Identification of the dynamic characteristics of nonlinear structures

CHAPTER 
POSSIBILITIES AND LIMITATIONS
OF ANALYTICAL MODEL IMPROVEMENT
7.1 INTRODUCTION
As one of the major applications of modal analysis, analytical model
improvement/updating using the measured dynamic properties of a structure has become
a major research topic in the dynamic modelling of practical engineering structures and
has generated many technical publications. A large number of different algorithms have
been developed, some of which have been proven to be quite successful, such as the new
method developed in Chapter 6. However, to the author’s knowledge, there has been
little technical discussion about what can be done (the possibilities) and what cannot (the
limitations) in the updating of an analytical model when practical measurement cases in
which both measured modes and coordinates are incomplete are considered. The purpose
of this Chapter is to identify some of these possibilities and limitations with the objective
of directing research in this subject towards more productive areas.
The discussion begins with a review of the limitations and difficulties of some of the
recently developed methods based on full matrix updating. The mathematical
underdeterminancy associated with these methods is explained. Then the possibility of
updating a condensed (Guyan-reduced) model with error location based on Kidder’s
expansion method is examined. It is demonstrated that, when measured modes and/or
coordinates are incomplete as they are in practice, updating of the analytical model using

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Possibilities and Limitations of Analytical Model Improvement
2 0 7
full matrix updating method(s) or based on Guyan-reduced model with error location is
very difficult, if not impossible. In order to solve the updating problem, it becomes clear
that the physical connectivity of the analytical model should be respected during the
updating process so that the number of unknowns involved can be reduced and the
limited measured data available can have the possibility of solving the problem.
When the physical connectivity of the analytical model is imposed, the data required in
order to update an analytical model are usually within the scope of practical
measurements. As discussed in Chapter 6, by imposing the physical connectivity,
measured FRF data covering few modes are, in most cases, enough to solve the updating
problem even when the measured coordinates are incomplete. Nevertheless, in this
present Chapter, criteria for the minimum measured data (modal data) required to solve
the updating problem are established based on the Eigendynamic Constraint Method
(where measured coordinates are complete) and the Inverse Eigensensitivity analysis
(where measured coordinates are incomplete). Such criteria are important because they
enable the analyst to judge whether an available set of measured modal data is able to
obtain a unique solution of the updating problem. These criteria are then 
by
using the measured FRF data.
Basically, the discussions are illustrated using the analytical model updating exercise
called ‘GARTEUR’ which is supposed to represent the true practical problem in terms of
the incompleteness of both measured modes and coordinates. A mass-spring model is
also used to illustrate the criterion developed.
7.2