The cross-orthogonality check (XOR) is a widely used correlation measure for validating finite element (FE) models, where the orthogonality between analytical and experimental mode shapes is measured as the inner product over the mass matrix. Ideally, this yields the identity matrix where any deviation from this matrix can be seen as a lack of correlation. One of the drawbacks of this measure is its sensitivity to noise on the experimental mode shapes, which can have a significant influence. The present paper presents a new way of calculating the XOR which provides robust results towards noise. The method, known as the principle of local correspondence (LC), is a mode shape-based technique for expanding experimental mode shapes using a unique linear combination of FE modes. The advantage of using the LC principle for calculating the XOR is that no reduced mass matrix is needed, and the influence towards noise on the mode shapes is reduced compared with other known techniques. In this paper, the method is validated using probabilistic numerical investigations. An FE model of a shell structure is used as a case study where Monte Carlo simulations are used to change the material properties and create a variety of different noise scenarios. The results are compared with similar simulations using Guyan and SEREP.

中文翻译：

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使用局部对应原理的鲁棒正交检验

交叉正交检查（XOR）是用于验证有限元（FE）模型的一种广泛使用的相关度量，其中分析和实验模式形状之间的正交性作为质量矩阵上的内积进行测量。理想情况下，这将生成单位矩阵，其中与该矩阵的任何偏差都可以视为缺乏相关性。该措施的缺点之一是它对实验模式形状上的噪声敏感，这可能会产生重大影响。本文提出了一种新的XOR计算方法，该方法为噪声提供了可靠的结果。该方法称为局部对应原理（LC），是一种基于模式形状的技术，用于使用FE模式的唯一线性组合扩展实验模式形状。使用LC原理计算XOR的优点在于，不需要缩减的质量矩阵，并且与其他已知技术相比，减少了噪声对振型的影响。在本文中，该方法通过概率数值研究得到了验证。壳结构的有限元模型用作案例研究，其中使用蒙特卡洛模拟来更改材料特性并创建各种不同的噪声场景。将结果与使用Guyan和SEREP的类似模拟进行比较。壳结构的有限元模型用作案例研究，其中使用蒙特卡洛模拟来更改材料特性并创建各种不同的噪声场景。将结果与使用Guyan和SEREP的类似模拟进行比较。壳结构的有限元模型用作案例研究，其中使用蒙特卡洛模拟来更改材料特性并创建各种不同的噪声场景。将结果与使用Guyan和SEREP的类似模拟进行比较。