Advanced Modal Analysis Techniques - Siemens … Modal Analysis Techniques Advanced Modal Seminar ... Business jet, wing-vane in-flight ... •Unknown input is assumed to be stationary

Advanced Modal Analysis

Techniques

Advanced Modal Seminar

Brasil, Februari 2017

Realize innovation.Unrestricted © Siemens AG 2016

20XX-XX-XX

Unrestricted © Siemens AG 2013 All rights reserved.

Page 2 Siemens PLM Software

Agenda

Operational Modal Analysis

Rigid Body Properties

Modification Prediction

Operational Modal

Analysis

20XX-XX-XX



How would you excite these structures ?

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In-operation testing

• Some applications permit the acquisition ofInput - 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

20XX-XX-XX



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

Hz

0.10

0.10e-3

Log

g/N

180.00

-180.00

Phase

°

Hz

0.10

1.00e-6

Log

g/N

180.00

-180.00

Phase

°

FRF w ing:vvd:+Z/F200:FED:+Z

FRF back:vde:+Y/F200:FED:+Z

Hz

1.00

0.05

Am

plit

ude

/

Coherence w ing:vvd:+Z/Multiple

Coherence back:vde:+Y/Multiple

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• What ?• Identification of modal

parameters from response data

only

Eigenfrequencies

Damping

Mode shapes

No scaling!

• Using measurements

(accelerations) in operational

conditions

• Why ?• Real operating conditions

laboratory conditions

Non-linearities

Environmental effects

Aero-elastic interaction

Temperature

Boundary conditions

• Inability to measure the inputs

Too difficult, time-

consuming, expensive

• Permanent monitoring

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Laboratory measurements Modal analysis (FRFs)

CMIF

LSCE,

PolyMax, ...

impact

random

stepped sine

Normal mode testing

Operational measurements

- time histories, spectra

- selection of reference stations

- multiple runsOperational modal analysis(freq, damping, mode shapes)

FRFs

F

E

M

/

B

E

M

Peak picking

- power spectra

- principal comp.

(oper. deflection shapes)


Positioning

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• Operational modal analysis = identifying H• Based on Y

• Without knowing U

• Additional ‘input’ poles identified

• No problem if:• poles input system

poles• Low damping,

related to rpm

HU Y

Input System Output

White noise

White noise + harmonic

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Typically, output-only data

• Fed by correlations between outputs and outputs serving as references

• direct in time domain

• inverse DFT of auto-and crosspower spectra

• Unknown input is assumed to be stationary white-noise (theoretical

assumption)

• in practice: colored noise, impulse excitation,

swept sine,.. = OK The frequency band of

excitation has to include the modes

• Mode shapes cannot be mass-normalized

Colored noise:

• Additional ‘input’ poles identified:

harmonics = low damping, related to rpm

• poles input system poles


Background

Sum of

Cross powers

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0.00 80.00 Hz

10.0e-6

0.10

Log

(g/N

)

0.00 80.00 LinearHz

0.00 80.00 Hz

-180.00

180.00

Phase

°

0.00 6.00 s

-1.07

0.91

Real

(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,

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PolyMAX

Pre-processing for Operational Modal Analysis

Spectrum estimation: leakage-free

and Hanning window-free

1. High-speed estimation of time-

domain correlations

• Data reduction

2. Exponential window

• Reduces the effect of leakage

• Reduces the influence of noise

• Compatible with the modal model (

Hanning window is not

compatible and leads to biased

damping)

3. Fourier transform of windowed

correlations

921.590.00 s

0.9928

0.9916

Real

g

Time ref:2b06:+Z

10.230.00 s

2.50e-9

-2.50e-9

Real

g2

AutoCorrelation ref:2b06:+Z

AutoCorrelation ref:2b06:+Z

50.000.00 Hz

-100.00

-130.00

dBg2

180.00

-180.00

Phase

°

AutoPow er ref:2b06:+Z

AutoPow er ref:2b06:+Z

Time-domain correlations

Fourier transform

20XX-XX-XX



Pre-processing for Operational Modal Analysis:

classical and non-classical spectrum estimate

Classical spectrum (“Periodogram”) “Half” spectrum (“Correlogram”)

Operational

data ky

]DFT[window )()( s

k

s yY

Hsss

yy YYS )()()(

P

s

s

yyyy SP

S1

)( )(1

)(

1

0

1 N

k

Tkiki yy

NR

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

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

2.00 8.00 Linear

Hz

1.00e-12

10.0e-9

Log

(m2/s

4

)

autopow er_spectr roof:1:+Z / roof:1:+Z

crosspow er_spect roof:1:+X / roof:1:+Z

2.00 8.00 Linear

Hz

2.00 8.00 Hz

-180.00

180.00

Phase

°

Periodogram

with

Hanning

window

2.00 8.00 Linear

Hz

1.00e-12

1.00e-9

Log

( m/s

2)2

AutoPow er roof:1:+Z

CrossPow er roof:1:+X/roof:1:+Z

2.00 8.00 Linear

Hz

2.00 8.00 Hz

-180.00

180.00

Phase

°

Correlogram

with

exponential

window

20XX-XX-XX



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

Real

( m/s

2)2

Time roof:1:+X Unw indow ed

Time roof:1:+X

0.00 10.00 Linear

Hz

-140

-90

dB

( m/s

2)2

AutoPow er roof:1:+X Unw indow ed

AutoPow er roof:1:+X

0.00 10.00 LinearHz

0.00 10.00 Hz

-180

180

Phase

°

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The Vasco da Gama Bridge

0.00 960.60s

-0.52

0.59

Rea

l

g

0.00 300.00s

-0.02

0.02

Rea

l

g2

0.00 2.50Hz

0.00

0.00

Log

g2

Vertical acc.

Transversal acc.

Time data

Correlations

Spectra

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20XX-XX-XX





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Measured Cross Spectra vs. Modal Model

0.20 1.05Hz

0.00

0.00

Log

g2

0.20 1.05LinearHz

0.20 1.05Hz

-180.00

180.00

Phase

°

10X-15Z

0.20 1.05Hz

0.00

0.01

Log

g2

0.20 1.05LinearHz

0.20 1.05Hz

-180.00

180.00

Phase

°

10Z-112Z

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Øresund Bridge

m

H

Lnf S

n2

1

Measurements of cable vibrations allow to

monitor cable forces (vibrating string theory)

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Other Operational Modal Analysis

Applications

In-flight testing

Flutter

High-speed train

Road test of a car

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Operational Modal Analysis in Ship-Building

Background：

Performing EMA(Experimental Modal Analysis)

on large ships is very difficult

Most customers only perform ODS

(Operational Deflection Shapes) using vibration data

Using the same vibration data, customer can determine

the modal properties of the ship with OMA

(Operational Modal Analysis)

Tokai University - Boseimaru

前後、左右、上下方向

1

1

1

2

Data Measurement

次数成分の周波数比較

0

1

2

3

4

5

6

7

8

9

10

0 0.5 1 1.5 2 2.5 3 3.5

次数（次）

周波数（Hz）

アンカリングテスト

ランアップテスト


1st Bending Mode

Correlation with Anchoring Test

Test.Lab & SCADAS-Mobile

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OMA on Tokai University ship

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First and second bending

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Torsion and third bending mode

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Scania: Enhanced exploitation of oilpan vibration

data by Operational Modal Analysis

• Design of a silent oilpan

• Single measurement for

• Sound level evaluation

• Operational Deflection Shapes creating

the sound

• Operational Modal Analysis

• Benefits

• Reduced testing time

• Consistent data130 650Hz

Big_Block:27:+Z (CH2)

859

2168

rpm

Fly

Wheel (

T1)

-50

0

dB

130 650Hz

Big_Block:44:+Y (CH1)

859

2168

rpm

Fly

Wheel (

T1)

-48

2

dB

130 650Hz

Small_Block:12:+Z (CH3)

859

2168

rpm

Fly

Wheel (

T1)

-38

12

dB

130 650Hz


860

2171

rpm

Fly

Wheel (

T1)

-50

0

dB

130 650Hz


860

2171

rpm

Fly

Wheel (

T1)

-48

2

dB

130 650Hz


860

2171

rpm

Fly

Wheel (

T1)

-38

12

dB

130 650Hz


859

2169

rpm

Fly

Wheel (

T1)

-50

0

dB

130 650Hz


859

2169

rpm

Fly

Wheel (

T1)

-48

2

dB

130 650Hz


859

2169

rpm

Fly

Wheel (

T1)

-38

12

dB

0.00 0.64s

-0.10

0.10

Real

g2

OMA vs. impact modes

(mass and temp diff)

20XX-XX-XX



Operational Modal Analysis (OMA)

More than Operational Deflection Shapes (ODS)

• Animate: Auto & Cross Spectra,

FRFs, Orders

• Peak picking

• Deformation at a chosen

frequency line

• No damping information

• Combination of modes and forced

responses

• Combination of closely spaced modes

• Phenomena

• Curve-fit: Auto & Cross Spectra

• Modal model

• Frequency

• Damping

• Mode shape

• (No modal scaling)

• Use of system identification

methods

• Structural characteristics

• Separation of closely spaced modes

• Root causes

OMAODS

Vibration problem “root cause” discriminator

20XX-XX-XX



Conclusions

Operational Modal Analysis is a mature technology

• High-quality data acquisition

• Advanced parameter estimation algorithms

• Commercial software implementations

• Industrial applications

• Only care on the assumption made

• Evolutions since more than 20 years

• Technology

• Usability

• Applicability: no isolated results but part of

engineering workflow

• Civil engineering

• Aerospace engineering

• Automotive engineering

Rigid Body Properties

20XX-XX-XX



Why are inertia properties needed ?

Verification of CoG & MoI values

Input for simulation models Kinematic and dynamic prediction (multibody

dynamics calculation) Coupling of an FE model with smaller “rigid”

components Accurate Modal based modification or

Substructuring requires flexible modes + rigid body modes

Complete modal model A complete modal model contains 3 components:

• Rigid body modes• Flexible modes• Residual terms

?

20XX-XX-XX



How to determine inertia properties ?

Pendulum test Based on measured Frequency response

functions

Typical modal test with hammer or

shaker excitation

At least 6 excitation locations (SDOF)

8 – 12 response locations (3 DOF)

Time consuming

Requires multiple suspensions -

difficult for complex structures

No extra equipment is needed

Limited measurement effort

Highly accurate alternative to

conventional pendulum test

20XX-XX-XX



Rigid body modes

To synthesize rigid body modes based on FRF measurements

Input:

• Geometry (nodes and coordinates)

• FRF data

Output:

• Inertial properties:

• Center of gravity

• Mass

• Moments of inertia

• Directions of the principle axes of inertia

• 3 translational rigid body modes

• 3 rotational rigid body modes

20XX-XX-XX



Rigid Body Properties Calculation

How does it work - Theory

Approximate structure as Single DOF system

Resonance frequency of this SDOF system is the first actual RBM of the structure

Line above resonance is called the mass line

20XX-XX-XX




How does it work – Test setup

Weigh the test item to obtain mass [kg]

Suspend Test item (once) in free-free conditions

Create geometry wire-frame model in global or local coordinates

Measure FRF matrix preferably with hammer

Test Setup:

20XX-XX-XX




How does it work - Mass line methods

Unchanged FRFs

Rigid body modes and first deformation modes are sufficiently spaced

Measured FRFs are used

Corrected FRFs

Rigid body modes and first deformation modes are not sufficiently spaced

Estimate first set of flexible modes from measured FRFs

Correct measured FRFs by subtraction of contribution of flexible modes

Lower Residual

No accurate FRFs are measured in the frequency range directly above rigid body modes

Lower residuals represent the influence of the modes below the deformation modes, and are

therefore representative of the rigid body modes.

Extract mass line:

20XX-XX-XX




How does it work - Calculation and results

Coordinates of center of gravity

Moments and products of inertia about CoG and any user defined reference point

Principal moments of inertia and their direction

Synthesis of 6 scaled rigid body modes with user defined frequency

and damping for use in simulation models

Least square solution over all measured DOF

Least squares over selected frequency band of mass-line

Validation through animation of rigid body motion

Calculate Rigid Body Properties:

Results:


20XX-XX-XX




Why?

The major advantages of Structural

Modification Prediction within prototype

optimization procedures are:

•Prediction of the effect of a

structural modification without

physically changing the structure.

•Evaluation of alternative design

variation without repeated testing

•Evaluation of the impact of a

selected modification on the

structure in a global sense

The LMS Test.Lab Modification

Prediction workbook helps you to:

•Efficiently dissipate vibration

energy using a tuned absorber

•Add masses or change local

stiffness to move resonant

frequencies

20XX-XX-XX



Modal models for structures with flexible coupling and viscous damping

1. Laplace domain

2. Extended system equation

3. Eigenvalue problem

4. Premultiply extended system equation with

5. Orthogonality condition

6. Transformation to modal space


Modification Prediction – Theoretical background (1)

pFpXKCpMp 2

F

FX

XpY

K

MB

CM

MA

FYBAp

0',,

0

0,

0

'

0 ii BA

i

ii

i

t

\\

\

\

\

\

\

\

\

\ abbBandaA tt

qY

20XX-XX-XX




Modification Prediction – Theoretical background (2)

Modification of structure

• Structure modification

• Modified system equation

• Applying modal transformation New Eigenvalue problem in modal space to be

solved

• Modified system poles and modified eigenvectors in modal coordinates

• Back substitution to physical coordinates gives new modal vectors

'FYBBAAp

mrq

mrm qψψ

BAKCM ,,,

20XX-XX-XX




Automotive example

Tuned absorbers in cars:

• 10 – 15 (sometimes up to 30) tuned

absorbers/vehicle

• 100-150 gr / absorber (exceptionally up to 1.5 kg)

20XX-XX-XX




Automotive example

Mass modification on attachment

bracket

Bi-directional tuned

absorber on an engine

anti-roll mount

20XX-XX-XX




Aero examples

Aircraft cabin noise

reduction

Engine vibration reduction

20XX-XX-XX




Aero example

Helicopter design

20XX-XX-XX




Civil construction

Modifications

58 Tuned Absorbers

4 Vertical dampers

17 Chevron dampers

16 Pier dampers

Cost

Construction: £18m

Modifications: £5m !!

Bridge closed for 2 years

“Wobbling Bridge Will Stay Shut” – BBC News

20XX-XX-XX




Other industries

Everyone else interested in the vibration

related product performance

http://www.railway-technology.com/contractors/noise/schrey/

http://www.railway-technology.com/contractors/noise/schrey/

Thank you!Advanced Modal Seminar

Brasil, Februari 2017

Realize innovation.Restricted © Siemens AG 2016

Documents

Advanced Modal Analysis Techniques - Siemens … Modal Analysis Techniques Advanced Modal Seminar ... Business jet, wing-vane in-flight ... •Unknown input is assumed to be stationary