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Herman Van der Auweraer SCORES Workshop Leuven, 12-10-2004

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

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Herman Van der Auweraer SCORES Workshop Leuven, 12-10-2004

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  1. System Identification: a Cornerstone of Structural Design in the Aerospace and Automotive Industries Herman Van der Auweraer SCORES Workshop Leuven, 12-10-2004

  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. IntroductionMechanical 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 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

  6. IntroductionTime 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. IntroductionMechanical 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 ApproachA Source-Transmitter-Receiver Model TACTILE Engine Steering Wheel Shake 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 System Transfer Source 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 AnalysisPrinciples f x x x f (t) f (t) (t) (t) (t) (t) n 1 2 1 n 2 k k 2 k n+1 1 m m m ground ground n 1 2 c c n+1 c 2 1 • 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

  11. Experimental Modal AnalysisPrinciples • 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 AnalysisPrinciples • Modal Shape: Eigenvector in the physical space: physical interpretation (Example “Skytruck”)

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

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

  15. Experimental Modal AnalysisPrinciples y(t) Y(ω) u(t) U(ω) H • 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 Output System Input

  16. 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” -> non-simultaneous data Experimental Modal AnalysisTest Procedure

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

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

  19. Experimental Modal AnalysisTypical FRFs Industrial Gear box Vehicle Subframe

  20. Experimental Modal AnalysisTypical FRFs Engine block driving point FRF Engine block FRF

  21. Experimental Modal AnalysisAmbient 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 AnalysisThe 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

  23. Experimental Modal AnalysisPrinciples • 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) Airspeed (kts) Damping (%)

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

  35. In-flight excitation, 2 wing-tip vanes 9 responses 2 min sine sweep Higher order harmonics Very noisy data EMA Example:Business Jet, Wing-Vane In-Flight Excitation 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 6.4 Hz mode MR-I ODS

  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 Øresund Bridge Output-only testing Input-output testing

  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 x1  1 x2  2 x2 hid1 hid2 Automatic Assessment and Classification of FRF Quality and Plausibility Coherence analysis (225 spectral lines X 540 DOFs)

  44. Uncertainty and Reliability: A Research Context IN OUT • 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? Uncertainty in front craddle • Young’s modulus (190-210 GPa) • mass density (7600-8000 kg/m3) • shell thickness (1.6-2.4 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 PolyMAX

  46. Industrial Model Analysis: What are the issues and challenges? Healthy structure Damaged structure 2nd mode shape • 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 • …..

  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 AnalysisExample: Aircraft Interior Noise f = 32.9 Hz  = 8.5% ATR42  = 7.0% f = 78.3 Hz 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

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