1043 O. Büyüköztürk et al. (eds.), Nondestructive Testing of Materials and Structures,
RILEM Bookseries 6, DOI 10.1007/978-94-007-0723-8_146, © RILEM 2013
Abstract Stochastic identification results are not sufficient to determine input-output
relations because one constant for each identified mode is missing. Since the prod-
uct of a mode and its constant is unique the constant can be absorbed into the modal
scaling and it is in this context that the term eigenvector normalization is used in this
paper. The seminal contribution in the normalization of operational modes is from
Parloo et. al., whom, in a paper in 2002, noted that the required scaling can be com-
puted from the derivative of the eigenvalues to known perturbations. This paper
contains a review of the theoretical work that has been carried out on the perturba-
tion strategy in the near decade that has elapsed since its introduction.
Keywords Eigenvector scaling • Modal models • Normalization • Operational
modal analysis • Output-only identification • Sensitivities
Introduction
Results from operational modal analysis cannot be used to establish input-output
relations because the information to properly scale the identified modes is unavail-
able. Since a number of applications in experimental dynamics and diagnostics are
based on input-output maps, procedures to determine the proper modal scaling are
of practical interest. The fundamental contribution in resolving the scaling issue is
credited to Parloo et. al., [1], who showed that the information required is encoded
in the derivatives of the eigenvalues with respect to known perturbations. The idea
being, of course, that these derivatives can be estimated experimentally from
changes in the eigenvalues obtained in two tests. Since perturbations of the mass are
easiest to implement most of the work on the perturbation strategy has been restricted
D. Bernal (*)
Civil and Environmental Engineering Department, Center for Digital Signal Processing,
Northeastern University, Boston 02115
e-mail: bernal@neu.edu
Eigenvector Normalization from Mass
Perturbations: A Review
D. Bernal