The Modal Assurance Criterion (MAC): Twenty Years of Use and Abuse

  • Allemang R
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This article reviews the development of the original modal assurance criterion (MAC) together with other related assur-ance criteria that have been proposed over the last twenty years. Some of the other assurance criteria that will be dis-cussed include the coordinate modal assurance criterion (COMAC), the frequency response assurance criterion (FRAC), coordinate orthogonality check (CORTHOG), frequency scaled modal assurance criterion (FMAC), partial modal assurance criterion (PMAC), scaled modal assurance criterion (SMAC), and modal assurance criterion using reciprocal modal vectors (MACRV). In particular, the thought process that relates the original MAC development to ordinary coherence and to or-thogonality computations will be explained. Several uses of MAC that may not be obvious to the casual observer (modal parameter estimation consistency diagrams and model updat-ing are two examples) will be identified. The common prob-lems with the implementation and use of modal assurance cri-terion computations will also be identified. The development of the modal assurance criterion 1-2 over twenty years ago has led to a number of similar assurance cri-teria used in the area of experimental and analytical structural dynamics. It is important to recognize the mathematical simi-larity of these varied criteria in order to be certain that con-clusions be correctly drawn from what is essentially a squared, linear regression correlation coefficient. The modal assurance criterion is a statistical indicator, just like ordinary coherence, which can be very powerful when used correctly but very mis-leading when used incorrectly. This article will first review the historical development of the modal assurance criterion. Other similar assurance criteria will then be identified although the list is not intended to be comprehensive. Typical uses of the modal assurance criterion will be discussed and finally, typi-cal abuses will be identified.

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  • Randall J. Allemang

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