This study proposes an interval model updating method based on interval overlap ratios and Chebyshev polynomials. The interval midpoints and interval radii of the uncertain parameters are determined by solving optimization problems separately. The objective function for determining the interval midpoints is constructed based on predicted and measured data. To determine the interval radii, Chebyshev polynomials are used to construct the uncertainty propagation between the updated and modal parameters. A small number of samples is required for Chebyshev polynomials, which improves the computing efficiency of the proposed method. Based on the interval overlap ratio, the objective function for determining the interval radii is constructed. The interval overlap ratio can effectively quantify the agreement between the intervals of modal parameters obtained from simulation and experimental models. Additionally, a surrogate model is used in the proposed method instead of a finite element model, which can be selected as needed. The proposed method is applied to a three-degree-of-freedom mass-spring system, and its computational accuracy in cases of well-separated and close modes is discussed in detail. Furthermore, the method is used in an engineering example, the GARTEUR aircraft model. The results show that the proposed method is effective for interval model updating with high accuracy.

中文翻译：

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基于区间重叠比和切比雪夫多项式的不确定模型更新优化算法


本研究提出了一种基于区间重叠比和切比雪夫多项式的区间模型更新方法。不确定参数的区间中点和区间半径是通过分别求解优化问题来确定的。用于确定区间中点的目标函数是根据预测和测量的数据构建的。为了确定区间半径，使用切比雪夫多项式来构建更新参数和模态参数之间的不确定性传播。切比雪夫多项式需要少量样本，提高了所提方法的计算效率。基于区间重叠比，构建了确定区间半径的目标函数。区间重叠比可以有效量化仿真和实验模型得到的模态参数区间之间的一致性。此外，所提出的方法中使用了代理模型而不是有限元模型，后者可以根据需要进行选择。将所提方法应用于三自由度质量弹簧系统，并详细讨论了其在分离良好和接近模式情况下的计算精度。此外，该方法还用于工程示例，即 GARTEUR 飞机模型。结果表明，所提方法对区间模型更新有效，精度高。