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**System Identification: a Cornerstone of Structural Design in the Aerospace and Automotive Industries**

. Herman Van der Auweraer SCORES Workshop Leuven,

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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 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 2000 warranty cost (Mercedes-Benz) : 1.5 b$ Warranty cost exceeds R&D cost Warranty cost x 3 in 2 years ...

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**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

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**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

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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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**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

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**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”

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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 x a4

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**Experimental Modal Analysis Principles**

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

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**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)

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

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**Experimental Modal Analysis: Aircraft Test Setup Example**

Inputs Responses 1 row or column suffices to determine modal parameters Reciprocity

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**Experimental Modal Analysis A Typical Experiment**

H 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

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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 ( %), 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 Nonlinear in the unknowns Common denominator methods Partial fraction expansion methods Linearized methods State space formulations (“Eigensystem Realization”)

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**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.

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**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

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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 Estimate [A] and [C] from output-only data (KUL…) covariances (INRIA):

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**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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**EMA Example: Aircraft Modal Analysis for Aeroelasticity (Flutter)**

Frequency (Hz) Damping (%) Airspeed (kts)

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**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

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**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

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**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

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**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)

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**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

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**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 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)

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

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**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

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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 Damaged structure 2nd mode shape

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**Innovative Applications: Building Hybrid System Models**

HSS Engine & Brackets Subframe & Crossmember Body Vibro-acoustics Hybrid System Synthesis Engine Mounts Bushings

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**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

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**Vibro-Acoustic Modal Analysis Example: Aircraft Interior Noise**

f = 32.9 Hz = 8.5% ATR42 f = 78.3 Hz = 7.0% F100

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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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