An overview of experimental modal analysis capabilities in SDT.

1. EMA (experimental modal analysis)
Overview of SDT capabilities
Guillaume Martin, SDTools
Etienne Balmes, SDTools

2. Structural Dynamics Toolbox
• Experimental Modal Analysis
• Test / Analysis correlation
• 3D Finite Element Modeling
• With a modular approach
– MATLAB environment
– OpenFEM : Core software for Finite Element
Modeling (co-developed with INRIA)
– FEMlink : Import / export industrial modules
– Runtime SDT : Customized and standalone compiled applications
2
GUI
Script

3. • FEM simulations
• System models (model reduction, state-space, active control)
• Experimental modal analysis
• Test/analysis correlation, model updating
• Necessity: programmatic access to all steps
• Proposed solution: flexible toolbox & custom applications
• Base commercial library : for quality, durability, capitalization
• Consulting/research
Company history : SDT software 1995, SDTools 2001, currently 4 engineers
always been profitable
SDTools core focus
CAD/Meshing
FEM
Simulation
Testing
CATIA, Workbench, …
NASTRAN, ABAQUS, ANSYS,...
Adams, Simpack, Simulink,...
LMS TestLab, ME-Scope, …
Simulation
Validation
3

4. AD SANDVIK COROMANT , AEROSPATIALE MATRA AIRBUS, AEROSPATIALE MATRA LANCEURS, AFIT ENY, ALCANTAR & BROWN , Agency for Defence Development, Alenia
Aeronautica, Finmeccanica, Arnold Air Force Base, Aérospatiale Matra Lanceurs, BAE Systems, BBN Technologies, BOFORS SA , BOSCH SYSTEMES DE FREINAGE S.A.S, Bassin d'Essai
des Carènes, Boeing Space and Communications, Bridgestone/Firestone, Bruel & Kjaer, CAMBRIDGE CONTROL Ltd, CCS Informationssysteme GmbH, CERN, CETIM, CIRA, CNAM, CNR -
ITESRE, CNR ITIA, CNRS - GDR Vibroacoustique, CNRS - L.M.A., CNRS LULI, CSIR - defencetek, Case Western R. University. , Ceanet, Centro Ricerche Fiat, Centro de Investigacicon
Cientifica de Yuca..., Chalmers University of Technology, Cybernet Systems Co., Ltd., Czech TU, D.I.C.E Tokyo Denki University , DALHOUSIE UNIVERSITY, DISAT Università
dell'Aquila, DISTART, DLR, DLR e.V., DORNIER LUFTFAHRT, DORNIER SATELLITENSYSTEME Gmbh, Daewoo Shipbuilding & Marine Engineering Co., Ltd., DaimlerChrysler AG, Deh Yu
College of Nursing & Mgmt, Denel Aviation, Det Norske Veritas, Technical Consulting, Deutsche Bahn AG, EADS LV, ECOLE CENTRALE DE LYON, ECP, EDF, EDF , EDF - POLE
INDUSTRIE, EMBRAER, ENSAM - CER FRANCO - ALLEMAND , ENSIB, ENSIM- UNIVERSITE DU MAINE, ENSTA, Ebara Research Co, Ltd, Ecole Centrale de Lille, Ecole Centrale de
Lyon, Eindhoven University of Technology, Elliptec Resonant Actuator AG, Elliptec co. Siemens, Etablissement Technique de Bourges, F.G. UNIVERSIDAD POLITECNICA MADRID, FH
AALEN, FH Wilhelmshafen, FORSCHUNGSZENTRUM KARLSRUHE , FUNDACION GENERAL DE LA UNIVERSIDAD POLITECNICA, Fachhochschule Aalen, Fachhochschule Braunschweig
/ Wolfenb|ttel, Fairchild Dornier GmbH, Ford Motor Company, Fugro Geotechnical Services (HK) Ltd, Hutchinson SA, IABG gmbh, IFMA, INGEMANSSON TECHNOLOGY , INRETS,
INRIA, INSA Lyon, INSA Rouen, INSA de Lyon, INSTITUT PASTEUR, IPSE, IRCAM, ISVR, Imperial College, Institute for Defense Analyses, Institute of Advanced Computing ,
Instituto Tecnológico de Aeronáutica-CTA, JPL, JRC ISPRA, KAIST, KOYO SEIKO CO.,LTD., KUL, KUL - BWK, Kaist University, Kanagawa Institute of Technology, Kanazawa Univ.,
Kurashiki Kako Co., Ltd., Kwangju Institute of Science and Technology, Kyoto Univ., Kyoto Univ. , L.C.P.C. NANTES, LASPI, LCPC, LEIBNIZ-RECHENZENTRUM , LMT, LNE, LOCKHEED
MARTIN MISSILE & SPACE CO, LRBA, LTH, Lund University, Laboratory for Experimental Audiology, Lawrence Livermore national Laboratory, Lockheed Martin Aeronautics Co, Lucent
Technologies - Bell Laboratories, MDI, MPI für Mathematik, Magnecomp Corp., Meiji University, School of Science and Tec..., Military University of Technology, Mitsubishi Electric
Corporation, Morgan State University, NASA Ames Research Center, NASA Goddard Space Flight Center, NASA Langley Research Center, NASA Marshall Space Flight Center, NEC,
NSWCCD, Nanjing University of Aeronautics & Astronautics, Nanyang Technological University, National Technical University of Athens, Naval Air Warfare Center Aircraft Division,
Nihon Univ., Northwestern University, ONERA, ONT, OPGRAMAMOWANIE NAUKOWO-TECHNICZNE, ORBITAL, ORBITAL SCIENCES CORPORATION , Oak Ridge National
Laboratory, Ono Sokki Co., Ltd., POLISH ACADEMY OF SCIENCES, PRODERA, PSA Peugeot Citroën, Pennsylvania State University, Pirelli Informatica Sistemi Informativi Ricerca e
Sviluppo, Politecnico di Bari, Progettazione e Produzione, Politecnico di Torino, Politecnico di bari Vie e Trasporti, Politecnico di torino, Pratt & Whitney, Pratt & Whitney Aircraft,
RENAULT VI, RENSSELAER POLYTECHNIC INSTITUTE, RWTH Aachen, Renault Sport, Rolls-Royce Marine Power, Ruhr- Universität Bochum, SANDIA NATIONAL LABORATORIES,
SCHENCK PEGASUS GMBH, SCHOOL OF ELECTRONIC & ELECTRICAL , SECOND SOURCE ELECTRONIC INC, SEGIME, SEP EC, SERAM - ENSAM, SILESIAN TECHNICAL
UNIVERSITY, SKF E&R Center, SMC Corporation, SNAMProgetti, SNCF, SNECMA, SSPA Sweden AB, STANDARD PRODUCTIONS LIMITED, Saarland University, Sandia National Lab,
Sandia National Laboratories, School of Mechanical, Materials, Manufacturing Engineering and Management, Shneider Electric, Siemens A&D, Siemens PL, Sony Corp., Southern Illinois
University, TECHNICAL UNIVERSITY BRATISLAVA , TECHNICAL UNIVERSITY OF ZIELONA GORA , TNIT, TNO TPD - TU Delft, TNO-Building and Constructions Research, TRW
Lucas Aerospace, TU Berlin, TU Braunschweig, TU Braunschweig, IWF, TU Chemnitz , TU Cottbus, TU Darmstadt, TU München, Takaoka Electric MFG Co, Ltd, Technical University of
Szczecin, Technion, Technische Universitaet Clausthal, Technische Universitaet Hamburg-Harburg, The MathWorks GmbH, The MathWorks, Inc., Tokyo Electric Power Svcs Co Ltd,
Toshiba Corp., UDS Ancona, UDS Catania, UDS Ferrara, UDS Genova, UDS Lecce, UDS Modena e Reggio Emilia, UDS Padova, UDS Pisa, UDS Roma, UDS Roma, Aerospaziale, UDS Trento,
UDS Trieste, UDS Trieste, Energetica, UNIV. CLAUDE BERNARD LYON 1, UNIVERSIDAD DE OVIEDO, UNIVERSITE DE REIMS , UNIVERSITE DE TOURS, UNIVERSITY OF
BIRMINGHAM, UNSW, UPMC Paris 6, UTRC, Univ. of Shiga Prefecture; The, Universidad Politecnica de Cartagena, Universidad del País Vasco, Universidade de Aveiro, Universitaet
Bremen, Universitaet Stuttgart, Universitaet Wuppertal, Universite De Marne La Vallee, Universite Libre de Bruxelles, University of Bristol, University of Central Florida, University of
Liverpool; The, University of Mississippi, University of Missouri Rolla, University of Pretoria, University of Queensland, University of Sheffield, University of Sheffield; The, University
of Southampton, University of Stellenbosch, University of Thessaly, University of Tokyo; The, University of Wales Swansea, Università di Roma La Sapienza, Universität GH Siegen,
Universität Hannover, Universität Kassel, Universität Weimar, Université de Reims Champagne Ardenne, Université de Valenciennes, Université du Littoral Côte d'Opale, VALEO
SYSTEME D'ESSUYAGE, VATTENFALL Data AB, VTT Manufacturing Technology, Vibration & Sound Solutions Limited, Virginia Tech, Volvo Trucks of North America, Inc., WICHITA
STATE UNIVERSITY, Yamaha Corporation, ZVVZ a.s., enea, takumi kenthiku kouzou kenkyusyo, …
Thanks to …

5. Outline
• Presentation of SDTools
EMA tutorial in d_training
Classical identification in SDT
Next
• Topology correlation
• Shape correlation
• Expansion
5

6. EMA
Quality
𝜆𝑗, 𝑐𝜓𝑗
Test
Mode
Computation
Obs. at
sensors
𝜔 𝑘, 𝜓 𝑘
FEM
𝜔 𝑘, 𝑐 𝜓 𝑘𝜆𝑗, 𝑐𝜓𝑗 , Qual
MAC
Expansion
Remove
Re-
measure
Model
updating
Test side : How to improve the identification quality ?
Model side : How to update the model ?
Evaluate the correlation quality
What and where are the sources of poor correlation ?
Correlation procedure

7. Opening data
7
• Geometry & transfers from uff file DbTest.unv
• Matlab LMS, Polytec, PAK, … (OpenODS soon)

8. Defining data
8
Define identification options :
• Complex modes from pole/residue model
• Acceleration/force
• High and low residual terms (1 1/s²)
• Roaming hammer -> PermuteIO

9. Stabilization diagram
9
High modal density : sequential LSCF by band
• Bandwidth : 1000Hz
• Band and study : 200-4000Hz
• Model order 100
Play with stabilization tolerance and extract automatically

10. Peak-picking (e button)
10
Some modes are missing
Local identification of missing poles

11. Modeshapes and quality
11
Quality : assists navigation through data, evaluate identification results
Sort modes & channels with error, contribution, MPC and NOS criteria.

12. AutoMAC
12
All shapes are independent : there are no “blocks” in the AutoMAC

13. SVD : MIMO detection of shape
13
3 shapes in the band
Next is 2.2%

14. Hybrid test & FEM
Identification error
• Noisy measurements
• Identification bias
• NL, time varying, …
14
FEM error
•Geometry
•Material paramete
…
Correlation = distance between test & FEM
Updating = estimate parameters using correlation
Expansion = estimate all DOF knowing test and model
Topology correlation= observe FEM @ sensors

15. Basic topology correlation process
15https://youtu.be/mDmAGskP1Zg

16. Topology correlation process
• Initial orient (coarse)
• Give reference points & reposition
• Optimize orientation to minimize distance
• Analyze errors
16

17. Basic shape correlation
17
https://youtu.be/tVV-R2r-3M8

18. MAC & sensors : MACCo variants
MACErr : Ignore sensors with bad
identification
MACCo : sort sensors by impact on MAC
Removed sensors may indicate
• Bad measurements
• Model errors
18

19. Family : FEM with updated geom.
Parameters : mat/junction
Data : test modes
Objective function Jfreq-MAC
Associated problems
• Mixed quantity (scaling)
• Jumps on mode pairing
• Sensitive range
• Parameter choice
Updating : freq-MAC objective
Data
Family of models
Objective
function
Optimization
Parameters
19

20. Expansion / hybrid models
20
Residuals for test and model error
- =
Test error:
Reverse sensor direction
Model error:
coupling stiffness
𝑐 𝜙 − 𝑦 𝑇𝑒𝑠𝑡 = 𝜖 𝑇𝑒𝑠𝑡
𝑅 𝐿 = 𝐾 − 𝜔𝑗
2
𝑀 𝜙 ≠ 0
𝑅 𝐷 = 𝐾 −1 𝑅 𝐿
Load residual
Displacement residual

21. MDRE : multi-objective cost function
21
Test error Model error
𝜖 𝑇𝑒𝑠𝑡
= 𝑐 𝜙 𝑒𝑥𝑝 − 𝑦 𝑇𝑒𝑠𝑡
𝑅 𝐿 = 𝐾 − 𝜔𝑗
2
𝑀 𝜙 𝑒𝑥𝑝 ≠ 0
𝜖 𝑀𝑜𝑑 = 𝐾 −1 𝑅 𝐿 𝐾
𝐽(𝜙 𝑒𝑥𝑝) = 𝜖 𝑇𝑒𝑠𝑡(𝜙 𝑒𝑥𝑝) 𝛾 + 𝜖 𝑀𝑜𝑑(𝜙 𝑒𝑥𝑝) multi objective cost function

22. Expansion : robust to model error
22
True
Coupling stiffness
Robustness band
Softer coupling Stiffer coupling

23. = +
Model error = clues for parameterization
23
Model error concentration at
sensors
Decoupling model error on
• Model modes
• Enrichment
Concentration of
model error close
to the coupling
Model error : guides model parameterization
Test error : can be used to locate poor sensors

24. Expansion : an old method with renewed interest
Early work : Ladeveze 72 -> [1] present
Independent start : Balmes [2] 00 -> present
Not much used for 40 years due to computation challenge (see [3])
Renewed interest at SDTools (last 3 years) due to reduction
• Modes / multi-model + sens 𝐾 −1[𝑏]
• A few thousand DOF, a few seconds per point
Potential uses
• Updating
• Frequency domain
structural dynamics modification [4]
• Time domain (extended Kalman Filtering)
[1] Deraemaecker, A., Ladevèze, P., Leconte, P. Reduced bases for model updating in structural dynamics based on constitutive relation error. computer methods in
applied mechanics and engineering. CMAME 2002
[2] E. Balmes, « Review and Evaluation of Shape Expansion Methods », IMAC, p. 555-561, 2000.
[3] N. Nifa, « Solveurs performants pour l’optimisation sous contraintes en identification de paramètres », Ph.D. thesis, Université Paris-Saclay, 2017
[4] M. Corus, « Amélioration de méthodes de modification structurale par utilisation de techniques d’expansion et de réduction de modèle. », ECP, 2003.

25. Summary : hybrid test/FEM
• With enough sensors (extreme case field measurement)
• Reasonable match between model and reality (LTI, no local modes, …)
… updating (=parametric identification) works
If it does not, don’t throw the model away
• Lots of things will never be measured : hidden faces, internal loads, …
• Many can be estimated even with somewhat wrong model
• Hybrid models have used efficiently for decades
• Reduction extends usability to vibration problems
“Digital twin” is the current hype keyword for this old idea
25