Modal Assurance Criteria (MAC)

Modal Assurance Criterion (MAC) is a parameter indicating the degree of consistency between a mode shape from the reference data and a mode shape from the work data. These mode shapes can be real or complex. A MAC parameter is a scalar value between zero and one. The value near one indicates a high degree of correlation or consistency between two mode shapes.

Suppose {ΨA} and {ΨX} are two mode shapes (for example, {ΨA} is a theoretically-predicted (work) mode shape and {ΨX} is an experimentally-measured (reference) mode shape) that you want to compare. The MAC number is defined as a scalar constant expressing the degree of consistency between the work mode shape {ΨA} and the reference mode shape {ΨX} as follows NOTE:

where N is the number of common work and reference mode shape components and the superscript * indicates the complex conjugate value.

There are LA x LX MAC numbers for given mode shape matrices [ΨA] and [ΨX] data sets where LA is the number of mode shapes in [ΨA] and LX is the number of mode shapes in [ΨX].

If two mode shapes are identical or differ by a simple scalar multiplier, they correlate perfectly:

MAC(A,X) =1

Auto-MAC

The Auto-MAC correlates two mode shapes from the same data set. For example, take two mode shapes of data set A, {ΨAk} and {ΨAl}, . The Auto-MAC is defined as follows NOTE:

where:

• ΨAkj is the jth value of the mode shape {ΨAk}.

• ΨAlj is the jth value of the mode shape {ΨAl}.

The Auto-MAC matrix is always a square matrix with LA2 elements.

The diagonal elements of the Auto-MAC are always equal to one as in that case the two correlated mode shapes are equal: {ΨAk} = {ΨAl} for k = l.

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)

Coordinate MAC (COMAC)

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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Modal Assurance Criteria (MAC), 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.

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

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