static and dynamic model update of an inflatable ......lucas g. horta and mercedes c. reaves...

Langley Research Center

Static and Dynamic Model Update of an Inflatable/Rigidizable Torus Structure

(Work In Progress)

Lucas G. Hortaand Mercedes C. Reaves

Structural Dynamics BranchNASA Langley Research Center

FEMCI Workshop 2005May 5, 2005


Background• The TSU* Hexapod is a generic test bed that incorporates design features of structures that can be packed for launch and deployed in space

•Inflatable/rigidizable structures can be inflated to more than 12 times their packaged size enabling new space mission scenarios

•However, new fabrication techniques also bring new modeling challenges

*TSU= Tennessee State University


Objective and MotivationObjective-To develop a mathematical and computational procedure to reconcile differences between finite element models and data from static and dynamic tests

Motivation- All missions envisioned for inflatable and rigidizable systems will require state of the art controls and accurate analytical models. In the Hexapod case, the initial model missed many important modes

10 20 30 40 50 60 70 80 90 100 11010

-5

10-4

10-3

10-2

10-1

Freq. (Hz)M

ag

Scale Factor = 0.11241 Sensor No. 12 Shaker 2

TestNASTRAN

10 20 30 40 50 60 70 80 90 100 110-150

-100

-50

0

50

100

Freq. (Hz)

Pha

se (

deg)

Initial ModelShaker No. 2


Approach•FEM developed using commercial tools

•Static test results used to update stiffness values

•Dynamic test results used to update mass distribution

•Probabilistic assessment used to compute most likely set of parameters

•Update parameters computed via nonlinear optimization (genetic and gradient based)

•Computational tools based on MATLAB

•System ID using the Eigensystem Realization Algorithm

•Incremental update of components starting with torus


Model Update Procedure

Develop baseline

finite element model Select

parameters for update

Define parameter bounds & probability

distributionCompute output

probability & sensitivity values

Reduce parameter set using sensitivity and

probability results Solve optimization for

updated parameters &

probability


Computational Framework

NASTRANStatic

Dynamic

Bulk DataFile

Output DataFile

MATLABOptimizationProbabilitySensitivitySystem ID

External Inputs

1- Parameter selection and prob. distribution

2- Experimental data


Torus Description and NomenclatureUrethane Joint (typ.)

Tube (typ.)O.D. 0.0181 m

1.858 m Joint flanget = 0.00508 m Inner joint

t = 0.0063 m

Outer jointt = 0.0032 m

Tube (typ.)t = 0.00042 m


Main Sources of Modeling Uncertainties

•Fabrication irregularities due to materials and fabrication methods (irregular cross-section, irregular geometry, etc)

•Unknown stiffness of adhesive bonded joints

•Composite material property uncertainties, “effective single ply” and rule of mixture approximations


STATIC TEST RESULTS


Static Test Configuration

Support 3

Point load

AluminumBracket

Support 1

Support 2

SteelBlock

Torus static test set-up Instrumentation set-up

Retro-reflectiveTarget

Laser displacement sensor


Input Load and Sensor Location for Static Tests

Support 1

Support 2Support 3

Loading Point

1 2 34

56

7

8

910

1112131415

1617

18

19

20

2122

2324


Static Test Parameters Selected for Update

1. Torus tube thickness

2. Urethane joint:- Inner joint thickness- Outer joint thickness- Joint flange thickness

3. Torus tube orthotropic material properties:E1, E2

4. Urethane joint modulus of elasticity E


Output Probability StatementHow probable is it to predict the measured

output?

Linear Torus Solution

Probability Bands

w range

w

v v range

Output No. 1Output No. 2

Updated parameters

Sample Space 300 points

Displacement Results: Test, Baseline, and Updated Model

Measurement locations

Target 1Z = -4.54 mm

Load =42.1 N

Support 1

Support 2

Support 3

Torus structure displacement under load

-6

-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 6 7 8 9 10 11 12 14 15 16 17 18 19 20 22 23 24

Measurement location

BaselineUpdateUpdate GenAverage Test

Ver

tical

Dis

plac

emen

t (m

m)

Torus static test results

σ/µ=1.1 σ/µ=0.01

Support 1

Support 2Support 3

Loading Point

1 2 34

56

78

910

111213141516

1718

1920

2122

23 24


Static Update Summary

14.1-13.90.008730.011570.011680.00860.01016Flange thickness

16.920.00.005270.005070.007610.005070.00634 Inner jointthickness

-11.019.60.003520.003790.00380.002530.00317Outer jointthickness

9.4130.00039120.0003760.0004960.00030240.000432Tubethickness

-6.103.21E+093.03E+093.33E+092.73E+093.03E+09Joint E

5.405.83E+106.16E+106.77E+105.5E+106.16E+10Tube E1,E2

% ChangeGenetic

% ChangeFMIN

OptimumGenetic

OptimumFMIN

UpperBound

LowerBoundBaselineParameters


Dynamic Test Results


Dynamic Test Configuration

Force gageSpring/cablesuspension

Suspension 1

Suspension 2

Laser Vibrometer

Shaker

Suspension 3

Retro-reflective

Target (typ.)


Shaker and Sensor Locations for Dynamic Tests

Suspension 1Shaker 1Z

Suspension 2Shaker 2Z

C

CC

C

C

C

C

C

C

C

C

C

1416

17

1

54

2

7

8

11

10

13 15

18

3

6

9

12

Shaker4 XY

Suspension 3


Sample Set of Identification Results (Drive Point 1 & 2)

0 20 40 60 80 100 12010

-5

100

105 Predicted (- -) and Real FRFs for input No. 1 and output No. 11

Frequency (Hz)

Am

plitu

de

0 20 40 60 80 100 120-200

-100

0

100

200

Frequency (Hz)

Pha

se (

deg)

0 20 40 60 80 100 12010

-4

10-2

100

102 Predicted (- -) and Real FRFs for input No. 2 and output No. 17

Frequency (Hz)A

mpl

itude

0 20 40 60 80 100 120-200

-100

0

100

200

Frequency (Hz)

Pha

se (

deg)

Shaker No. 1

Shaker No. 2


Principal Values for Experimental Frequency Response Functions

20 40 60 80 10010

-2

10-1

100

Frequency (Hz)

Pri

nci

pal

Va

lue

s

1279.81433.81194.8955.8Joint 7 density

990.761433.81194.8955.8Joint 8 density

1063.51433.81194.8955.8Joint 10 density

1150.51433.81194.8955.8Joint 11 density

1239.21433.81194.8955.8Joint 13 density

1433.81433.81194.8955.8Joint 14 density

1080.21433.81194.8955.8Joint 16 density

1231.41433.81194.8955.8Joint 17 density

10931433.81194.8955.8Joint 1 density

980.591433.81194.8955.8Joint 2 density

996.081433.81194.8955.5Joint 4 density

1204.61433.81194.8955.5Joint 5 density

1770.42200.81834.01467.2Torus tube density

2400.43502.22918.52334.8Spring 3

3169.83502.22918.52334.8Spring 2

2752.93502.22918.52334.8Spring 1

Optimum ValueUpper BoundNominal ValueLower BoundParameter^

Dynamic Update Summary*

* list of parameters not based on statistical analysis


Principal Component Comparison Test/Nominal/Updated

100

101

102

10-3

10-2

10-1

100

Principal Value := 1

Mag

Frequency (Hz)

TestUpdatedNominal

100

101

102

10-3

10-2

10-1

Principal Value := 3

Mag

Frequency (Hz)

TestUpdatedNominal

Maximum Principal ValueMaximum Principal Value Minimum Principal Value


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1.123

1.123

1.228

4.138

4.138

4.338

13.734

13.734

20.798

20.803

38.463

38.969

52.754

52.785

68.307

68.310

86.639

86.673

92.301

92.302

101.684

113.262

113.295

123.661 4.3

6

4.4

3

4.5

5

4.7

5

14.1

6

14.

25

14.

33

14.

51

14.

54

14.

58

18.

23

36.

94

37.

17

49.

75

85.3

4

91.1

4

ERA Identified Modes

Ana

lysi

s M

odes

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Orthogonality of Test/Analysis Modes

Animation ofAnalysis Mode

Animation of Test Mode


Work To Be Done• Establish repeatability of test data• Complete probabilistic assessment of dynamic FRF to verify

parameter selection• Compute updated parameters for dynamic case using non-

gradient based optimizer • Verify computational accuracy with refined FEM• Implement error localization algorithm to examine potential FEM

problem areas• Compute Modal Assurance Criterion using reduced mass matrix• Re-test with increased sensor count to improve spatial

resolution for test and analysis modes• Refine system ID results to improve areas near FRF zeros


Concluding Remarks•Computational procedure using MATLAB in place•Initial updates completed using static and dynamic tests results

•Updated solution for static case is in good agreement with test

•Selected parameters for static analysis showed low output probability values when used to predict observed solution

•Two step approach using output probabilities followed by optimization provides good physical insight into the problem

•Dynamic test and analysis results need to be re-visited

•Procedure computationally intensive but well suited for multi-processor systems

static and dynamic model update of an inflatable ......lucas g. horta and mercedes c. reaves...

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