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DeterminatiOn of structural modes via the Prony model: System
order and noise induced poles
S. Braun a) and Y. M. Ram
TechnionIsrael
Institute
of Technology,
Faculty
of Mechanical
Engineering,
Haifa, Israel
(Received
2 November 1985; accepted
for publication
13 November 1986)
The parameters
of multiple degree of freedom structural systems
can be identified
from their
impulse
response
via the Prony method. Overdetermining
the system's
order
is shown
to
improve
the identification
accuracy
in noisy situations,
but introduces
additional mathematical
poles. Described
are methods
to determine
the necessary
overdetermination
and the true
system
poles. A novel, efficient
perturbation
method,
based
on the singular
value
decomposition,
is shown
to be effective
under noisy situations.
PACS numbers: 43.60. Gk
INTRODUCTION
The identification of structural systems consists of ob
taining estimates
of natural frequencies
and damping
factors
(global parameters
of system
eigenvalues)
as well as modal
constants
(local parameters
or system
eigenvectors).
From
a system point of view, this
is equivalent
to identifying poles
and residues
for the partially fractioned
transfer
functions
which describe
input/output relationships
between struc
ture points.
Dedicated
instrumentation
systems
for structural
test
ing
(with FFT based
computations)
compute
transfer
func
tions
in the frequency
domain, but time domain
impulse
re
spunsos
are also readily available via an inverse Fourier
transform.
Time
domain
identification
methods,
using
the
said
impulse
response,
have
thus become
popular
in the
last
decade. One such approach
is based on the Prony method,
whereby
the impulse
response
is approximated
as a set of
complex
exponential
functions.
A major problem associated
with the identification
of
system parameters
is caused by a need to set a priori the
(unknown) model order.
It has been noted
•'2
that, using
an
overdetermined
system
improves
the accuracy of identifica
tion, and many researchers
advocate
the use of said overdo
termination.
Various problems
are associated
with such an approach.
One concerns
the existence
of the additional poles (or pa
rameters), artificially induced by the overdetermination.
The necessary
extent of overdetermination
has often
to be set
by an "educated
guess." Appropriate computational meth
ods may be called
for, as
the overdetermination
can cause
the
system
equation
to become
illconditioned.
A further prob
lem is that of separating
between
system
poles and those due
to the overdetermination
or the unavoidable
existing
noises.
The Prony decomposition
is known
to be noise
sensitive
TM
and the identification of extraneous
system parameters
is a
phenomenon
well known to practitioners
in the field of dy
namic structural
testing.
In this article, we present a theoretical basis
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This note was uploaded on 12/02/2011 for the course ME 7533 taught by Professor Staff during the Summer '11 term at LSU.
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