithms nor stochastic search algorithms can guarantee global optimality. To obtain the global optimum and improve the accuracy of FE model updating, this paper proposes the branch-and-bound (B&B) algorithm for solving non-convex optimization problems in FE model updating. The paper focuses on the modal property difference formulation that minimizes the difference between experimental and simulated eigenvalues and eigenvectors. We propose a reformulation of the modal property difference approach using epsilon-constraint, to enable the application of the B&B algorithm in FE model updating. The proposed approach is first investigated in simulation and compared with the interior-point method and the genetic algorithm. The model updating results using the B&B algorithm are next validated by the shaking table test data of an 18-story steel frame structure.

本文研究18层实验结构的有限元（FE）模型更新。FE模型更新需要解决通常是非凸的并且具有未知数量的局部最优的优化问题。对于此类问题，随机局部优化算法和随机搜索算法均不能保证全局最优。为了获得全局最优值并提高有限元模型更新的准确性，提出了一种求解有限元模型更新中非凸优化问题的分支定界（B＆B）算法。本文着重于模态特性差异公式化，该公式可最大程度地减少实验特征值和模拟特征值与特征向量之间的差异。我们建议使用epsilon约束重新定义模态性质差异方法，以使B＆FE模型更新中的B算法。首先在仿真中研究了提出的方法，并将其与内点法和遗传算法进行了比较。接下来，使用B＆B算法更新模型的结果将通过18层钢框架结构的振动台测试数据进行验证。