A frequency response function (FRF) is a function used to quantify the response of a system to an excitation, normalized by the magnitude of this excitation, in the frequency domain. FRF correlation analysis between pairs of FRFs at each frequency point is evaluated in terms of cross-signature assurance criterion (CSAC) and cross-signature scale factor (CSF).

Cross Signature Assurance Criterion (CSAC)   —  The cross signature assurance criterion is a measure of the shape correlation between experimental and FE generated responses with value ranging from 0 to 1, as described in Equation 17–145. The CSAC is an adaptation of MAC for the frequency domain. This criterion is sensitive to changes in mass and stiffness.

(17–145)

where:

is the FE generated FRF, is its conjugate transpose,

is the measured FRF, is its conjugate transpose,

is the number of frequency points.

Cross Signature Scale Factor (CSF)   —  The cross signature scale factor is a measure of the difference in amplitude between measured and FE generated responses with value ranging from 0 to 1 as well, as shown in Equation 17–146. The CSF is sensitive to changes in damping and is often used with the CSAC.

(17–146)