Coordinate MAC (COMAC)

Coordinate Modal Assurance Criterion (COMAC) is a parameter that helps identifying parts of the structure, which are responsible for low degrees of correlation. The COMAC correlates two sets of mode shapes, either from test or finite element models, and identifies the degrees-of-freedom (DOFs), at which the mode pairs do not agree.

Before using COMAC, the mode pairs between two sets of mode shapes must be identified using, for example, the MAC numbers. For more information, see Modal Assurance Criteria (MAC). Having constructed the set of L mode pairs, the software computes a COMAC value for each DOF over all the correlated mode pairs as follows NOTE:

{COMAC}j = \frac{(\sum{l=1}^L|\psi^H_{A_{l,j}}\widehat{\psi_{X_{l,j}}}|)^2}{(\sum_{l=1}^L|\psi_{A_{l,j}}|^2)(\sum_{l=1}^L|\widehat{\psi_{X_{l,j}}}|^2)}

\widehat{\psi_{X_{l,j}}} = \frac{\psi_{X_{l,j}}}{{MSF}_l}

Where:

• j is the index of a single DOF.

• L is the number of modes.

• \psi_{A} is the known set of measured, test, or reference modes.

• \psi_{X} is the set of analysis or work modes.

• \psi^H_{A_{l,j}} is the conjugate gradient of \psi_{A_{l,j}}.

• {MSF}_l is the modal scaling factor.

At each DOF, COMAC has a value between 0.0 and 1.0. If a particular degree-of-freedom has poor correlation across the set of mode shapes, it will have a value close to 0.0.

Both sets of mode shapes must be scaled similarly, because individual elements contributing to each COMAC value are taken from separate modes. To automatically account for phase differences between two paired mode shapes, the software calculates and applies the modal scale factor (MSF) for each mode pair. Once the analysis modes are scaled by the MSF, the software unit-scales both analysis and reference modes before computing the COMAC values.

Note:

Starting in Simcenter 3D 2020.1, the correlation solver internally converts all real mode shapes to complex ones by assigning a zero imaginary component, and uses a slightly different COMAC formulation. To use the heritage COMAC method with real mode shapes, specify the UGII_CORREL_COMAC_IDEAS=1 environment variable before starting the software.

Learn more

Correlation metrics

Pre-test solution process

Correlation solution process

Look up more details

Modal Analysis

Converting complex modes to real modes

Accounting for repeated modes

Modal Scale Factor (MSF)

Modal Assurance Criteria (MAC)

Cross-orthogonality (X-Ortho)

Frequency Response Assurance Criterion (FRAC)

Min-MAC algorithm

MODMAC algorithm

Normal Mode Indicator Function (NMIF) algorithm

Driving Point Residue algorithm

Scientific literature references for correlation

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Pre/Post video examples

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Simcenter 3D tutorials

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Coordinate MAC (COMAC), Simcenter 3D 2021.1 Series

© 2020 Siemens

Ewins, D.J., “Modal Testing: Theory, Practice and Application”, Second Edition, Research Studies Press LTD., Baldock, England, 2000.

Allemang, R.J., “The Modal Assurance Criterion — Twenty Years of Use and Abuse”, Sound and Vibration, August 2003.

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