Brincker_1

8/12/2019 Brincker_1

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Recent advances of Operational ModalRecent advances of Operational ModalAnalysis and applications in StructuralAnalysis and applications in Structural

Health MonitoringHealth Monitoring

Part one (OMA)Part one (OMA)Rune Brincker


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MotivationsMotivations

2

The mechanical engineer The civil engineer

SISO

MIMO

ODS

SISO

MIMO

ODS

OMAOMA


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Classical Modal AnalysisClassical Modal Analysis

3

Input

Output Signal

Time(Excitation) - Input

Working : Input : Input : FFT Analyzer

0 40m 80m 120m 160m 200m 240m

-200

-100

0

100

200

[s]

[N]

Time(Excitation) - Input


0 40m 80m 120m 160m 200m 240m

-200

-100

0

100

200

[s]

[N]

Time(Response) - Input


0 40m 80m 120m 160m 200m 240m

-80

-40

0

40

80

[s]

[m/s]

Time(Response) - Input


0 40m 80m 120m 160m 200m 240m

-80

-40

0

40

80

[s]

[m/s]

FFT

FFTInput Signal

Frequency Response H1(Response,Excitation) - Input (Magnitude)


0 400 800 1,2k 1,6k 2k 2,4k 2,8k 3,2k

10m

1

100

[Hz]

[(m/s)/N]

Frequency Response H1(Response,Excitation) - Input (Magnitude)


0 400 800 1,2k 1,6k 2k 2,4k 2,8k 3,2k

10m

1

100

[Hz]

[(m/s)/N]

Output Spectrum

Small structures

- easily tested

Artificial input provided no problemOutput


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Thinking of Civil EngineersThinking of Civil Engineers

4

Larger structures More slender structures Bigger loads

longer service New materials

Codes are getting bigger and bigger

Buildings are falling down

Even civil enginners NEEDS to know reallity

Cheaper and more accurate equipment

September 11, 1916.

Quebec Bridge (Canada)

*Images from http://www.engineeringcivil.com/theory/civil-engineering-disasters

December 15, 1967.

Silver Bridge (USA)

March 17, 1945.

Ludendor ff Bridge (Remagen, Germany)November 7, 2005.

(Almunecar, Spain)


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Idea of operatinal modal analysisIdea of operatinal modal analysis

5

MeasuredResponses

Stationary

Zero MeanGaussian

White Noise

Excitation Filter

(linear,

time-variant)

Structural System

(linear, time-

invariant)

Unknown excitation

forces

Combined System

Loading modes

Time-variant

Broad banded

Structural modes

Time-invariant

Narrow banded


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History on OMAHistory on OMA

6

Bendat & many others: Basic Frequency Domain

Andreas Felber PhD thesis

=

NNN

N

GG

GGGGG

L

OM

K

1

2221

11211

G


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Time domain techniqusTime domain techniqus

7

Sam Ibrahim and the Time Domain

Random Decrement Technique for Identification of Structures, J.

Spacecraft and Rockets, Vol. 14, No. 11, 1977

Sam Ibrahim and the Time Domain

Random Decrement Technique for Identification of Structures, J.

Spacecraft and Rockets, Vol. 14, No. 11, 1977

Henry Cole was looking for...

A simple and direct method for translating the time histori into a form

meaningful to the observer (1971)

Henry Cole was looking for...

A simple and direct method for translating the time histori into a form

meaningful to the observer (1971)

Vandiver, Brincker and Assmussen and the Random

Decrement (1982-1990)

Vandiver, Brincker and Assmussen and the Random

Decrement (1982-1990)


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0 2 4 6 8 10 12-5

0

5

10

15

20

25

30

SystemO

rder

Frequency(Hz)

20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2

2.5

3

3.5Singular values of the system Hankel Matrix

index number of the singular values = 2*Model Order

IdentificationIdentification

8

PRCEH. Vold et al et al,1982

PRCEH. Vold et al et al,1982

ERAJuang and Pappa, 1985

ERAJuang and Pappa, 1985

MIMOMIMO

Could be used for OMA

Use RDD or correlation functions

Could be used for OMA

Use RDD or correlation functions

Developed on the basis of traditional

modal testing

Developed on the basis of traditionalmodal testing

But it did not (really) happenBut it did not (really) happen

Reasons: mode selection problem, no software...

Civil engineers were still sleeping...

Reasons: mode selection problem, no software...

Civil engineers were still sleeping...


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Begining of aplicationsBegining of aplications

9

First real test reported in

1993

Felber uses

the frequency domainsuccessfully

Felber uses

the frequency domainsuccessfully


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ApplicationsApplications

10

A.J.Felber & R.CantieniIntroduction of a new Ambient Vibration Testing System, EMPA,

1993-1996.

A.J.Felber & R.CantieniIntroduction of a new Ambient Vibration Testing System, EMPA,

1993-1996.

C.E.Ventura, A,J, Felber, S.F.StiemerDetermination of the dynamic characteristics of the colquiz Bridgebe full-scale testing, 1992.

C.E.Ventura, A,J, Felber, S.F.StiemerDetermination of the dynamic characteristics of the colquiz Bridge

be full-scale testing, 1992.

Tom Carne 1986Called it NExT= Correlation

functions+ Polyrefernce and

ERA

Tom Carne 1986Called it NExT= Correlation

functions+ Polyrefernce and

ERA


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ApplicationsApplications

11

Basic freq domain

SSI/ERA?

Updating

M.Hoeklie, O.E. HansteenMeasured and Predicted Dynamic Behavior

of the Gulfaks A Platform, 1988.

Basic frequency domain

Random decrement + Polyreference

J.C.Asmussen, R.Brincker, A.RytterAmbient modal testing of the vestvej bridge using random

decrement, 1998.


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Stochastic Subspace Identification: revival ofStochastic Subspace Identification: revival of

the time domainthe time domain

12

BUT: It sounds like black magic; Kalman gain matrix??? Projection of the Hankel matrix???

If you just need modal parameters forget about the Kalman gain matrix !

Bart de Moor and Overshees book in 1996 Data driven SSIBart de Moor and Overshees book in 1996 Data driven SSI

Very much like Random Decrement and time domain solved by SVD???


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Frequency domain decomposition: revival of theFrequency domain decomposition: revival of the

frequency domainfrequency domain

13

=

= UU

GGG

GGG

GGG

nnnnn

n

n

0

00

00

2

1

21

22221

11211

OMM

L

L

L

MOMM

L

L

G

( ) { } ( ) ( ) ( ) =

=

++ =

=

N

k

N

ik

jiji

kN

n

j

kn

i

nkjiji ekRGyykNyyEkR 0

2

,,

1

0

*

,

1

,

PSD Mag. Example SVD of PSD Matrix Decoupled Modes

Modal coordinate

auto spectral density( )1


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OverviewOverview

15

Reliable frequency domain techniques

Reliable time domain techniques

Using several data sets mode shapes

Many applications

Still problems: mode shape scaling... software, harmonics....

Reliable frequency domain techniques

Reliable time domain techniques

Using several data sets mode shapes

Many applications

Still problems: mode shape scaling... software, harmonics....

What do we have (around year 2000)?What do we have (around year 2000)?


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Scaling mode shapes (Mass change method)Scaling mode shapes (Mass change method)

16

Un-scaled mode shapes 1=T

=

1=MTScaled mode shapes

Scaling factor

Parloo et. al

MT

2=

Nomenclature :

Method:

Classical equation

KM =21

KM)(M =+

2

2

22

22

21 )( M 2M =

22221

MT22

=

Make a mass change

Subtraction

Solve forApproximation

Solve for

M

T2

2

22

21

=

Brincker et. al

1 2


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Approximation errorsApproximation errors

17

Simulation study

=

=

21

1..

.21

12

1

..

10

.01

km KM

20 DOF chainlike system

Mass change 0-20 % of DOF mass

Mathematical Model

22

2

2

1


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Approximation errorsApproximation errors

18

Errors should vanish for mass changes in increasing DOFsErrors should vanish for mass changes in increasing DOFs

Improved equationImproved equationM

T22

22

21

=Parloo equationParloo equation

MT

2=


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Error reductionError reduction

19

MM =

How to do it!

Do good ID and make large shift

Use improved equation

Do good ID and use many DOFs

Distribute mass change

How to do it!

Do good ID and make large shift

Use improved equation

Do good ID and use many DOFs

Distribute mass change

Error types

Random Error on frequency shift

Linearization error

Random Error on mode shape

Mode shape change error

Error types

Random Error on frequency shift

Linearization error

Random Error on mode shape

Mode shape change error

How can it be done (in an easy way) ?

Make a mass change and estimate the frequency shift

Easy: Shift masses around while using several data sets

How can it be done (in an easy way) ?

Make a mass change and estimate the frequency shift

Easy: Shift masses around while using several data sets

What is the accuracy ?

In a lausy test the typical uncertainty will be

around 10-20 %

In a well prepared test the typical uncertainty will

be around 2-5 %

What is the accuracy ?

In a lausy test the typical uncertainty will be

around 10-20 %

In a well prepared test the typical uncertainty will

be around 2-5 %


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Harmonic removalHarmonic removal

20

WithHarmoni

c

W

ithoutHarmonic

Harmonic Removal

Algori thm


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21

( )( )2

2

2

22

1,|

==

x

exfy

( ) ( ){ }( ) ( ).sin.sin

sincos1|

1

1

Arc

ax

axfy

=

==

( ) ( )[ ] 3,|

4

4

=

xE

x

( ) 5.1. measmedian

Structural Modes:

Harmonics:


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22

HarmonicRem

oval

Algorithm

HarmonicRemoval

Algorithm

Excluding Harmonic

Including Harmonic

Damping RatioNatural Frequency


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Known Harmonic RemovalKnown Harmonic Removal

23

* Notation adopted from P.Mohanty & D.J.Riexen

P.Mohanty & D.J.Riexen (2003-2005)

Modifications of Time domain Algorithms for Removing known Harmonic components


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Known Harmonic RemovalKnown Harmonic Removal

24


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[ ]is

f

f

ff

d

1

0f

1f 2f

f

Automated OMAAutomated OMA

25

Finding modes by FDDFinding modes by FDD

Modal coherenceModal coherence

Modal domainModal domain

Harmonics RemovalHarmonics Removal

FDD automatedFDD automated


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Modal CoherenceModal Coherence

26

)()()( 01101 fffd T

uu=

0)()( 101 =ffE T

uu NffVar T /1)()( 101 =uu

Discriminator function:

Low modal coherence: Noise

High modal coherence: Modal dominance

Random vectors:

Requirements:

. MAC level

. AveragingNumber

Requirements:

. MAC level

. AveragingNumber


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Modal DomainModal Domain

27

The modal domain is found as the Region around the peak whereThe modal domain is found as the Region around the peak where

)()()( 0112 fffd T

uu=

22 d

Discriminator function:

Mode property defined for all modes

Defines the frequency region dominated by

the mode

[ ]is

f

f

ff

d

1

0f

0f

1f 2f

f

Requirements:

MAC levelRequirements:

MAC level


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Example: Plate with HarmonicsExample: Plate with Harmonics

28


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Example: Heritage BuildingExample: Heritage Building

29


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Example: Z24 Highway BridgeExample: Z24 Highway Bridge

30


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ConclusionsConclusions

31

Valuable tools:Modal Coherence

Modal Domain

Harmonic discrimination

Dynamic headroom etc.

Important to note:It works..

Easier OMAApplications in health monitoring

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