Post on 22-May-2020
KU Leuven vibro-acoustics activities in an Industry 4.0 context
Wim Desmet
KU Leuven – Department of Mechanical EngineeringFlanders Make - Virtual Department Mechatronics & Design
overview
• KU Leuven team
• Industry 4.0 - research strategy and approach
• some vibro-acoustic innovations:
o virtual sensing
o “metamaterials by design”
o model based geometry characterisation
o model based material characterisation
www.kuleuven.be
KU Leuven
• founded in 1425
• 70000 students
• 15 faculties, 50 departments
• 62 academic programmes
• 800 MEUR total revenues
who we are
team
• KU Leuven
o Department of Mechanical Engineering• Division of Production engineering, Machine design and Automation (PMA)
• Noise and Vibration Research Group (MOD)
• research staffo 5 academic and 1 associated
o 1 industrial research manager
o 11 postdoctoral researchers
o 61 PhD incl. 10 industrial PhD res.
• areas of research application domainso vibro-acoustics
o aero-acoustics
o multi-body dynamics
o smart system dynamics
o structural reliability & uncertainty
• core lab of the Strategic Research Centre for Smart Manufacturing
(Flanders Make)
- energy and environment
- transport and mobility
- health
- advanced manufacturing
Industry 4.0
enablers
full digitization of the value chain
smart connected customized
cyber-physical systems
Model Based System Engineering
digital twin
Industry 4.0
strategy
creating added value
by embedding dynamic behavior information
in a digital twin
during every phase (design – manufacturing – operations)
approach
physical behaviour models
• vibro-acoustics• (flexible) multibody dynamics • multi-physical mechatronic system models• aero-acoustics
research innovations
• methodological • MBSE applications
model usage
• purely virtual (virtual prototyping)• blended with sensors (virtual sensing)
overview
• KU Leuven team
• Industry 4.0 - research strategy and approach
• some vibro-acoustic innovations:
o virtual sensing
o “metamaterials by design”
o model based geometry characterisation
o model based material characterisation
some vibro-acoustic innovationsmodel based virtual sensing
objectives
• obtain information on hard-to-measure quantities from high-
fidelity first-principles dynamic models, of which the inputs and
parameters are estimated on-line and in-situ using
affordable/non-intrusive sensor data
• to be used in all phase (design – manufacturing – operational
life) of a cyber-physical system
virtual sensingmodels time-stable
estimators
non-intrusive
sensors
HW/SWarchitecture
Naets, F., Croes, J., Desmet, W. (2015). An online coupled state/input/parameter estimation approach for structural dynamics. Computer Methods in Applied Mechanics and Engineering. 283 (1) 1260-1277
Kalman Filter
EKF/UKF
Moving Horizon Estimators
some vibro-acoustic innovationsmodel based virtual sensing
approach
Estimator
Input
hpredicted
xestimated
hestimated
Model
xestimated
Measurements
Kalman filter
hmeasured
some vibro-acoustic innovationsmodel based virtual sensing
approach
some vibro-acoustic innovationsmodel based virtual sensing
approach
some vibro-acoustic innovationsmodel based virtual sensing
objectives
• obtain information on hard-to-measure quantities from high-
fidelity first-principles dynamic models, of which the inputs and
parameters are estimated on-line and in-situ using
affordable/non-intrusive sensor data
challenges
• efficient, time stable physical behaviour models
• observability
approach
• stable observers
• high-fidelity physical behaviour models
• non-intrusive sensors
some vibro-acoustic innovationsmodel based virtual sensing
time-stable coupled vibro-acoustic model order reduction
vibro-acoustic finite element modelvibro-acoustic finite element model
Time-Domain simulation
Time-Domain simulation
Reduced-Order Model
Reduced-Order Model
Xtoo expensive Xstandard MOR:
becomes unstable!Stability-preserving MOR
van de Walle, A., Naets, F., Deckers, E., Desmet, W. (2017). Stability-preserving model order reduction for time-domain simulation of vibro-acoustic FE models. International Journal for Numerical Methods in Engineering. (in press)
some vibro-acoustic innovationsmodel based virtual sensing
time-stable coupled vibro-acoustic model order reduction
��� t + ��� t + � t = �(t)
���� t + ���� t + �� t = ��(t)
n equations in n unknowns
r equations in r unknowns
some vibro-acoustic innovationsmodel based virtual sensing
time-stable coupled vibro-acoustic model order reduction
• coupled vibroacoustic FE system of equations:
is stable!
• MOR:
with reduced matrices
• after projection of K, C and M matrices: partial symmetry and definiteness is destroyed, resulting in a loss of stability
some vibro-acoustic innovationsmodel based virtual sensing
time-stable coupled vibro-acoustic model order reduction
• one-sided projection
• transform into linear descriptor formulation
• stiffness matrices : symmetric positive (semi)definite
• mass matrices : symmetric positive definite
• damping matrices : positive (semi)definite
finite element model reduced-order model
number of DOFs 564 228 260
model reduction time n/a 2,7h
FRF computation time 76,4h 3,6s
some vibro-acoustic innovationsmodel based virtual sensing
time-stable coupled vibro-acoustic model order reduction
some vibro-acoustic innovationsmodel based virtual sensing
validation: (real-time) vibro-acoustic digital twin
some vibro-acoustic innovationsmodel based virtual sensing
validation: (real-time) vibro-acoustic digital twin
Virtual sensing at microphone R2
close-up
some vibro-acoustic innovationsmodel based virtual sensing
validation: (real-time) vibro-acoustic digital twin
Virtual sensing at microphone R2
some vibro-acoustic innovationsmodel based virtual sensing
validation: (real-time) vibro-acoustic digital twin
some vibro-acoustic innovationsmodel based virtual sensing
validation: (real-time) vibro-acoustic digital twin
virtual measurement of plate stiffness
� = �� ��0 ��
estimate scaling factor � on structural stiffness matrix => identify
plate E-modulus
� = ��� ��0 ��
coupling matrix
acoustic stiffness matrix
structural stiffness matrix
some vibro-acoustic innovationsmodel based virtual sensing
validation: microphone based parameter estimation
identified value
initial guess
Computational time ≅ 2 minutes
different start values converge to the same estimate
some vibro-acoustic innovationsmodel based virtual sensing
validation: microphone based parameter estimation
some vibro-acoustic innovationsmodel based virtual sensing
validation: microphone based parameter estimation
overview
• KU Leuven team
• Industry 4.0 - research strategy and approach
• some vibro-acoustic innovations:
o virtual sensing
o “metamaterials by design”
o model based geometry characterisation
o model based material characterisation
some vibro-acoustic innovations“metamaterials by design”
objectives
material systems with good noise and vibration insulation properties
at
o low-mass
o low-volume
o low-frequency
o low-manufacturing cost
approach
• resonant meta-materials
• stopband behaviour at selected design frequencies
+20% mass
(local)
+20% mass
(spread)Target
Frequency [Hz]
AverageDisplacement
[dB]
Propagation Direction
unit cell modelling
Stop Band
some vibro-acoustic innovations“metamaterials by design”
Resonant Inclusions
some vibro-acoustic innovations“metamaterials by design”
12.5 mm12.5 mm
mass
spring
some vibro-acoustic innovations“metamaterials by design”
http://youtu.be/hMCfRHshjXc
some vibro-acoustic innovations“metamaterials by design”
unit cell modelling
Finite structure
modelling
Propagation direction
?
what about• attenuation factors• topology optimisation• sound transmission loss
predictions
some vibro-acoustic innovations“metamaterials by design”
• from classical inverse approach
• to direct solution approach based
on Wave FEM Approach, allowing
o imaginary and real wavenumbers
o and inclusion of damping in materials
L. Van Belle, C. Claeys, E. Deckers, W. Desmet, Modelling, analysis and experimental validation of locally resonant metamaterials including damping, Journal of Sound and Vibration, under review
some vibro-acoustic innovations“metamaterials by design”
unit cell modelling - damping
• density-based topology optimization: single phase layouts
(solid-void) are considered.
o starting from solid plate
o enforcing resonant behaviour
L. Noël, C. Claeys, E. Deckers, W. Desmet, WCSMO 12 (5-9 June 2017, Braunschweig, Germany): Designing metamaterials for enhanced noise and vibration properties.
some vibro-acoustic innovations“metamaterials by design”
unit cell modelling – topology optimization
• hybrid method
o wave based method: acoustic domains
o FEM: structural domain
• predicts absorption and transmission for 2D infinite periodic structures
FEM
WBM
WBM
E. Deckers, S. Jonckheere, L. Van Belle, C. Claeys, W. Desmet, Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based - Finite Element unit cell method Journal of Comp.Physics, under review
some vibro-acoustic innovations“metamaterials by design”
unit cell modelling – sound transmission loss
70 mm70 mm
overview
• KU Leuven team
• Industry 4.0 - research strategy and approach
• some vibro-acoustic innovations:
o virtual sensing
o “metamaterials by design”
o model based geometry characterisation
o model based material characterisation
some vibro-acoustic innovationsmodel based geometrical characterisation
objectives
• dimensional quality control of manufactured structures
through vibro-acoustic testing
approach
• vibro-acoustic models with a direct link to the geometrical
parameters
• vibro-acoustic testing (dynamic input – accelero/mic responses)
• inverse method: retrieve geometrical parameters from dynamic
response measurements
challenge
• isogeometrical analysis models – linking digital geometry with
functional (vibro-acoustic) performance
some vibro-acoustic innovationsmodel based geometrical characterisation
IGA – IsoGeometrical Analysis for vibro-acoustics
design throughanalysis
CAE bottleneck = pre-processing: CAD geometry ≠ CAE geometry
isogeometric: use CAD descriptions directly in CAE
⤷ NURBS for both geometry & field variable
⟹⟹⟹⟹ no meshing
⟹⟹⟹⟹ smoother shape functions
⤷ less numerical dispersion
quadratic splines quadratic polynomials
some vibro-acoustic innovationsmodel based geometrical characterisation
IGA – IsoGeometrical Analysis for vibro-acoustics
• lack of volumetric discretizations: CAD = object envelope= surface
• complex representations of free-form geometriesNURBS = tensor product ≠ free-form
⤷ free-form CAD = multipatch NURBS
= trimmed
some vibro-acoustic innovationsmodel based geometrical characterisation
IGA – IsoGeometrical Analysis for vibro-acoustics
IGA for vibro-acoustics: main challenges
• Lack of volumetric discretizations: CAD = object envelope= surface
• Complex representations of free-form geometriesNURBS = tensor product ≠ free-form
⤷ free-form CAD = multipatch NURBS
= trimmed
⟹ isogeometric BEM
⟹ multipatch coupling techniques
L. Coox, O. Atak, D. Vandepitte, W. Desmet. An isogeometric indirect boundary element method for solving acoustic
problems in open-boundary domains, Comput. Methods Appl. Mech. Engrg., 316:186-208, 2017.
L. Coox, F. Greco, O. Atak, D. Vandepitte, W. Desmet. A robust patch coupling method for NURBS-based isogeometric
analysis of non-conforming multipatch surfaces, Comput. Methods Appl. Mech. Engrg., 316:235-260, 2017.
Isogeometric BEM: bass-reflex loudspeaker
49
37 NURBS patches72 interfaces
Isogeometric BEM: bass-reflex loudspeaker
50
Isogeometric BEM: bass-reflex loudspeaker
51
2000 Hz
Directivity plot [dB]
1m radius
1000 Hz500 Hz
• to be exploited for geometrical characterization
• to be exploited for dimensional quality control.
some vibro-acoustic innovationsmodel based geometrical characterisation
• starting from a reference CAD model of the component, the
geometry is updated using the information from the
measurements.
• following the framework of IGA shape optimization, the
control points can be directly used as optimization variables.
some vibro-acoustic innovationsmodel based geometrical characterisation
• an optimization problem is solved and the exact geometry can be extracted from the updated IGA model.
• since a high accuracy is required, many control points are used for the optimization and MOR is applied.
some vibro-acoustic innovationsmodel based geometrical characterisation
overview
• KU Leuven team
• Industry 4.0 - research strategy and approach
• some vibro-acoustic innovations:
o virtual sensing
o “metamaterials by design”
o model based geometry characterisation
o model based material characterisation
some vibro-acoustic innovationsmodel based material characterisation
objectives
• retrieving material parameters through vibro-acoustic testing
approach
• vibro-acoustic model including parameterized material models
• vibro-acoustic testing (dynamic input – accelero/mic responses)
• inverse method: retrieve material parameters from dynamic
response measurements
challenge
• efficient vibro-acoustic models for a family of material parameter
values .... parametric Model Order Reduction (pMOR)
parametric Model Order Reduction (pMOR)
o accurate model for large parameter range
o high on-line performance • small reduced order model
• stable
o off-line calculation time is not that important
� goal:
where
some vibro-acoustic innovationsmodel based material characterisation
two main approaches:
1) global basis � and �concatenate the local bases
2) interpolation of local information
local bases or local reduced order matricesp1
p2
p3 ••
••
parametric Model Order Reduction (pMOR)
some vibro-acoustic innovationsmodel based material characterisation
pMOR application – model updatingby parameter optimization
Full order modelDOF : 22904Computational time : 5h
parametric reduced order modelDOF : 180Computational time : 2s
pMOR application – model updatingby parameter optimization
Initial design parameters Optimized design parameters
���� ��0 �� + �� �!� + "����� 0
0 �!� + "��� # �$ !� 0#�%& !�
'( = )�
)�
argmin01,34516(78),34516(98),34516(7:),34516(9:)
log�= > ()?)@A0 # )?)BCD)$BEFGH
IJ�
pMOR application – model updatingby parameter optimization
Matrix-free MOR scheme - Basics
= Reduced Order Modelling scheme to further speed-up FRF calculations
• Iterative Adaptively enriched
• Rational Rational interpolation functions
• Krylov Based on system responses (non-modal)
• Matrix-free No explicit system matrices necessary
= BLACK BOX
, �,� , �,�
Matrix-free MOR scheme – Procedure
1. Get the system transfer functions for the input-output pairs you are interested in, e.g. from LTI formulation:
2. Apply matrix-free formulation of rational Krylov projection to build theROM matrices [∎M]OP using left (i) and right (j) projection vectors
3. Calculate the approximated full system response from the ROM at allfrequencies
4. (Iterative enrichment until convergence)
[Q RS]OP =ωR$HOP ωR #ωS$HOP ωS
ωR$ # ωS$[�Q RS]OP =
HOP ωR # HOP ωSωR$ # ωS$
[VQ R]OP = HOP ωR [WX SY]OP = HOP ωS
HQOP � = HOP ωS #ω$�QOP + QOPZ�HOP ωR
Matrix-free MOR scheme – Application
Plate (0.5x0.25x0.0006m)• Steel
• Boundary condtions
o Symmetry edges (red)
o Clamped edges (green)
• Boundary acceleration
• Center point response
Treatment (0.49x0.34x0.0015m)
• CLD
o 1.373mm soft rubber
o 127µm aluminium sheet)
100 102 104 106103
106
109
Frequency [Hz]
100
102
104
106
0
2
4
Matrix-free MOR scheme – Results
Bare Constr.
# Full DOF 6482 38601
# Iterations 27 11
# Frequencies (red.)
54 22
# Frequencies(full)
999 999
Speed-up 18.5x 45.5x
thank you
Wim Desmet
Celestijnenlaan 300B – box 24203001 Leuven, Belgiumtel +32 16 32 25 57mobile +32 479 531578
wim.desmet@kuleuven.be
www.mech.kuleuven.be/mod