Vibration Mode Shape Recognition Using the Zernike Moment Descriptor

Vibration mode-shape comparison between numerical models and experimental data is an essential step in the study of structural finite element model (FEM) updating. The Modal Assurance Criterion (MAC) is the most popular method for such comparison at the moment, which works perfectly well for small and medium sized structures. MAC provides a measure of closeness between the predicted and measured eigenvectors but contains no explicit information on shape features. This is especially significant for large and complicated industrial systems where the MAC index can rapidly degenerate over the course of just a few modes so that a very detailed finite element model, which surely represents the physical system with good accuracy, cannot be reliably compared to measurements. New techniques, based upon the well-developed philosophies of image processing (IP) and pattern recognition (PR) are considered in this paper. The Zernike moment descriptor (ZMD) is a region-based shape descriptor having outstanding properties in IP including rotational invariance, expression and computing efficiency, ease of reconstruction and robustness to noise. In this paper the ZMD is applied to the problem of mode shape recognition for a circular plate. Result shows that the ZMD has considerable advantages over the traditional MAC index when identifying the cyclically symmetric mode shapes that occur in axisymmetric structures with repeated eigenvalues.