1. System Identification: a Cornerstone of Structural Design in the Aerospace and Automotive Industries.
Herman Van der Auweraer
SCORES Workshop
Leuven,

2. 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

3. 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

4. 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

5. Introduction Economic Impact: Some Figures
Typical vehicle development programs require investment budgets of 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

6. Introduction Time Pressure Increases Recall Risks
Warranty costs may explode the overall budget
2000 warranty cost (Mercedes-Benz) : 1.5 b$
Warranty cost exceeds R&D cost
Warranty cost x 3 in 2 years ...

7. 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
A priori (Finite Element) and experimental (Modal)
Analyze the effect of dynamic loads
Understand the intrinsic structural dynamics behaviour
Derive optimal design modifications

8. Introduction: A Systems Approach A Source-Transmitter-Receiver Model
Engine
Steering Wheel Shake
TACTILE
Total Vehicle System
Seat Vibration
Wheel & Tire Unbalance
VISUAL
Rearview mirror vibration
Road Input
Accessories
Environmental Sources
Noise at Driver’s & Passenger’s Ears
ACOUSTIC
Source
System Transfer
Receiver = X

9. 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

10. Experimental Modal Analysis Principles
Structural dynamics modelling: relating force inputs to displacement/acceleration outputs
Multiple D.o.F. System:
Continuous structures approximated by discrete number of degrees of freedom -> Finite Element Matrix Formulation
Majority of methods and applications: Linear and Time-Invariant models assumed
ground m 1 c k f
(t) 2 n
n+1 x

11. Experimental Modal Analysis Principles
Modal Analysis: Related to Eigenvalue Analysis
Time domain equation
Laplace domain equation
Eigenvalue analysis -> system poles and Eigenvectors
System pole -> Resonance frequency and damping value
Eigenvector -> Mode shape
Transformation vectors to “Modal Space”

12. Experimental Modal Analysis Principles
Modal Shape: Eigenvector in the physical space: physical interpretation (Example “Skytruck”)

13. Modal Analysis Principle; Decomposition in Eigenmodes
Modal Analysis: The modal superposition a1 x a2 x + + … = + … + + x a3 x a4

14. Experimental Modal Analysis Principles
Modal Analysis: An input/output relation
Transfer Function Formulation:
Model reduction (Finite number of modes):

15. Experimental Modal Analysis Principles
Experimental Analysis: using input/output measurements
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
Input
System
Output H
u(t)
U(ω)
y(t)
Y(ω)

16. 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 ( channels)
“patching” -> non-simultaneous data

17. Experimental Modal Analysis: Aircraft Test Setup Example
Inputs
Responses
1 row or column suffices to determine modal parameters
Reciprocity

18. Experimental Modal Analysis A Typical ExperimentH F X
Input
System
Output
Vehicle Body Test
F : 2 inputs
Indicated by arrows
X : 240 outputs
All nodes in picture
H has 480 elements
X = H * F
Vertical force
Horizontal force

19. Experimental Modal Analysis Typical FRFs
Industrial
Gear box
Vehicle Subframe

20. Experimental Modal Analysis Typical FRFs
Engine block driving point FRF
Engine block FRF

21. 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

22. 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 ( %), Large dynamic range
Specific approach:
Simultaneous (“global”) analysis of all reduced (FRF) data
Order problem: Repeated analysis for increasing orders
-> The stabilisation diagram

23. Experimental Modal Analysis Principles
Experimental Modal Analysis: using FRF measurements in a reduced set of structural locations

24. 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

25. Modal Model Parameter Identification Main Methods
Frequency domain methods: rational polynomial FRF model
Nonlinear in the unknowns
Common denominator methods
Partial fraction expansion methods
Linearized methods
State space formulations (“Eigensystem Realization”)

26. Modal Model Parameter Identification Main Methods
Linear frequency domain method
Weighted or not
LS, TLS
Maximum Likelihood: takes data variance into account -> Non-linear error formulation -> iterative; Error bounds!!
Continuous or discrete frequency domain
Preferred approach: “PolyMAX”, Least Squares Discrete Frequency Domain LS/TLS, originating from VUB.

27. Modal Model Parameter Identification Main Methods
Time domain: Complex damped exponential approach (UC)
Impulse responses or correlations are solutions of the “characteristic equation”
Poles: found as eigenvalues of [Wi] companion matrix
Modeshapes: Least-squares fit of FRF matrix

28. Modal Model Parameter Identification Main Methods
Time domain: Discrete time state space model -> Subspace method
In particular used with output-only data: stochastic subspace
Estimate [A] and [C] from
output-only data (KUL…)
covariances (INRIA):

29. Modal Model Parameter Identification Main Methods
Stabilisation diagram: discrimination of physical poles versus mathematical/spurious poles -> heuristic approach

30. 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

31. 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

32. EMA Example: Aircraft Modal Analysis (Dash 8)

33. EMA Example: Aircraft Modal Analysis for Aeroelasticity (Flutter)
Frequency (Hz)
Damping (%)
Airspeed (kts)

34. EMA Example: Aircraft FE Model Correlation and Updating
Eigenfrequency
correlation
+ 5%
- 5%
GVT
GVT
GVT
Mode shape
Correlation (MAC)
FEM
Courtesy H. Schaak, Airbus France

35. 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
PolyMAX

36. 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
MR-I ODS
6.4 Hz mode

37. EMA Example: Car Body and Suspension Tests
Suspension EMA for a rolling-noise problem : Booming noise at 80Hz
Main contribution from rear suspension mounts
Body EMA for basic bending and torsion analysis (vehicle stiffness)

38. EMA Example: Civil Structures Dynamics
Input-output testing
Output-only testing
Creatieve oplossingen in literatuur om grote constructie aan het trillen te brengen.
Øresund Bridge

39. Example: Civil Structures - The Vasco da Gama Bridge
In-operation Modal Analysis
Covariance Driven
Stochastic Subspace

40. 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

41. 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

42. 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

43. Innovation and Challenges: Data Quality Assessment
Automatic Assessment and Classification of FRF Quality and Plausibility
 1 x2 x1
hid hid2
 2
ANN (namely a Multi-Layer Perceptron Network) can very well perform repetitive tasks. By using the black box approach, we can imagine that an ANN is a device like a trafic light: in input we have measurements (in this case FRFs as measured on a car and namely the demo car of the LMS demo database). At the output the quality assessment (green or red light meaning good ar bad quality FRF).
On the 3 inputs of the ANN we feed the 3 different FRFs measured in 3 points of the car. It is possible to notice that the green FRF is quite noisy at low frequency, therefore it might negativelly affect the analysis (like the modal parameter extraction). It important to quickly identify and reject bad quality measurements before the analysis starts.
ANN process FRF based on fixed criteria lernt in the training session and applies the engineering knowledge to discriminate between good and bad measurements.
In the case illustrated, we used the following crieterion: approximate the the noisiness of an FRF based on the number of peacks and dips encountered in a given frequency band.
By processing a lot of FRF in the training session, the ANN lerns the boundaries (upper an lower) in the peack and dips that identify a good FRF. If an FRF with an abnormal value of peacks and dips is processed, the ANN identifies it as bad FRF and put it in a separate cluster (the green FRF does not passes the NN check and a red light is hit in the Network output).
As result the green FRF is rejected and the overall FRF quality can be improved.
The tool is still a prototype (I.e. it needs validation!!!!) but it is fully integrated in Test.Lab via Windows Automation. The application is developped in C++ but it runs under TL: data can be selected from the navifgator worksheet and imported to the Neural Network sheet, result can be exported to the navigator sheet and stored.
Coherence analysis (225 spectral lines X 540 DOFs)

44. 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
Young’s modulus ( GPa)
mass density ( kg/m3)
shell thickness ( mm)

45. 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
Since the amount of testing will actually increase, we will have a need for higher productivity & test reliability.
Systematic standardized, simplified, and semi-automated testing will be required.
And the typical user will probably not be an engineer as it was in the past – but a technician who will have to execute pre-defined measurement tasks with a minimum of training.
All this testing will create massive amounts of data. This data must be made available to anyone within the extended organization.
The focus of the recently introduced LMS Test.Lab product is to address these needs. Our design team focussed on one goal: within a day of starting, a technician, an untrained engineer, or even a complete novice had to be able to run the most advanced of tests and publish their report onto the web
PolyMAX

46. 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
Damaged structure
2nd mode shape

47. Innovative Applications: Building Hybrid System Models
HSS
Engine
&
Brackets
Subframe
&
Crossmember
Body
Vibro-acoustics
Hybrid
System
Synthesis
Engine Mounts
Bushings

48. Innovative Applications: Vibro-Acoustic Modal Analysis
Acoustic resonances, coupled structural-acoustical behaviour can be modelled by vibro-acoustic modal models
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

49. Vibro-Acoustic Modal Analysis Example: Aircraft Interior Noise
f = 32.9 Hz
 = 8.5%
ATR42
f = 78.3 Hz
 = 7.0%
F100

50. 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