In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers’ preference and experience, various FE models can be constructed for a specific structure in practice. However, no one can guarantee that a specific model representation is always best (Model-form uncertainty). Conventional method should perform model updating for each FE model independently and select a best one among them, so that it becomes computationally intensive with many candidate FE models. To handle model-form uncertainty, this study formulates FEMU as the MINLP problem. The proposed method assigns an integer variable for model choice, while continuous real variables are used for the updating parameters. With this formulation, the optimization algorithm can explore both model and parameter space simultaneously to deal with the model-form uncertainty in FE models. Firstly, three numerical experiments were explored to evaluate the performance of the proposed method by considering possible situations in reality as follows: (1) a true FE model exists in model space with an admissible FE model; (2) only admissible FE model exists in model space; and (3) no true and admissible FE models exist in model space. Then, the proposed method was experimentally validated through a real bridge. The results show that the proposed method can find a best FE model with optimal estimates of the updating parameters with much less computational efforts against the conventional FEMU.

中文翻译：

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有限元模型中模型形式不确定下基于混合整数非线性规划的模型更新

在本文中，提出了一种基于混合整数非线性规划（MINLP）的新的有限元模型更新（FEMU）方法来处理有限元模型中的模型形式不确定性。根据建模者的偏好和经验，在实践中可以为特定结构构建各种有限元模型。但是，没有人可以保证特定的模型表示总是最好的（模型形式不确定性）。传统的方法应该独立地对每个有限元模型进行模型更新并从中选择一个最好的，这样对于许多候选有限元模型来说计算量很大。为了处理模型形式的不确定性，本研究将 FEMU 公式化为 MINLP 问题。所提出的方法为模型选择分配一个整数变量，而连续实变量用于更新参数。有了这个配方，优化算法可以同时探索模型和参数空间，以处理有限元模型中模型形式的不确定性。首先，通过考虑现实中可能的情况，探索了三个数值实验来评估所提出方法的性能：（1）模型空间中存在真实的有限元模型，有限元模型是可接受的；(2) 模型空间中只存在可接受的有限元模型；(3) 模型空间中不存在真实且可接受的有限元模型。然后，通过实际桥梁对所提出的方法进行了实验验证。结果表明，与传统 FEMU 相比，所提出的方法可以找到具有更新参数最佳估计的最佳有限元模型，而计算量要少得多。