The Challenge of Dynamic Similarity Assessment

  • Adam C. MoyaEmail author
  • Julie M. Harvie
  • Mike J. Starr
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Throughout the development cycle of structural components or assemblies that require new and unproven manufacturing techniques, the issue of unit to unit variability inevitably arises. The challenge of defining dynamic similarity between units is a problem that is often overlooked or forgotten, but can be very important depending on the functional criteria of the final product. This work aims to provide some guidance on the approach to such a problem, utilizing different methodologies from the modal and vibration testing community. Expanding on previous efforts, a non-intrusive dynamic characterization test is defined to assess similarity on an assembly that is currently being developed. As the assembly is qualified through various test units, the same data sets are taken to build a database of “similarity” data. The work presented here will describe the challenges observed with defining similarity metrics on a multi-body structure with a limited quantity of test units. Also, two statistical characterizations of dynamic FRFs are presented from which one may choose criterion based on some judgment to establish whether units are in or out of family. The methods may be used when the “intended purpose” or “functional criteria” are unknown.


Modal testing Correlation Frequency response functions Similarity 



Complex average of all FRF’s in data set


Degree of freedom


Total number of DOF’s


Individual test run


FRF for individual DOF


Total number of variability tests


Individual test unit


Complex average of all FRF’s for individual test unit L

\( \overline{X}\left(\omega \right) \)

Mean of all average FRF’s, P L (ω)


Total number if test units available


Bounding scale factor

\( \overline{\sigma}\left(\omega \right) \)

Average standard deviation from all test units


Experimental Cross Signature Scale Factor


Experimental Cross Signature Assurance Criterion


Experimental Cross Signature Correlation value


Hermitian transpose


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Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Adam C. Moya
    • 1
    Email author
  • Julie M. Harvie
    • 2
  • Mike J. Starr
    • 2
  1. 1.Experimental Mechanics, NDE, and Model Validation DepartmentSandia National LaboratoriesAlbuquerqueUSA
  2. 2.Program and Test Integration DepartmentSandia National LaboratoriesAlbuquerqueUSA

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