nvh lecture 7: operational modal analysis · time animation – operational deflection shapes ......

Copyright LMS International 1

Marie Curie Graduate School on Vehicle Mechatronics & Dynamics, Leuven, 5-8 February 2013 Bart Peeters

NVH Lecture 7: Operational Modal Analysis

2 copyright LMS International - 2011

Operational Modal Analysis

Why?

Identify models that represent real behaviour

Real operating conditions laboratory conditions Effects due to:

• Non-linearities e.g. car suspension

• Environment Experimental models that give best linear representation

under the relevant operating conditions Practical problems for executing lab-test

Access to the actual structure Problems for applying adequate input forces

• Impossible, difficult • Expensive

Presence of substantial ambient excitation Health monitoring / damage detection: in-situ Make extended use of available data (ODS)

Any public or commercial use requires the agreement of the author.




In-operation testing

Some applications permit the use of Input - output (FRF) data during normal operation

Require special setups for forced excitation • Rotating wing-tip vanes • Electromagnetic bearings • Low-frequency exciters • Drop-weights • Unbalance shakers • Pyrotechnics • Control Surface Input • Servo-drive inputs (robots) • …

Testing complexity Data quality (undesired ambient sources)

Some applications permit simulating in-operation

conditions in I/O (FRF) tests (car suspension…) The normal EMA processes can be followed

© NASA

© EMPA © KUL


In-operation EMA example:

Business jet, wing-vane in-flight excitation

In-flight excitation, 2 wing-tip vanes 9 responses 2 min sine sweep Higher order harmonics Very noisy data

4.00 20.00LinearHz

0.00

0.10

Log

(g/N

)

4.00 20.00LinearHz

Hz-180.00

180.00

Phas

e°

PolyMAX

4.00 20.00Linear

Hz

10.0e-6

1.00

Log

(m/s

2)/N

4.00 20.00LinearHz

Hz

-180.00

180.00

Phas

e°

Hz

0.05

1.00

Ampl

itude

/

Coherence w ing:vvd:+Z/MultipleCoherence back:vde:+Y/Multiple




Majority of applications: use of output-only data

Objective: Identification of modal parameters from output-

only data measured on a structure during standard operation. Eigenfrequency Damping Mode shape

Output-only operational modal analysis = identifying H

Based on Y

Without knowing U

Desired (but unknown) ambient sources: “white” spectrum

What is Operational Modal Analysis? Operational Modal Analysis

The output-only system identification problem

H U Y

Input System Output



The output-only system identification problem

In the remainder, we will focus on output-only methods for in-operation modal analysis. We will refer to this as OMA

Operational Modal Analysis (= operational response modal analysis). In general (papers, software vendors, test procedures), OMA hence implies ―output-

only modal analysis‖

White noise

H U Y

White noise + harmonic Ideal operational excitation

Less ideal operational excitation




Operational Modal Analysis in the presence of rotating machinery

Sweeping harmonics (run-up) Harmonics excite broad frequency band Useful excitation – no filtering! ―End-of-order‖ effects

Fixed (or slowly varying) harmonics Harmonics hamper the identification

process Have to be removed from data

Helico

pte

r in

-flig

ht

data

C

ar

en

gin

e r

un

-up


Direct animation of signals in time

domain

Animation of Structures

Time Animation – Operational Deflection Shapes

Actual deformation as a function of time or frequency Explanation & model through modal analysis

Direct animation of frequency-domain

functions





More than operational deflection shapes

Auto & Cross Powers

Peak picking

Deformation at a chosen frequency line

No damping information

Combination of modes and forced responses

Combination of closely spaced modes

Data reduction through coherence or SVD analysis (Principal Component Analysis)

Phenomena

Modal model Frequency Damping Mode shape (No modal scaling)

Use of system identification methods

Structural characteristics

Separation of closely spaced modes

Root causes

OMA ODS

Vibration problem “root cause” discriminator


OMA as part of an engineering workflow

Wind turbine operational testing

Component testing Classical Modal Analysis Validation of component models

Assembled structure testing Operational Modal Analysis Validation of assembly models

OCT 2 2003

PLOT NO. 2

NODAL SOLUTION

STEP=1

SUB =2

FREQ=32.423

USUM

TOP

RSYS=0

DMX =.065211

SMX =.065211

1

MN

MX

2

MN

MX

3

MN

MX

4

MN

MX

XY

Z

0

.007246

.014491

.021737

.028983

.036228

.043474

.05072

.057965

.065211

X

Y

Z

0

.007246

.014491

.021737

.028983

.036228

.043474

.05072

.057965

.065211

X Y

Z

0

.007246

X

YZ

FE MODEL

EMA MODEL

UPDATED

FE MODEL

Source: Laurent Bonnet, GE Energy

LMS Conference Europe, Nürburg, 2-3 March 2005




0.00 80.00 Hz10.0e-6

0.10

Log

(g/N

)

0.00 80.00 LinearHz

0.00 80.00 Hz-180.00

180.00

Phas

e°

0.00 6.00 s-1.07

0.91

Rea

l(g/

N

)

“Traditional” (IO) modal parameter estimation

Modal model

Inverse

Fourier

transform

Frequency

domain

Time

domain

FRF IRF

n

i i

i

i

i

j

A

j

AH

1*

*

)(

n

i

ii

ii

tA

tAth

1

** ee)(

T T

i i i i i iA Q v l iiiiii j 2* 1,


Stabilization diagram

Try a whole range of model orders Compare modal parameters at current order with

previous order

Stability

: new

: freq

: damp + freq

: part. vector + freq

: all

o

f

d

v

s

n

n

i i

H

ii

i

T

ii

j

lv

j

lvH

1*

*

)(




Stabilization diagram

? PolyMAX ! Model order problem shifted to problem of separating true from computational poles?


Operational

data

Preprocessing operational data

]DFT[window )()( s

k

s yY

Hsss

yy YYS )()()(

P

s

s

yyyy SP

S1

)( )(1

)(

2.00 8.00 Linear

Hz

1.00e-12

10.0e-9

Log

(m2/

s4

)

autopow er_spectr roof:1:+Z / roof:1:+Zcrosspow er_spect roof:1:+X / roof:1:+Z

2.00 8.00 LinearHz

2.00 8.00 Hz

-180.00

180.00

Phas

e°

ky

Periodogram (“classical”)

Periodogram

with

Hanning

window

1

0

1 N

k

Tkiki yy

NR

}],...,2/{DFT[window)( 0 Lyy RRS

2.00 8.00 Linear

Hz

1.00e-12

1.00e-9

Log

( m/s

2 )2

AutoPow er roof:1:+ZCrossPow er roof:1:+X/roof:1:+Z

2.00 8.00 LinearHz

2.00 8.00 Hz-180.00

180.00

Phas

e°

}],...,,...,{DFT[window)( 0 LLyy RRRS

Correlogram (“half spectra”)

Correlogram

with

exponential

window




Why “half spectra”?

Lower order models

Exponential window Reduces the effect of leakage Reduces the influence of the higher

time lags having a larger variance

Compatible with the modal model ( Hanning window with biased damping)

Hyyyyyy SSS )()()(

n

i i

ii

i

iiyy

j

gv

j

gvjS

1*

**

)(

0.00 52.00 s-10e-9

10e-9

Rea

l( m

/s2 )2

Time roof:1:+X Unw indow edTime roof:1:+X

0.00 10.00 LinearHz

-140

-90

dB( m/s

2 )2

AutoPow er roof:1:+X Unw indow edAutoPow er roof:1:+X

0.00 10.00 LinearHz

0.00 10.00 Hz-180

180

Pha

se°


No window

Operational Modal Parameter Estimation

Exponential Window

10% exponential window 1% exponential window




Overview of OMA methods – frequency domain

Basically, all EMA methods that operate on FRFs can be transferred to OMA methods operating on auto- and cross-spectra

FRF (EMA) Auto/cross spectra (OMA) Methods evolution:

0.00 80.00 Hz

-90

-35

dB(g/N

)

-0.13 0.13 Real((m/s2)/N)

-0.05

0.21

Imag

((m/s

2)/N

)

-0.05

0.21

Imag

((m/s

2)/N

)

0.00 50.00 Hz

1:1

FRF moto:15:+Z moto:15:+ZFRF moto:15:+Z / moto:15:+Z

Method Features Non-parametric

Peak picking / ODS Subjective No damping

SVD-based PCA, CMIF, FDD Can be complimented by simple SDOF curve-fitters

Still picking peaks (subjective / difficult) Better than PP for closely spaced modes SDOF curve-fitting

Parametric PolyMAX Clear stabilization Highly automatic

(Polyreference) Maximum Likelihood

Stochastic (incl. noise information) Iterative


0.00 52.00 s-10e-9

10e-9

Rea

l( m

/s2 )2

Time roof:1:+X Unw indow edTime roof:1:+X

Overview of OMA methods – time domain

Basically, all EMA methods that operate on IRFs can be transferred to OMA methods operating on auto- and cross-correlations

IRF (EMA) Auto/cross correlations (OMA) Methods evolution:

Method Features Output time histories

Stochastic time series modelling; e.g. ARMA models

Not practical for OMA No convincing cases in literature

Subspace identification (BR, CVA, …: differences very subtle)

Successful applications Limited number of samples / channels, large computation time

Output correlations

Polyreference LSCE Fast

Subspace identification Data reduction step (time series correlations) Relatively fast

0.00 6.00 s

-1.00

1.00

Rea

l(g/

N

)

Data reduction w/o loss of information




Case studies

Aerospace engineering Civil Engineering Automotive Engineering


Test – FEM correlation

Frequency correlations within 5%

FEM updating with ―delta stick‖ approach




Next: aero-elastic simulation and in-flight flutter testing

FE Model Test Model (GVT) Aerodyn. Panel Model Physical prototype

0)()()()( xFtKxtxCtxM a

Traditional FEM, GVT-updated FEM, or direct GVT

Aerodynamic panel method

Due to presence of aero-dynamic term, modes of structural

system are changing with airspeed and altitude

Flutter analysis = assessing evolution of modes (zero-crossing

of damping value)


Flight flutter testing – turbulence excitation

s

Rea

l(m

/s2 )

0.00 3.20 LinearHz

Am

plitu

deg2

0.00 3.20 LinearHz

Hz-180.00

180.00

°

Da

mp

ing

Airspeed

Flutter

Telemetry link

Background Testing Analysis

Context: FLITE 2 research project with Airbus France, Dassault Aviation, PZL, LAE, VUB,

KUL, AGH, UMAN, INRIA, SOPEMEA, ONERA, LMS




Application to aircraft flight test data

Generally only a few sensors


A380 in-flight tests

But sometimes a bit more: 150 accelerometers




OMA – PolyMAX

0.71 6.05Linear

Hz

dB

Sum Crosspow er SUMSynthesized Crosspow er SUM0.71 6.05Linear

Hz

Hz-180.00

180.00

Phas

e°


In-flight OMA mode shape (1/4)






Conclusions

In-flight testing

OMA: some important flutter-critical modes not excited EMA: some modes mainly excited by the turbulences

may not be identified Conclusion: beneficial to use artificial excitation, but

data analysed with stochastic methods that also take into account the unknown excitation

Airbus flight test team evaluated LMS Test.Lab using large-aircraft data

―We actually achieved better results using operational techniques than with classical EMA. We found more modes. The synthesis was better with higher correlation and fewer errors. And the in-flight mode shapes looked much nicer!‖

―We found that the exponential window, which allowed for cross-correlation calculations was a good de-noising tool for our in-flight data.‖

True Air Speed(knots)

Altitude (feet)

40,000

30,000

20,000

10,000

100 200 300 400 500

MACH 0.95

MACH 0.90

MACH 0.85

True Air Speed(knots)

Altitude (feet)

40,000

30,000

20,000

10,000

100 200 300 400 500

MACH 0.95

MACH 0.90

MACH 0.85




OMA has its roots in Civil Engineering

7 November 1940 – Tacoma (USA) 10 June 2000 – London (UK)


Applications: civil engineering

Design verification FE model correlation / updating Identification of damping properties Indirect identification of cable forces Structural health monitoring Verify effectiveness of rehabilitation

0.30 3.00 LinearHz

-130.00

-100.00

dBg2

Deck:117:+ZSynthesized Crosspow er Deck:117:+Z

0.30 3.00 LinearHz

0.30 3.00 Hz-180.00

180.00

°

Guadiana Bridge

Millennium Bridge

Øresund Bridge




23/11/2002: Bradford City – Sheffield United: 0 – 5

Data acquisition: 4 h Sampled at 80 Hz (down-sampled to 20 Hz) Sliding RMS value ( — )

1000 samples, 50% overlap

0.00 15000.00 s-0.02

0.02 R

eal

(m/s

2 )

-0.20

0.20

Rea

l

(m/s

2 )

F time_record roof:1:+X / Root Mean SquareB time_record roof:1:+X

Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Half time Empty Filling Seated Emptying

End of game


Continuous monitoring of the

Bradford and Bingley Stadium

Data: Paul Reynolds, Sheffield University




Ambient Vibration Testing of the Millau Viaduct


Millau Viaduct – LMS Test.Lab PolyMAX results

Source: E. Caetano,

F. Magalhaes, A.

Cunha (univ. Porto),

O. Flamand, G.

Grillaud (CSTB)

EVACES Conference,

Porto, 2007




Guadiana Bridge – Modal parameters

Mode Freq.

[Hz]

Damp.

[%]

1 0.384 1.32

2 0.522 1.20

3 0.558 1.57

4 0.951 0.69

5 1.036 0.49

6 1.299 0.46

Mode Freq.

[Hz]

Damp.

[%]

7 1.448 0.54

8 1.654 0.66

9 1.880 0.57

10 2.248 0.60

11 2.547 0.72

12 2.778 0.23

PolyMAX – single analysis results


Ship hull vibration measurements

5 Three-axis acceleration sensors At forward, aft ends and center of upper deck At end of front & aft of compass deck (longitudinal,

lateral and torsion vibrations measurement of deckhouse)

7 Mono-axis acceleration sensors (vertical direction)

On the right side of upper deck

前後、左右、上下方向

11 12

Data Measurement

Test.Lab & SCADAS-Mobile

Long., trans. and vert. direction

Vertical direction

Upper deck

Compass deck

Master/Slave configuration




Change of Vibration Acceleration at aftbody

Change of order components for engine speed

Change of frequency component for

engine speed

0 50Hz

DeckL:1:+Z (CH3)

380

680

rpm

Rp

m E

xtr

(T

1)

-140.00

-40.00

dB g

1.00 2.00

6.00

380 680rpm

0.00

7.40e-3

g

545.00 665.00

F Order 1.00 DeckL:1:+ZF Order 2.00 DeckL:1:+ZF Order 6.00 DeckL:1:+Z

0 50Hz

DeckL:1:+Z (CH3)

380

680

rpm

Rp

m E

xtr

(T

1)

-140.00

-40.00

dB g

0.37 1.00 1.49

3.40 9.1011.10

14.20

380 680rpm

0.00

7.40e-3

g

545.00 665.00

F Frequency 3.40 Hz DeckL:1:+ZF Frequency 9.10 Hz DeckL:1:+ZF Frequency 11.10 Hz DeckL:1:+ZF Frequency 14.20 Hz DeckL:1:+Z

Measurement point 1, Z direction


OMA results: hull vertical vibration modes

Hull Vertical

3 nodes 6.1 Hz

Hull Vertical

4 nodes 9.1 Hz

Hull Vertical

5 nodes 11.1 Hz

Hull Vertical

6 nodes 14.3 Hz

0

5

10

15

20

25

30

0 5 10 15 20 25

Mode number

Fre

qu

en

cy [

Hz]

Glabal vibration mode Hull lateral mode

Hull vertical mode Upper structure mode

Hull Vertical

2 nodes 3.4 Hz




Ship hull vibration measurements – conclusions

Classical modal analysis requires excitation devices Costly / cumbersome Not enough excitation energy for large-dimension ships (poor

SNR)

Operational Modal Analysis is powerful tool for identifying the vibration behavior of the global and local structure of a large ship in operational conditions

Ambient excitation = white noise + harmonic forces from propulsion (engine and propeller system)

Higher-frequency modes successfully identified from engine run-up data

Results are in good agreement with anchor drop test and wave-induced vibrations

Unbalance shaker Impact test


Validation of Complete Vehicle Model (CVM)

LMS Virtual.Lab correlation LMS Test.Lab PolyMAX

Test wireframe

NASTRAN FEM

Source: Martin Olofsson, Peter Nilsson (Volvo Truck)

IOMAC, Copenhagen, 2007

• Simulated operation data • 4-poster measurements • Test track measurements




Mode shape correlation (MAC)

OMA shows better correlation with FEM than ODS

Not all FEM modes could be found in operational data (not well excited by 4-poster, too highly damped)

Others have high correlation

ODS

ODS / OMA vs. FEM

FEM

Reduced FEM vs. OMA mode shape

OMA


Testing and identification of active systems

Intelligent and complex systems engineering Multi-physics system simulation: 1D,

3D, control State estimator: processing data by

models • Applied to Vehicle Dynamics

Control (Flanders’ Drive project) Testing of active system

Model validation and updating Case study

Ford S-MAX 4-poster and Proving Ground tests

Steering

Suspension force

elements

Suspension force

elements

15 DOF

Compliances

Sensors

Tires

Road input / 4 Post Shaker

Steering

Suspension force

elements

Suspension force

elements

15 DOF

Compliances

Sensors

Tires


Steering

Suspension force

elements

Suspension force

elements

15 DOF

Compliances

Sensors

Tires


Steering

Suspension force

elements

Suspension force

elements

15 DOF

Compliances

Sensors

Tires





Full-scale modal wind turbine tests: comparing shaker excitation

with wind excitation

© NREL: U.S. Wind Resource (50m)


EMA – Mode shapes (avi)

Tower fore-aft Tower side-to-side 1st rotor symmetric flap




Shaker excitation (EMA) vs. wind excitation (OMA)

Excellent agreement between EMA & OMA Modes not well excited by wind not identified by OMA


Conclusions

Operational Modal Analysis is a mature technology

High-quality data acquisition Advanced parameter estimation algorithms Commercial software implementations Industrial applications

Last decade, evolution in

Technology Usability Applicability: no isolated results but part of

engineering workflow

• Civil engineering • Aerospace engineering • Automotive engineering



Marie Curie Graduate School on Vehicle Mechatronics & Dynamics, Leuven, 5-8 February 2013 Bart Peeters

Thank you

Related technical papers can be downloaded from

www.lmsintl.com


http://www.lmsintl.com/

nvh lecture 7: operational modal analysis · time animation – operational deflection shapes ......

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