7.2. PART 2: TEST-ANALYSIS RECONCILIATION 133
model studies. Most recently, RMA was employed to investigate parametric sensitivities for the
ISPE structure. As a result of this work, two enhancements of the method have been introduced.
a. Preliminary screening of candidate parametric sensitivities based on reference frequency
shifts and cross-orthogonality metrics was defined to differentiate “sensitive” from “insen-
sitive” cases (eliminating “insensitive” parametric variations from further consideration).
b. A frequency and cross-orthogonality (SVD) convergence metric for determination of an
augmented residual trial vector set that satisfies RMA accuracy requirements.
7.2 PART 2: TEST-ANALYSIS RECONCILIATION
7.2.1 INTRODUCTION
Reconciliation of a test article’s finite element model with experimental modal data, if conducted
in an objective and systematic manner, requires minimization of a cost function. A variety of
modal cost functions are employed by many investigators. e present discussion describes a
particular cost function that describes a balanced modal frequency and mode shape “error” rela-
tionship. Minimization of the modal cost function’s error norm employing gradient based and
Monte Carlo strategies are evaluated.
7.2.2 MODAL COST FUNCTION .C
/ AND OPTIMAL TEST-ANALYSIS
RECONCILIATION
Consider the standard expression for the undamped structural dynamics eigenvalue problem,
Œ
K
Œ
ˆ
Œ
M
Œ
ˆ
Œ
D
Œ
0
: (7.36)
When modal test data is substituted into the above expression,
Œ
K
Œ
ˆ
t
Œ
M
Œ
ˆ
t
Œ
t
D
Œ
R
; (7.37)
there is a residual error, ŒR, due to (a) differences between the FEM and modal test data and
(2) measurement error.
Pre-multiplication by the FEM mode shapes results in
ˆ
T
Kˆ
t
ˆ
T
Mˆ
t
Œ
t
D
ˆ
T
R
:
(7.38)
By substituting the transpose of ŒKŒˆ from Equation (7.36), the above relationship be-
comes
Œ
ˆ
T
Mˆ
t
ˆ
T
Mˆ
t
Œ
t
D
ˆ
T
R
: (7.39)
Finally, pre-multiplication of the above result by the inverse of the FEM eigenvalues de-
fines the modal cost function ŒC
ˆ
as
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