Comments on the MAC and the NCO, and a linear modal correlation coefficient

Remarks on the MAC [1, 2] and the NCO [2, 3] are presented. A modal correlation coefficient is proposed whose development is based on working on deficiencies of the widespread MAC and the NCO. The modal assurance criterion, MAC, is an extensively used parameter to estimate the degree of correlation between modal vectors. It is commonly used to pair experimentally extracted eigenvectors with theoretically derived ones. Naturally, this criterion has advantages and drawbacks which are discussed in detail next; it suffices in this preface (1) to point out that this function is simple to apply and does not demand experimental-eigenvector completeness or system matrices and (2) to note three shortcomings: it is not an orthogonality check, does not have a meaningful domain for its [0, 1] rank and is nonlinear. The normalized cross orthogonality, NCO, is a modification of the MAC tailored to solve its first noted shortcoming. Interestingly, it is herein shown that the NCO also fixes the second MAC defect. Nevertheless, the NCO is still a nonlinear function. In this technical letter, a critical review and new insights on modal correlation coefficients are presented, both analytically and through examples. Moreover, a linear modal correlation coefficient is suggested.