field reconstruction by inverse methods in acoustics and ... · jva, 137(2), 2015 . forget s.,...
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Field reconstruction by inverse methods in acoustics and vibration N. Totaro, Q. Leclère, J.L. Guyader
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Lyon
We are here Solar map in France
French riviera
Paris
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Lyon
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Laboratoire Vibrations Acoustique
http://lva.insa-lyon.fr
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One of the biggest Engineering School in France
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Full professors 4
Assistant professors 11
PhD Students 30
Post-doc 5
50 Research staff
Research staff
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Structural acoustics
4 research area
Noise and vibration Perception
Non destructive
testing
Source Identification Inverse methods
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Experimenta facilities
Large anechoic chamber
Large reverberant room
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8 Engine test benches
Experimenta facilities Hydraulic pump
test bench
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Experimenta facilities Audimetric
room for jury testing
US and RX facilities
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Field reconstruction by inverse methods in acoustics and vibration N. Totaro, Q. Leclère, J.L. Guyader
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Inverse methods Source fields reconstruction using acoustic measurements
Both ! Local identification of Young Modulus and damping
Structural excitation field reconstruction
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Inverse methods Source fields reconstruction using acoustic measurements
Both ! Local identification of Young Modulus and damping
Structural excitation field reconstruction
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Physical phenomenon
Causal factors (sources)
Model
Model characterization: Causal factors + phenomenon = model
Direct problem : causal factors + model = phenomenon
Inverse problem: phenomenon + model = causal factors
? ? ?
Definition of inverse problem : An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them
Inverse methods
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Inverse methods Source fields reconstruction using acoustic measurements
Both ! Local identification of Young Modulus and damping
Structural excitation field reconstruction
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Let’s imagine a real 3D structure If the structure is excited, it vibrates…
and makes noise…
(Normal velocity map)
Source field reconstruction using acoustic measurements
Inverse method ? Find the velocity field by measuring the radiated pressure
(Pressure field)
Direct simulation ? Compute the radiated pressure knowing the velocity field
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Source field reconstruction using acoustic measurements
In acoustics, the best known techniques are based on Near-field Acoustic Holography (NAH)
Advantages: Uses a simple experimental device (array of microphones), low computational cost
Drawbacks: Limited to reconstruction on simple geometries (planes); dependent on the acoustic environment
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Source field reconstruction using acoustic measurements
How to develop a new acoustic inverse method ?
able to handle complex 3D geometries
Intrinsically independent of the acoustic environment
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Green’s identity on a volume Ω:
‘’
‘’
‘
‘
Data in the volume Data on the boundary surfaces
Ψ and Φ can be arbitrary functions (continuous and twice differentiable)
… so let’s choose !
Source field reconstruction using acoustic measurements
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Choice of arbitrary functions Ψ and Φ
Classically (in acoustic radiation problem) Ψ is the pressure p(N) in the volume Ω
It verifies the Helmholtz’ equation and the Euler equations on boundary surfaces:
Euler equations
Source field reconstruction using acoustic measurements
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Choice of arbitrary functions Ψ and Φ
For Φ, we want to choose a mode φn(N) of the virtual cavity Ω. This mode respects the Helmholtz’equation:
And the boundary conditions are… arbitrary !
φn(N) is an orthonormal basis of functions. The real pressure p(N) can be expressed as a summation of these functions:
Source field reconstruction using acoustic measurements
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Using the real and the associate problem in the Green’s identity:
The integrals can be replaced by sums (division of the surfaces into patches):
And for several points in the virtual cavity:
virtual cavity
(in a matrix form)
One choice for the BC of the function Φ can be :
BC : « blocked »
- Blocked on the vibrating surface Σ - Blocked on the rigid surface Σ’
BC : « open »
- Open on the virtual surface Σ’’
Source field reconstruction using acoustic measurements
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And by inverting the problem, the patch velocities on surface Σ are:
Unknowns measured measured Computed Computed
virtual cavity
Model
Finite elements Measurements
To sum up: -1
As usual in inverse problems, the matrix to be inverted is ill-posed and the inversion needs a regularization step
Source field reconstruction using acoustic measurements
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A car engine excited by an
electrodynamic shaker Acoustic measurements 23 23
Source field reconstruction using acoustic measurements
Source field reconstruction using acoustic measurements Real experimental test
Setup
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We have defined a virtual surface surrounding the source
We want to reconstruct the velocity field on the surface of the engine
Ok, maybe on that coarse surface it will be ok
and we have divided it into « patches »
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Real experimental test
Definition of the virtual cavity
Source field reconstruction using acoustic measurements
and the pressure has been measured
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Direct numerical simulation (frequency response)
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Bottom view
Top view
Inverse reconstruction with real measurements
Model updating is possible using results of the inverse approach
Real experimental test Source field reconstruction
using acoustic measurements Results
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Source fields reconstruction using acoustic measurements Structural excitation field reconstruction Both ! Local identification of Young Modulus and damping
Inverse methods
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Structural excitation field reconstruction
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The objective is here to use vibration of the structure to identify the structural excitation field
Laser with scanning head
…that can be approximated by a finite difference scheme
The deflection of the plate is driven by the equation of motion :
Objective :
The pressure at one point is obtained measuring the deflection at 13 points
The method is local and does not depend on boundary conditions The equation of motion of the structure is needed
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Source of vibration
Defect on the structure
Structural excitation field reconstruction
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Source fields reconstruction using acoustic measurements Force distribution Both ! Local identification of Young Modulus and damping
Inverse methods
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F
Is it possible to combine NAH and Force Analysis Technique ?
The plate velocity field is reconstructed using NAH (velocity-velocity NAH)
The identified velocity field is used as an input to Force Analysis Technique
5cm
pU probe Microflown
Both !
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F
The plate velocity field is reconstructed using NAH (velocity-velocity NAH)
The identified veloicty field is used as an input to Force Analysis Technique
NAH FAT
Both !
Is it possible to combine NAH and Force Analysis Technique ?
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Both !
From laser measurements From acoustic measurements
1 cm 5 cm
Experimental setup
Comparison of the classical approach with vibratory measurements and the FAT/NAH approach with acoustic measurements
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Source fields reconstruction using acoustic measurements Force distribution Both ! Local identification of Young Modulus and damping
Inverse methods
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Locally, in zones where no force applies, the equation of motion should be equal to zero
Identification of the equivalent complex Young Modulus
Force Analysis Technique on non-excited zones
Local identification of Young Modulus and damping
This property can be used to deduced the complex Young Modulus
Real part Imaginary part
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Thank you for your attention
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References
Totaro N., Vigoureux D. , Leclère Q., Lagneaux J., Guyader J.L., Sound fields separation and reconstruction of irregularly shaped sources, JSV, 336, 2015.
Pézerat C., J.L. Guyader, Force Analysis Technique: Reconstruction of force distribution on plates, Acta Acustica 86, 2000.
Pézerat C., Leclère Q., Totaro N., Identification of vibration excitations from acoustic measurements using near-field acoustic holography and the Force Analysis Technique, JSV, 326, 2009.
Leclère Q., Ablitzer F., Pézerat C., Practical implementation of the corrected Force Analysis Technique to identify the structural parameter and load distributions, JSV, accepted for publication.
Vigoureux D. , Totaro N., Lagneaux J., Guyader J.L., Inverse Patch Transfer Functions method as a tool for source field identification, JVA, 137(2), 2015.
Forget S., Totaro N., Guyader J.L., Schaeffer M., Source fields reconstruction on a 3D structure in noisy environment, Proceedings of NOVEM 2015, 2015.
Source field reconstruction using acoustic measurements
Structural excitation field reconstruction
Structural excitation field reconstruction
Both !
Local identification of Young Modulus and damping