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# Optimization process for correlation of experimental and numerical modal analysis

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### Optimization process for correlation of experimental and numerical modal analysis

1. 1. Optimization process for correlation of experimental andnumerical modal analysisEuropean HyperWorks Technology Conference EHTC 2011November 8th – 9th, 2011, Bonn, GermanyDr.-Ing. Martin H. Müller-Bechtel, Dipl.-Ing. Simon Tschirpke,TECOSIM Technische Simulation GmbH
2. 2. TECOSIM TECOSIM: Facts & Figures  Foundation: 1992 Solutions  Business Area: TECOSIM is Europe’s largest, independent service provider in Computer Aided Engineering (CAE) – Introduction Perspectives the computer-based development and optimization Problem Definition of components, structures and products Analysis  Markets: Original Equipment Manufacturers (OEMs) Discussions and suppliers in following industries Conclusions - automotive - aerospace - chemical - energy - railway - medical …  Vision: Global Leader in Computer Aided Engineering Turn over (Mio. €) Employees 30 28 400 25 22 400 20 300 20 300 240 Forecast 15 12 Forecast 7,7 8,5 200 150 10 6,8 80 90 100 65 5 0 0 2000 2002 2004 2006 2008 2010 2011 2000 2002 2004 2006 2008 2010 2011
3. 3. TECOSIM Problem Definition  Aim: verification of NVH simulation models Solutions  Essential for virtual vehicle development Introduction Perspectives  Complex dependencies to wide range of parameters Problem Definition Analysis Discussions  Method: Usage of optimization for parameter identification Conclusions  Better correlation in less time  Correlation should consider frequency and mode shape:  Relative frequency of simulation mode compared to test  MAC (modal assurance criterion) value for comparison of mode shapes MACi, j       2  ai  b j with ai shape vector of test mode i     ai  ai   b j  b j bj shape vector of sim mode j 4/22
4. 4. TECOSIM Problem Definition  Typical NVH models: coupled structures Solutions  Full vehicle: Introduction modes of suspension, engine Perspectives Problem Definition  Trimmed body: Analysis coupled masses like cooler, battery, or mass damper Discussions  Body in white: Conclusions with elastically connected subframes Full vehicle mode Subframe mode ML BiW with subframe mode 2 5/22
5. 5. TECOSIM Problem Definition  Typical parameters to identify: Solutions  Coupling element stiffness (bushings, engine mount, …) Introduction Perspectives  Joining technique: modeling method dependent properties: Problem Definition glue material stiffness, weld line thickness Analysis  Properties for not exactly known materials like: Discussions fiber reinforced plastics Conclusions  …  Distribution of masses of hang on parts Structural glue Laser weld Weld line 6/22
6. 6. TECOSIM Analysis  Example model: rear subframe out of TEC|BENCH™ process Solutions Introduction Perspectives Problem Definition Analysis Discussions Conclusions Hardware Purchasing NVH testing Scanning rear subframe Geometry data preparation FE modeling FE simulation 7/22
7. 7. TECOSIM Analysis  Example model: rear subframe out of TEC|BENCH™ process Solutions  Initial correlation status: Introduction Perspectives Test 1 2 3 4 5 Problem Definition frequency 72.00 102.06 173.97 181.34 213.69 Analysis correlation status 3 3 0 0 2 Discussions MAC value 0.99 0.99 0.30 0.38 0.85 rel. Frequency 97% 103% 1% 141% 86% Conclusions sim 7 70.05 3 0.994 0.000 0.001 0.016 0.097 8 105.36 3 0.000 0.993 0.288 0.171 0.012 9 139.63 0 0.044 0.000 0.000 0.013 0.673 10 140.09 0 0.267 0.001 0.008 0.006 0.008 11 184.02 2 0.001 0.008 0.011 0.011 0.855  Nearly perfect match for 1st and 2nd mode (MAC > 0.99)  Reduced frequency for 5th mode (mass damper effect)  Parameters to identify:  Bushing stiffness  Distribution of masses inside rubber bushings 8/22
8. 8. TECOSIM Analysis  Example model: rear subframe out of TEC|BENCH™ process Solutions  Criterion for correlation considers frequency AND mode shape: Introduction  MAC value for comparison of modePerspectives shapes Problem Definition  Relative frequency of simulation mode compared to test Analysis 1.2 Discussions Fi,j penalty function with gradient 1 Conclusions to correlation window ±5% 0.8 0.6 mid section uses Runge function 0.4 0.2 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8  Correlation criterion: Test 1 2 3 4 5 frequency 72.00 102.06 173.97 181.34 213.69 Fi,j·MACi,j correlation status 3 3 0 0 0 MAC value 1.03 1.02 0.05 0.12 0.58 frequency filtered rel. Frequency 97% 103% 61% 141% 86% MAC value sim 7 70.05 3 1.029 0.000 0.000 0.000 0.001 8 105.36 3 0.000 1.021 0.048 0.024 0.001 9 139.63 0 0.004 0.000 0.000 0.006 0.151 10 140.09 0 0.023 0.000 0.004 0.002 0.002 11 184.02 0 0.000 0.001 0.011 0.011 0.577 9/22
9. 9. TECOSIM Analysis  Example model: rear subframe out of TEC|BENCH™ process Solutions  Correlation criterion considers best matching simulation mode: Introduction Perspectives  For each test mode take Test 1 2 3 4 5 Problem Definition the best matching frequency 72.00 102.06 173.97 181.34 213.69 Analysis simulation mode: correlation status 3 3 0 0 0 Discussions MAC value 1.03 1.02 0.05 0.12 0.58 maxfMACi = Conclusions max(Fi,j·MACi,j) rel. Frequency sim max 97% 103% 61% 141% 86% 7 70.05 3 1.029 0.000 0.000 0.000 0.001 8 105.36 3 0.000 1.021 0.048 0.024 0.001 9 139.63 0 0.004 0.000 0.000 0.006 0.151  Optimization objective: 10 140.09 0 0.023 0.000 0.004 0.002 0.002 11 184.02 0 0.000 0.001 0.011 0.011 0.577  Maximize correlation of best matching simulation Test 1 2 3 4 5 modes for all test modes frequency 72.00 102.06 173.97 181.34 213.69 correlation status 3 3 0 0 0 maximize  max fMACi MAC value rel. Frequency Σ 1.03 1.02 97% 103% 0.05 0.12 61% 141% 0.58 86% sim 7 70.05 3 1.029 0.000 0.000 0.000 0.001 8 105.36 3 0.000 1.021 0.048 0.024 0.001 9 139.63 0 0.004 0.000 0.000 0.006 0.151 10 140.09 0 0.023 0.000 0.004 0.002 0.002 11 184.02 0 0.000 0.001 0.011 0.011 0.577 10/22
10. 10. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: TCL programming Introduction Perspectives  Implementation of test data: Problem Definition Analysis  Reading test data file in csv format Discussions  Measurement point IDs (9)  Node IDs  Nodes SET Conclusions  Test modes (5): Frequency  DTABLE entry (5)  Test modes (5): shape vectors (27)  DTABLE entries(135) Test 1 2 3 4 5 Frequency 72.00 102.06 173.97 181.34 213.69 amplitude 0.91433 0.68783 0.56059 0.67002 0.69682 Shapes 1 0.24282 0.03218 -0.01758 0.01333 2.76E-01 0.46801 -0.03529 0.00371 -0.02999 4.48E-01 -0.01334 -0.31399 -0.27625 0.18199 -2.65E-02 2 0.04657 0.07936 0.02257 0.00164 2.01E-02 0.25833 -0.01541 0.02229 -0.03488 1.57E-01 -0.00081 -0.12870 -0.31011 0.34853 6.06E-04 3 -0.08430 0.08442 0.17604 -0.16444 -1.70E-01 0.00066 0.05959 0.00033 0.00534 -7.23E-02 11/22
11. 11. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: TCL programming Introduction Perspectives  Response definition for simulation modes: Problem Definition Analysis  EIGRL card with fixed number of modes (15) Discussions  Simulation modes (15): Frequency  DRESP1 entry (15) Conclusions  Simulation modes (15): shape vectors (27)  DRESP1 entries (405) Δ Mode specific displacement response not supported by OptiStruct! Solver switched to NASTRAN Δ Mode specific displacement response not defined in NASTRAN template! Direct programming of NASTRAN code (replacement.nas) referencing replacement.nas in bulk unsupported section moving of DRESP1 to separate include (waste_basket.nas) 12/22
12. 12. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: TCL programming Introduction Perspectives  Calculation of single frequency filtered MAC: Problem Definition Analysis  Definition of DEQATN DEQATN 2 f( Discussions  Parameters out of DTABLE: + t001x,t001y,t001z, + Conclusions Test shape (27), test freq (1) + t009x,t009y,t009z, + T,  Parameters out of DRESP1: + s001x,s001y,s001z, sim shape (27), sim freq (1) + + s009x,s009y,s009z,  Equation for MAC calculation + S)=(( + t001x*s001x+t001y*s001y+t001z*s001z+ + + t009x*s009x+t009y*s009y+t009z*s009z + )**2/((  Frequency filtered MAC + t001x*t001x+t001y*t001y+t001z*t001z+ test (5) vs. simulation (15): + + t009x*t009x+t009y*t009y+t009z*t009z + )*( Fi,j·MACi,j  DRESP2 (75) + s001x*s001x+s001y*s001y+s001z*s001z+ + + s009x*s009x+s009y*s009y+s009z*s009z + ))) + *MIN((S/(0.95*T))**4,(T/(0.95*S))**4, + 0.2+0.85/(1.+25.*(S/T-1.)*(S/T-1.))) 13/22
13. 13. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: TCL programming Introduction Perspectives  Selection of best correlating sim mode for each test mode: Problem Definition DEQATN 4 f( Analysis  Definition of DEQATN + m1, + Discussions  Parameters out of DRESP2: + m15, Conclusions test mode related simulation + )= + Max( mode filtered MACs (15) + m1, +  Selection of maximum MAC + m15, for each test mode  DRESP2 (5) + ) ΔDRESP2 referencing DRESP2 not supported by NASTRAN template NASTRAN template modified with specific section out of OptiStruct template 14/22
14. 14. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: TCL programming Introduction Perspectives  Sum of best correlating frequency filtered MAC values: Problem Definition Analysis  Definition of DEQATN DEQATN 3 f( + m1, Discussions  Parameters out of DRESP2: + + m5 Conclusions maximum MAC for each + )= test mode (5) + m1+ +  sum of maximum MAC + m5 for each test mode  DRESP2 (1) ! DRESP2 referencing DRESP2 now supported by modified NASTRAN template  Definition of design objective  Sum of maximum MAC  DESOBJ(MAX) (1) 15/22
15. 15. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: manual definition Introduction Perspectives  Request for optimization output: Problem Definition Analysis  Output of responses restricted to frequency and best correlating filtered MAC  DSAPRT (1) Discussions Conclusions Δ DSAPRT not supported by HyperWorks Manual definition in unsupported section  Definition of responses for output  SET (1) Δ SET of responses not supported in NASTRAN template Manual definition in unsupported section 16/22
16. 16. TECOSIM Analysis  Setup of optimization process in HyperWorks Solutions  Method used: manual definition Introduction Perspectives  Problem specific definition of design variables: Problem Definition  Stiffness of front/rear bushing 6DOF  DESVAR (12) Analysis Discussions  Stiffness of rubber bands 3DOF  DESVAR (3) Conclusions  PBUSH-property relations  DVPREL (15) Δ DVPREL for PBUSH not supported by NASTRAN Template  Direct definition of NASTRAN cards (replacement.nas) moving of DVPREL to separate include (waste_basket.nas)  Mass distribution for bushing bolts  DESVAR (4)  PMASS-propery relations  DVPREL (4) Δ DVPREL for PMASS not supported by NASTRAN Template  Direct definition of NASTRAN cards (replacement.nas) moving of DVPREL to separate include (waste_basket.nas) 17/22
17. 17. TECOSIM Analysis  Example model: rear subframe out of TEC|BENCH™ process Solutions  Optimized correlation status: Introduction Test 1 2 3 4 5 Perspectives frequency 72.00 102.06 173.97 181.34 213.69 Problem Definition Analysis correlation status MAC value 3 0.99 3 0.99 2 0 0.94 0.30 2 0 0.81 0.38 2 0.81 0.85 Discussions rel. Frequency 97% 103% 126% 121% 98% 100% 1% 141% 98% 86% sim Conclusions 7 70.82 70.05 3 0.994 0.000 0.001 0.016 0.096 0.097 8 102.10 105.36 3 0.001 0.000 0.986 0.993 0.311 0.288 0.190 0.171 0.012 9 142.30 139.63 2 0 0.000 0.044 0.709 0.000 0.130 0.000 0.049 0.013 0.010 0.673 10 171.78 140.09 0 0.000 0.267 0.399 0.001 0.019 0.008 0.004 0.006 0.302 0.008 11 173.26 184.02 2 0.023 0.001 0.002 0.008 0.003 0.011 0.011 0.883 0.855 12 193.51 0 0.025 0.006 0.015 0.005 0.290 13 208.92 3 0.024 0.006 0.009 0.009 0.814  Nearly perfect match for 1st and 2nd mode (MAC ~ 0.99)  Improved match of frequency and shape for 5th mode (mass damper effect)  Parameters identified:  Bushing stiffness  Distribution of masses inside rubber bushings 18/22
18. 18. TECOSIM Discussions  How does HyperWorks support the process? Solutions  All keywords necessary for the process are supported by HyperWorks Introduction Perspectives  Tcl programming interface allows for very efficient setup of a huge Problem Definition number of entities. Analysis  Tcl programming benefits of command logging (used like macro Discussions recording for easy access to command syntax). Conclusions  Different ways of work around  But there is a variety of entities not or not fully supported:  Mode specific nodal displacement response missing in OptiStruct, not supported in NASTRAN template  DRESP2 referring DRESP2 supported in OptiStruct template but not in NASTRAN template (identical syntax)  DVPREL for PBUSH missing in NASTRAN template  SET definition for DRESP entries missing 19/22
19. 19. TECOSIM Conclusions  Definition of a complex optimization process Solutions  Applicable for a wide range of structures Introduction Perspectives  Enabled by HyperWorks using tcl programming Problem Definition Analysis Discussions  But there is room for improvements: Conclusions  More consequent support of NASTRAN keywords DRESP2 (just update the template) DVPREL (add further property types: PBUSH, …) SET (add further types: DRESP, …) 20/22
20. 20. TECOSIM SolutionsIntroduction PerspectivesProblem DefinitionAnalysis Q&ADiscussionsConclusions Thank you! Contact TECOSIM Technische Simulation GmbH Dr.-Ing. Martin Müller-Bechtel Tech. Manager Virtual Benchmarking Ferdinand-Stuttmann-Straße 15 D-65428 Rüsselsheim Phone +49 (0)6142 / 8272-230 Fax +49 (0)6142 / 8272-249 Mail m.muellerb@de.tecosim.com www.tecosim.com 22/22