Field reconstruction by inverse methods in acoustics and ... · JVA, 137(2), 2015 . Forget S.,...

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

http://lva.insa-lyon.fr/



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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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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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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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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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 !


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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


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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:


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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’’


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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


A car engine excited by an

electrodynamic shaker Acoustic measurements 23 23


Source field reconstruction using acoustic measurements Real experimental test

Setup

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


and the pressure has been measured

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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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


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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.




Both !

Local identification of Young Modulus and damping

Field reconstruction by inverse methods in acoustics and ... · JVA, 137(2), 2015 . Forget S.,...

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