Dynamic model verification is the process whereby an analytical model of a dynamic system is compared with experimental data, and then qualified for future use in predicting system response in a different dynamic environment. There are various ways to conduct model verification. The approach adopted in MOVER II employs Bayesian statistical parameter estimation. Unlike curve fitting whose objective is to minimize the difference between some analytical function and a given quantity of test data (or curve), Bayesian estimation attempts also to minimize the difference between the parameter values of that function (the model) and their initial estimates, in a least squares sense. The objectives of dynamic model verification, therefore, are to produce a model which: (1) is in agreement with test data, (2) will assist in the interpretation of test data, (3) can be used to help verify a design, (4) will reliably predict performance, and (5) in the case of space structures, facilitate dynamic control

Chrostowski, J. D.

Hasselman, T. K.

English

NASA Technical Reports Server

N87-22710
- MOVER II -
A COMPUTER PROGRAM
FOR
MODEL VERIFICATION OF DYNAMIC SYSTEMS
J.D. Chrostowskl and T.K. Hasselman
Engineering Mechanics Associates, Inc.
Torrance, California
Workshop on Structurat Dynamics
and
Control Interaction of F1exlble Structures
Marshall Space Fllght Center
April 22-24, 1986
_'_E.C_ PAGE BLANK NOT FILMED
199
https://ntrs.nasa.gov/search.jsp?R=19870013277 2020-03-20T10:33:58+00:00Z
- MOVER II -
DYNAMIC MODEL VERIFICATION
Dynamic model verification is the process whereby an analytical model of a
dynamic system is compared with experimental data, adjusted if necessary
to bring it into agreement with the data, and then qualified for future
use in predicting system response in a different dynamic environment.
There are various ways to conduct model verification. The approach
adopted in MOVER II employs Bayesian statistical parameter estimation.
Unlike "curve fitting" whose objective is to minimize the difference
between some analytical function and a given quantity of test data (or
"curve"), Bayesian estimation attempts also to minimize the difference
between the parameter values of that function (the model) and their
initial estimates, in a least squares sense. The objectives of dynamic
model verification, therefore, are to produce a model which (1) is in
agreement with test data, (2) will assist in the interpretation of test
data, (3) can be used to help verify a design, (4) will reliably predict
performance, and (5) in the case of space structures, facilitate dynamic
control.
w
w
IAJ
e_
I HARDWAREI
I
COMPARE p
I
NO@NO
_..ODEL VERIFIED-_
fl TEST
o
0
X
OBJECTIVES
o MATCH ANALYSIS AND TEST
e INTERPRET DATA
e VERIFY DESIGN
e PREDICT PERFORMANCE
- IMPEDANCE
- DISPLACEMENT
- LOADS
- FATIGUE
- ETC,
e FACILITATE CONTROL
200
- MOVER II -
HISTORY OF DEVELOPMENT
One of the earliest attempts in automating the Bayesian parameter
estimation procedures was begun in 1972. Under Contract to NASA, a
computer code called MOUSE was developed and demonstrated on the Saturn V
launch vehicle. Although the methodology used in developing MOUSE was
quite general, it was only applicable to one-dimensional shear beam
models. In 1976, two efforts funded by NASA were begun in parallel to
further develop the MOUSE concept. The first effort was directed towards
general dynamic systems, i.e., models which might be constructed from
lumped parameter, finite elements, modal coordinates, or some combination
of the three, and which might also contain heavy damping. The computer
code MOVER was developed to automate the verification of such systems, and
won a NASA New Technology award in 1982. The second effort was geared
towards efficient model verification of large, lightly damped systems
typified by aerospace structures, with specific application to the Space
Shuttle Orbiter finite element model; the computer code CATELAST was
developed to automate this procedure. Over the past several years, an
advanced version of MOVER has evolved. Called MOVER II, it incorporates
modal synthesis and substructuring techniques for modeling large
multi-component systems and provides a variety of graphic outputs to
facilitate interpretation of results. MOVER II has been used to verify
models of turbo-pumps rail vehicles, launch vehicles and high-speed
rotating machinery.
e 1973 - MOUSE (MODEL 0_PTIMIZATION _SING _TATISTICAL ESTIMATION)
e 1977 - MOVER (__0_DELVERIFICATION)
e 1978 - CATELAST (_ORRELATION OF ANALYSIS AND IEsT FOR LARGE
_L.RUCTURES)
e 1984 - MOVER II
201
- MOVERII -
MOTIVATION
Compared with the state-of-the-art of model generation and analysis, which
has matured considerably over the past decade or so, the state-of-the-art
in experimental model verification is still very much in its infancy.
Structural testing, particularly dynamic testing and data processing, has
also progressed significantly in recent years, but the proven ability to
assimilate experimental data systematically into a specified model
configuration to obtain an improved set of model parameters values, has
not experienced the same steady growth. The original objectives for the
MOUSE code were (I) to revise the mass and stiffness parameters of a
finite element model using a Bayesian statlstical estimator, (2) impose no
limits on the amount of test data required, and (3) provide a quantitative
measure of the significance of the revised parameter values based on the
quantity, quality and suitability of the data. Practical experience with
MOUSE, however, indicated the need to satisfy several additional
objectives: (4) incorporate a modeling capability applicable to general
structural models, regardless of configuration or size; (5) estimate
damping, as well as mass and stiffness parameters, even for structures
with closely spaced modes; (6) eliminate the requirement for "pure" modal
data; (7) require that the program resolve experimental data (to obtain
natural frequencies, orthogonal mode shapes and modal damping) from
sinusoidal response which may contain contributions of several closely
spaced modes; and (8) require that the program be compatible with
conventional analytical and experimental data.
1) RETAINSTATE-SPACE/FREOUENCYDOMAINFORMULATIONFORLINEAR
TIME-INVARIANT SYSTEMS
2) REPLACENETWORKMODELINGCAPABILITY IN MOVERWITH ADDITIONAL
CAPABILITY FORMODELINGSTRUCTURAL/MECHANICALSYSTEMS
3) INCORPORATESUBSTRUCTURING
q) ADDPARAMETERSENSITIVITY ANALYSIS IN THE FORMOF RESPONSE
DERIVATIVESTO FACILITATE PARAMETERSELECTION
5) ADD INTERPRETIVE/DIAGNOSTICOUTPUTANDGRAPHICS
e CONVERGENCEHISTORYOF OBJECTIVEFUNCTIONAND
PARAMETERESTIMATES
i COMPARISONOF PRIOR MODEL AND REVISED MODEL TO
DATA USED IN ESTIMATION
e SIGNIFICANCEINDICATORFOR PARAMETER ESTIMATES
I CORRELATIONMATRIX OF REVISED PARAMETER ESTIMATES
202
- MOVER I I -
MODELING AND PARAMETER ESTIMATION CAPABILITIES
MOVER II has been structured to allow the verification of general dynamic
systems. Lumped parameter models can be input by providing the
equation(s) of motion for simple elements and/or components; this
facilitates the analysis of discrete springs, dampers and simple
components. Complex structural/mechanical models can be verified by
inputting either a finite element representation (i.e., mass, damping,
stiffness matrices) or by a modal representation (i.e., generalized mass,
damping, stiffness). Flnally, complex dynamic systems can be synthesized
from combinations of lumped, finite element and modal models through the
applicatlon of displacement constraints between individual components and
subassemblies.
MOVER II has the capability of updating initial parameter estimates
associated with lumped, modal and finite element models. In addition,
submatrix scaling parameters can be estimated rather than individual
finite element parameters. The submatrix scaling parameters are capable
of increasing or decreasing the overall mass and stiffness of selected
components and/or subassemblies. This step makes the analysis of large
problems more tractable by reducing the number of variable parameters,
while at the same time avoiding numerical difficulties associated with
estimation of the individual parameters of small structural elements.
e LUMPEDPARAMETERMODELS
e FINITEELEMENTMODELS
, SUBSTRUCTURING
PARAMETER ESTIMATION -
e DISCRETE PARAMETERS
- LINEARIZEDFINITE ELEMENT PARAMETERS
- LUMPED STIFFNESS,MASS AND DAMPING
e DISTRIBUTEDPARAMETERS
- LINEARIZEDLINKED FINITE ELEMENT PARAMETERS
- SUBMATRIXSCALING COEFFICIENTS
- MODAL MATRIX PARAMETERS
203
- MOVER II -
LUMPED PARAMETER MODELS
The figure below shows an example of a damper component that was
successfully verified using MOVER II. The damper component was modeled as
an axi-symmetric, lumped parameter system with two rotational degrees of
freedom in- and out-of-plane of the paper. The mass of the weight
assembly was accurately measured, and its value was fixed during the
verification process. The rotational damping, CR, and the translational
damping, CL, were then estimated using load cell data acquired from
random input shake tests. The results of the verification process showed
that the prior model was grossly in error and that MOVER II adjusted the
damping parameters to bring the revised model into good agreement with
experimental response measurements.
WrIGHt
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204
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m-- PRIORHOOEL
REVISEDHOOEL
o TESTDATA
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I I I I I I
I I !
I 0 20 50 ! O0
O1HENSIONLESSFREQUENCY
- MOVER -
FINITE ELEMENT/MODAL MODELS
The figure below shows a cantilevered column, fixed at one end,
constrained by a spring at the opposite end, with a pendulum damper
assembly (previously verified). Transfer function data acquired during
slngle-point random and sine testing were used to verify both a finite
element and modal representation of the column assembly. Submatrix
scaling parameters were used to update prior estimates of stiffness and
mass properties of three distinct sections of the assembly, as well as the
generalized mass and stiffness of the first two column bending modes• The
results of this verification effort were successful at both the finite
element and modal level as demonstrated by the improved correlation
between revised model frequency response and experimental test response.
UA%_qlA*q/_X',,'/A%%
K1
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- -
10"2:i ---PRIOR XODEL _ "
:' _ REVISEDMOOEL r
i 0 TESTDATA
10-3--, .............................. ,............................ , ................. ,........... ,......... , ....... ,-
s ].o 20 3o 40 so 60
D_._s zo_Ess ruqu_
205
- MOVER II-
SUBSTRUCTURED MODELS
MOVER II's real strength lies in its ability to synthesize complex dynamic
systems from component and subassembly models. As demonstrated in the
figure below, a complex model of rotating machinery can be synthesized by
combining lumped, modal and finite element models. In terms of model
verification, MOVER II can first be used to verify component and
subassembly models, thereby reducing verification efforts at the system
level. Note that the damper component and column assembly were previously
verified, allowing their parameters to be fixed during verification of the
system. To construct the system dynamic model, the spinning rotor is
attached to a modal representative of the case by lumped parameter models
of the upper and lower suspensions. The column assembly is attached to
.the top of the casing, and a modal model of the case Is attached to ground
by a lumped model representing the support mount. This synthesis is
accomplished through application of displacement constraints. Once
constructed, system parameters (including lumped, modal, and/or finite
element parameters) may be updated using the submatrix scaling option.
l
H r'_' l"r"
_T
206
- MOVERI I -
DATA REQUIREMENTS
HOVER II requires the mass, damping and stiffness matrices for component
and subassembly models. These can be derived from finite element models,
lumped models, or from reduced modal models. The user can then synthesize
the complete dynamic system by defining physical coordinates and supplying
appropriate displacement constraints between components and
subassemblies. To perform Bayesian parameter estimation, submatrix
scaling parameters to be updated must be defined and initial estimates of
their values assigned, along with confidence in those estimates. In
addition, the force distribution used during testing must also be
reflected in the model.
HOVER II updates parameter estimates based on experimentally obtained
Frequency Response Functions (FRF). The user must therefore supply
amplitude and phase data at discrete test frequencies for comparison with
model estimates. In addition, the user must input the confidence
associated with the FRF; these can be estimated from coherence data
obtained from time series analysis of the vibration data.
MODEL --
TEST --
• SUBSTRUCTUREMASS,DAMPING,
STIFFNESSMATRICES
o FORCEDISTRIBUTION
o SUBSTRUCTURECONNECTIVITY
• INITIALPARAMETERVALUESAND
CONFIDENCESTIMATES
• COMPLEXFREQUENCYRESPONSE
FUNCTIONS(AMPL/PHASE)
o CONFIDENCELEVELON FRF (COHERENCE)
207
- MOVERII -
COMPUTATIONAL TOOLS
MOVER II incorporates several features which facilitate the analysis and
model verification of complex structural/mechanical dynamic systems. To
accommodate dynamic systems that may contain heavy damping or asymmetric
damping matrices, the equations of motion are handled internally in
first-order form. A complex elgensolver is then used to extract the
complex modes; the problem size can then be reduced by usinff MOVER II's
modal truncation option. During the parameter estimation phase of the
analysis, sensitivity calculations (response changes due to parameter
perturbations) are performed closed-form using eignevalue/eigenvector
derivatives calculated internally. These sensitivity calculations feed
into a Bayesian estimator which compares analytical FRF response/parameter
confidence with experimental FRF response/confidence to update critical
modellng parameter estimates. The Bayesian estimator allows quantitative
confidence levels to be assigned to revised parameter estimates and
experimental data to be processed sequentially.
e FIRST-ORDER EQUATION FORMULATION
(ASYMMETRICM, C, K)
o COMPLEX EIGENSOLVER
e CLOSED-FORM SENSITIVITY CALCULATIONS
e MODAL TRUNCATION
e BAYESIAN ESTIMATOR
e SEQUENTIAL DATA PROCESSING
208
- MOVERII -
PRINTEDOUTPUT
MOVER II allows the user to obtain varlous types of printed output. To
aid during initial problem setup, intermediate calculations are available
to the user for assessing (I) Model generation, (2) Modal extraction, (3)
Sensitivity calculation, (4) Response calculations, and (5) Bayesian
estimation. During normal execution, MOVER II outputs during each
estimation cycle updated (1) Eigenvalues/Eigenvectors, (2) Complex
frequency response, (3) RMS response variation (model vs. data), (4)
Original, prior and revised parameter estimates. When MOVER II has
converged on a solution, a revised parameter convariance matrix is printed
which allows the user to assess the confidence in the updated parameter
values.
INITIALOUTPUT
OUTPUTFOR
EACH ITERATION
FINALOUTPUT
{, ECHOPRINTOF INPUTDATA
e EIGENVALUES/EIGENVECTORS
, COMPLEXFREQUENCYRESPONSE
, RMS RESPONSEVARIATION
(CALC'D VS, MEAS'D)
e ORIGINAL,PRIOR,REVISED
PARAMETERESTIMATES
[, REVISEDPARAMETERCOVARIANCE
MATRIX
209
MOVERII
process.
- MOVER II -
GRAPHICAL OUTPUT
includes a graphics package to facilitate the model verification
The package allows the user to obtain the following x-y plots:
Amplitude and phase of complex frequency response as functions of
frequency; plots of both prior model and revised model frequency
response as well as measured frequency response, are overlaid on
the same graph.
FREQUENCY RESPONSE COMPARISONS
eL.
+180
-180
10°
I I I
--- Prior Model
--Revised Model
o Data
r _ ' "
I
%%k .
..-1
L, -1
_ 10
e_
10-2
"s / f_
0 0
i I'o lo 30
DL_.NSIONLESS FREQUENCY
210
- MOVER I I -
GRAPHICAL OUTPUT (CONTINUED)
MOVER II also plots -
Sensitivity of response to selected parameters; plots of
perturbed frequency response amplitudes as a function of
frequency for individually varied parameters, showing comparisons
with nominal frequency response amplitude and measured data.
SENSITIVITY PLOTS
(Ampl w.r.t. Parameters M3 and &K)
i00 _
U
R
N lo-;
i i _ J,
Original Model
Perturbed Model
iA o Data
FAo.
|. I
20
_32_l_ION LESS FREQUENCY
(a) Parameter M3
• I
100
e_
io-._
_a
• ........ I ..... I ....... I
o
//- %_
l -!8 _ ib 2o
DIMENSIONLESS FREOUENCY
(b) Parameter AK
211
- MOVER II -
GRAPHICAL OUTPUT (CONTINUED)
Additional x-y plots provided by MOVER II include:
• History of parameter adjustments as a function of lterative
Bayesian estimation cycle showing convergence characteristics of
each estimated parameter.
m Statistical significance of individual parameter estimates as a
function of their variation from intial parameter estimates.
These graphics greatly facilitate the model verification procedure and are
particularly useful during the initial and intermediate phases of ground
testing, model verification and structural modification.
CYCLE # PARMVALUE
1 l.OOOOOE+00
Z 7.68081E-01
3 7.98866E-01
4 8.57914E-01
5 8.46938E-01
6 8.52537E-01
*** MODE NO. 2 GENERALIZED MASS (GAMMA2) ***
0.0 1.0 2.0
I ......... I ......... I ......... I ......... I ......... I ......... I ......... I .........
!
i
I
°°o..°.°.°°.°.o° ..... . ..... . ................. .°.°.°°°..°..°..o°.°.°. .... .°°°°.°°°
I i I I I i i I I
0.0 I .0 Z.O
PARAMETER ESTIMATE STATISTICAL SIGNIFICANCE
-4 ................... 2 ........ - .......... 0-= ................. 2 ............... ---=4
PARAMETER 1 ____l_______________I__________________III_______________I_______________I_______
PARAMETER 2 ________________--__-__________I_III______________I_I_I__II_____I_I___I___I___I__
PARAMETER 3 ______I_______I____________________________I___I_I__I_I____I_I___I____I_II__II___
PARAMETER 4 ______________________________________I__________________________________________
PARAMETER 5 llllllIllllllllIllllllllIlllllX ............. 0 ............. XllllllllIIIlllIlllllll
-4===-- .............. :' ................... 0 ................... Z ....... -===-- ...... 4
212
- MOVER II -
CONCLUSIONS
HOVER II has been used extensively and successfully over a period of
several years to verify the structural/mechanical models of civil,
mechanical and aerospace systems. Experience has shown the importance of
using both component and system level test data in a structured
verification effort. The techniques utilized in MOVER II should flnd
further appllcatlon in the space program. The control of large structures
in space will require accurate structural models for maneuvering,
pointing, and shape maintenance. These models will be verified to the
maximum extent possible prior to launch, but will most likely require
final adjustment to reflect as-built conditions in a zero-g environment.
It is apparent that some form of model verification techniques will play
an important role in the successful deployment of these large systems.
1)
2)
3)
MOVER II IS AN OUTGROWTHOF A SERIESOF MODEL
VERIFICATIONCOMPUTERPROGRAMSORIGINALLYFUNDED
BY NASA/MSFCBEGINNINGIN 1971
MOVER II HAS BEEN USEDEXTENSIVELYTO VERIFYHIGH-SPEED
ROTATINGMACHINERYUSINGA SUBSTRUCTURINGAPPROACHFOR
MODELVERIFICATIONAS WELLAS MODELLINGITSELF
A SIMILARSUBSTRUCTUREMODELINGAND MODELVERIFICATION
APPROACHISENVISIONEDFOR LARGESPACESTRUCTURES
213


A computer program for model verification of dynamic systems

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