Robust Cross-Orthogonality Check Using the Principle of Local Correspondence

Abstract

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.