System Identification: a Cornerstone of
Structural Design in the Aerospace and
Automotive Industries
Herman Van der Auweraer
SCORES Workshop
Leuven, 12-10-2004
Overview
 Objective: To discuss the vital importance of System
Identification in the Mechanical Design Engineering Process
 To identify the specific challenges for this kind of problems and
to illustrate the research needs
 Illustrate with typical products: cars, aircraft, satellites, …. where
adequate mechanical product behaviour is vital
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Overview
 Introduction: the role of Structural Dynamics in
Mechanical Design Engineering
 Approach and methodology for Structural Dynamics
Analysis: Experimental Modal Analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
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Introduction
Mechanical Design Engineering
 Market Demand: Delivering products with the required
mechanical characteristics: Excel in
 Operational quality (performance specifications…)
 Reliability (load tolerance, fatigue, life-time…)
 Safety (vehicle crash, aircraft flutter….)
 Comfort (noise, vibration, harshness)
 Environmental impact (emissions, waste, noise,
recycling…)
 Process process challenges: Excel in
 Time-to-Market: reduce design cycle
 Reduce design costs
 Product customization
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Introduction
Economic Impact: Some Figures
• Typical vehicle development programs require investment
budgets of 1 .. 4 B$
• New Mercedes C-class (Automotive Engineering Intl., Aug. 2000):
• 600 M$ development + 700M$ production facilities
• Developed in less than 4 years
• New Mini: 200M£ development costs (+ as much in marketing...)
• Chrysler minivan (“The Critical Path” by Brock Yates):
• 2 B$ development budget, of which 250 M$ R&D
• 36 different body styles, 2 wheelbases, 4 engines
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Introduction
Time Pressure Increases Recall Risks
Warranty costs may explode the overall budget
•
•
•
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2000 warranty cost (Mercedes-Benz) : 1.5 b$
Warranty cost exceeds R&D cost
Warranty cost x 3 in 2 years ...
6
Introduction
Mechanical Design Engineering
 Early Design Optimization is Essential
 Product design has to go beyond the “Form and Fit”
 Focus on “Functional Performance Engineering”
 For mechanical performances: structural analysis
 Static: strength, load analysis
 Kinematic: mechanisms, motion
 Dynamic: vibrations, fatigue, noise
 Basic approach: is through the use of structural models




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A priori (Finite Element) and experimental (Modal)
Analyze the effect of dynamic loads
Understand the intrinsic structural dynamics behaviour
Derive optimal design modifications
7
Engine
Steering Wheel
Shake
Total Vehicle
System
Seat Vibration
VISUAL
Wheel & Tire
Unbalance
Accessories
Noise at Driver’s
& Passenger’s
Ears
Environmental Sources
Source
X
System Transfer
8
=
Receiver
ACOUSTIC
Rearview mirror
vibration
Road Input
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TACTILE
Introduction: A Systems Approach
A Source-Transmitter-Receiver Model
Overview
 Introduction: the role of Structural Dynamics in
Mechanical Design Engineering
 Approach and methodology for Structural Dynamics
Analysis: Experimental Modal Analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
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Experimental Modal Analysis
Principles
 Structural dynamics modelling: relating force inputs to
displacement/acceleration outputs
ground
f (t)
1
f (t)
2
f (t)
n
k n+1
k2
k1
m 1
c
M x(t )  C x(t )  K x(t )  f (t )
m 2
m n
c
c2
1
x (t)
2
x (t)
1
ground
 Multiple D.o.F. System:
n+1
x (t)
n
 Continuous structures approximated by discrete number of
degrees of freedom -> Finite Element Matrix Formulation
 Majority of methods and applications: Linear and TimeInvariant models assumed
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Experimental Modal Analysis
Principles
 Modal Analysis: Related to Eigenvalue Analysis
 Time domain equation
M x(t )  C x(t )  K x(t )  f (t )
 Laplace domain equation
( s 2 M  sC  K ) X (s)  F (s)
 Eigenvalue analysis -> system poles and Eigenvectors
 System pole -> Resonance frequency and damping value
k , *k   k k  j 1   k2 k
 Eigenvector -> Mode shape
 Transformation vectors to “Modal Space”
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Experimental Modal Analysis
Principles
 Modal Shape: Eigenvector in the physical space: physical
interpretation (Example “Skytruck”)
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Modal Analysis Principle;
Decomposition in Eigenmodes
 Modal Analysis: The modal superposition
a1 x
=
a2 x
+
+ …
+
+ …
+
x a3
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x a4
Experimental Modal Analysis
Principles
 Modal Analysis: An input/output relation
 Transfer Function Formulation:
X ( s)  H ( s) F ( s)
H ( s )  [ s 2 M  sC  K ]1
 Model reduction (Finite number of modes):

B ( s, ) 
H (s) 
Ak  Qk {k }  Tk 
Ak
Ak*
H (s)  

*
s


s


k 1
k
k
k , *k   k k  j 1   k2 k
D ( s, )
n
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Experimental Modal Analysis
Principles
 Experimental Analysis: using input/output measurements
Input
System
u(t)
U(ω)
Output
y(t)
Y(ω)
H
 Non-parametric estimates (FRF, IR) -> Data reduction
 Black box models (ARX, state-space)
 Modal models
 Standard experimental modal analysis approach: Fitting the
Transfer Function model by Frequency Response Function
measurements
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Experimental Modal Analysis
Test Procedure
• Excitation
• Shakers (Random, Sine)
or Hammer (Impulsive)
• Load cell for force meas.
• Response
• Accelerometers
• Laser (LDV)
• Cross-spectra averaging to
estimate FRFs
• Measurement system
• FFT analyzer (2-4 channel)
• PC & data-acquisition
front-end (2-1000
channels)
• “patching” -> nonsimultaneous data
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Experimental Modal Analysis:
Aircraft Test Setup Example
Inputs
Responses
Ground Vibration Test
(GVT) System
Responses
F3
F4
F1
F2
•
Force Inputs
((m/s2)/N)
Log
0.10
•
0.00 0.00
Hz
Linear
80.00
Hz
80.00
Hz
80.00
°
Phase
180.00 0.00
-180.00
0.00
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 H11

 H 21
 H 31

 H 41
H12 H13 H14 

H 22 H 23 H 24 
H 32 H 33 H 34 

H 42 H 43 H 44 
1 row or column
suffices to determine
modal parameters
Reciprocity
H pq  H qp
Experimental Modal Analysis
A Typical Experiment
Vehicle Body Test
•
Input
System
Output
F
H
X
F : 2 inputs
•
•
Indicated by arrows
X : 240 outputs
•
All nodes in picture
 H has 480 elements
X=H*F
Vertical force
Horizontal force
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Experimental Modal Analysis
Typical FRFs
Industrial
Gear box
Vehicle
Subframe
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Experimental Modal Analysis
Typical FRFs
Engine block
driving point FRF
Engine block
FRF
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Experimental Modal Analysis
Ambient Excitation Tests
 Many applications do not allow input/output tests
 No possibility to apply input
 Typical product loading difficult to realise (non-linear effects)
 Large ambient excitation levels present
 Specific approach:
 Use output-only data (responses)
 Assume white noise excitation
 Reduce output data to covariances or cross-powers
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Experimental Modal Analysis
The Analysis Process
 Modal Analysis: identification of modal model parameters
from the FRF (or Covariances)
 Specific problems:
 Large number of inputs/outputs, long records (noisy data)
 Non-simultaneous I/O measurements
 High system orders, order truncation, modal overlap
 Low system damping (0.1 .. 10%), Large dynamic range
 Specific approach:
 Simultaneous (“global”) analysis of all reduced (FRF) data
 Order problem: Repeated analysis for increasing orders
-> The stabilisation diagram
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Experimental Modal Analysis
Principles
 Experimental Modal Analysis: using FRF measurements in
a reduced set of structural locations
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Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Usually taking into account the physical model
 Use of raw time data exceptional -> reduced FRF models
 Time and frequency domain approaches
 Industrial and societal applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
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Modal Model Parameter Identification
Main Methods
 Frequency domain methods: rational polynomial FRF model
N
H(  ) 
  (  ).B
j 0
M
j
j
  j (  ).Aj
N
M
j 0
j 0
H ( )  [  j ( ).B j ][   j ( ). A j ]
j 0





Nonlinear in the unknowns
n
Common denominator methods
Ak
Ak*
H () 

Partial fraction expansion methods
j  *k
k 1 j   k
Linearized methods
State space formulations (“Eigensystem Realization”)
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
25
1
Modal Model Parameter Identification
Main Methods
• Linear frequency domain method
N
  (  )B
j 0
j
M
j
 H(  )  j (  )A j  0
j 0
• Weighted or not
• LS, TLS
• Maximum Likelihood: takes data variance into account -> Nonlinear error formulation -> iterative; Error bounds!!
• Continuous or discrete frequency domain
• Preferred approach: “PolyMAX”, Least Squares Discrete
Frequency Domain LS/TLS, originating from VUB.
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Modal Model Parameter Identification
Main Methods
• Time domain: Complex damped exponential approach (UC)
Nm
[ Rk ]    r e
  r kt
{L}    e
T
r
r 1
*
r
  r *kt
{L}Tr *
• Impulse responses or correlations are solutions of the
“characteristic equation”
 
 
 



Rk I   Rk 1 W1   ...  Rk t Wt   0
• Poles: found as eigenvalues of [Wi] companion matrix
• Modeshapes: Least-squares fit of FRF matrix
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Modal Model Parameter Identification
Main Methods
• Time domain: Discrete time state space model -> Subspace method
• In particular used with output-only data: stochastic subspace
xk 1   Axk   wk 
[ A]  [ ][ ][ ]1
 y    Cx   v 
k
k
r  er t  r   r  ir
k
• Estimate [A] and [C] from
• output-only data (KUL…)
• covariances (INRIA):
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 r
 [C ] r
Modal Model Parameter Identification
Main Methods
 Stabilisation diagram: discrimination of physical poles
versus mathematical/spurious poles -> heuristic approach
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Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
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EMA Example:
Aircraft Modal Analysis
• Component Development
• Engine, landing gear, ….
• Aircraft Ground Vibration Tests
•
•
•
•
Low frequency: 0 … 20… 40 Hz
> 50 orders, > 250 DOF
Model Validation & updating
Flutter prediction
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EMA Example:
Aircraft Modal Analysis (Dash 8)
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Frequency (Hz)
EMA Example:
Aircraft Modal Analysis for Aeroelasticity (Flutter)
Damping (%)
Airspeed (kts)
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EMA Example:
Aircraft FE Model Correlation and Updating
6
FEM
FEM
Eigenfrequency
correlation
+ 5%
Analytical Frequencies [Hz]
5
4
- 5%
3
2
1
0
0
1
2
3
Measured Frequencies [Hz]
Courtesy H. Schaak, Airbus France
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5
Mode shape
Correlation (MAC)
GVT
GVT
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GVT
FEM
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
g/N
( )
Log
0.10
°
Phase
0.00 4.00
180.00 4.00
Hz
Linear
20.00
Linear
20.00
Hz
-180.00
PolyMAX
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Hz
In-Operation Modal Analysis Example:
PZL-Sokol Helicopter Testing
•
•
•
•
Flight tests in different conditions (speed, climbing, hover…)
3 flights needed, 90 points
Correlation lab. / flight results
No problem with rotor frequencies
SNR GROUND TEST
MODE 6.40 Hz
CLIMBING FLIGHT TEST
MODE 6.37 Hz
MR-I ODS
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6.4 Hz mode
EMA Example:
Car Body and Suspension Tests
•
•
)
Log
(
Body EMA for basic
bending and torsion
analysis (vehicle
stiffness)
0.00 25.00
179.98 25.00
Hz
Linear
75.00
Linear
75.00
Hz
°
Phase
(m/s2)/N
0.13
-179.96
25.00
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Hz
37
75.00
Suspension EMA for a
rolling-noise problem :
Booming noise at 80Hz
Main contribution from
rear suspension mounts
EMA Example:
Civil Structures Dynamics
Input-output
testing
Øresund Bridge
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Output-only
testing
Example:
Civil Structures - The Vasco da Gama Bridge
In-operation Modal Analysis
Covariance Driven
Stochastic Subspace
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Overview
 Introduction: the role of structural dynamics in
Mechanical Design Engineering
 Approach and methodology for structural dynamics
analysis: experimental modal analysis
 Modal Parameter Identification methods
 Applications of modal analysis
 Recent evolutions and challenges for the future
 Conclusions
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Industrial Model Analysis:
What are the issues and challenges?
• Optimizing the Test process
• Large structures (> 1000 points, in operating vehicles…)
– Novel transducers (MEMS, TEDS…)
– Optical measurements
• Complex structures, novel materials, high and distributed damping
(uneven energy distribution)
– Multiple excitation (MIMO Tests)
– Use of a priori information for experiment design
– Nonlinearity checks, non-linear model detection and
identification
– Excitation Design: Get maximal information in minimal time
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Industrial Model Analysis:
What are the issues and challenges?
• Optimizing the Analysis process
• High model orders, numerical stability
• Discrimination between physical and “mathematical” poles
• Automated modal analysis
• Test and analysis duration and complexity
• Test-right-first-time
• Support user interaction with “smart results”
• Automating as much as possible the whole process
• Quantifying data and result uncertainty
-> bring intelligence in the test and analysis process
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Innovation and Challenges:
Data Quality Assessment
Automatic Assessment and Classification of FRF Quality and Plausibility
x1
1
x2
x2
2
hid1
hid2
/
Amplitude
1.00
F
F
Coherence lfw :38:-Z/Multiple
Coherence rgw :38:-Z/Multiple
0.00
2.00
Hz
30.00
Coherence analysis (225 spectral lines X 540 DOFs)
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Uncertainty and Reliability:
A Research Context
• Methods to assess uncertainty and variability of CAE models:
•
•
•
•
Input distribution -> response distribution
Fuzzy-FE, transformation method, Monte-Carlo…
Robust design and reliability considerations
What about test data confidence limits?
IN
OUT
Uncertainty in front craddle
•
•
•
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Young’s modulus (190-210 GPa)
mass density (7600-8000 kg/m3)
shell thickness (1.6-2.4 mm)
44
Innovation and Challenges:
Automating Modal Parameter Estimation
•
•
•
Mimic the human operator (rules, implicit -> NN)?
Iterative methods (MLE)
Fundamental issue: discriminate mathematical and physical poles
• Indicators (damping value, p-z cancellation or correlation…)
• Fast stabilizing estimation methods
• Clustering techniques
PolyMAX
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Industrial Model Analysis:
What are the issues and challenges?
• Novel applications
• Combined Ambient – I/O testing
• Nonlinear system detection and identification
• Build system-level models combining EMA and FE models
• Vibro-acoustic modal analysis: include cavity models
• Mechatronic and control
• End-of-line control
•
Model-based monitoring
• …..
Healthy structure
2nd mode shape
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Damaged structure
Innovative Applications:
Building Hybrid System Models
Engine
&
Brackets
Hybrid
System
Synthesis
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Subframe
&
Crossmember
HSS
Engine Mounts
47
Body
Vibro-acoustics
Bushings
Innovative Applications:
Vibro-Acoustic Modal Analysis
• Acoustic resonances, coupled structural-acoustical
behaviour can be modelled by vibro-acoustic modal models
K S

 0
 K C  x 
C S
 j 
f  
p
K  
 0
0
Cf
S
M

 x 
2
  p    M c
 

• Excitation by shakers and
loudspeakers -> Balancing of test
data needed (p/f, x/f, p/Q, x/Q)
• Non-symmetrical modal model
• Through structural acoustic
coupling
• Different right and left
eigenvectors
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0
Mf
 x 
  
  p
 f 
 
 pq 
Vibro-Acoustic Modal Analysis
Example: Aircraft Interior Noise
f = 32.9 Hz
 = 8.5%
ATR42
f = 78.3 Hz
F100
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 = 7.0%
Summary and Outlook
• Early product optimization is essential to meet market demands
• Mechanical Design Analysis and Optimization heavily rely on
Structural Models
• Experimental Modal Analysis is the key approach, it is a de-facto
standard in many industries
• While EMA is in essence a system identification problem,
particular test and analysis issues arise due to model size and
complexity
• Important challenges are related to supporting the industrial
demands (test time and accuracy) and novel applications
• Research efforts should also pay attention to “state-of-the-use”
breakthroughs
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