Field reconstruction by inverse methods in acoustics and vibration N. Totaro, Q. Leclère, J.L. Guyader

Field reconstruction by inverse methods in acoustics and vibration N. Totaro, Q. Leclère, J.L. Guyader

Lyon Paris French riviera Solar map in France We are here 2

3 Lyon

Laboratoire Vibrations Acoustique 4 http://lva.insa-lyon.fr

Research staff One of the biggest Engineering School in France 4 Full professors 50 Research staff 11 Assistant professors 30 PhD Students 5 Post-doc 5

4 research area Structural acoustics Noise and vibration Perception 6 Source Identification Inverse methods Non destructive

Large anechoic chamber Experimenta facilities Large reverberant room 7

Hydraulic pump test bench Experimenta facilities 8 8 Engine test benches

Audimetric room for jury testing Experimenta facilities US and RX facilities 99

Field reconstruction by inverse methods in acoustics and vibration N. Totaro, Q. Leclère, J.L. Guyader

Inverse methods Source fields reconstruction using acoustic measurements Structural excitation field reconstruction Both! Local identification of Young Modulus and damping 11

Inverse methods Source fields reconstruction using acoustic measurements Structural excitation field reconstruction Both! Local identification of Young Modulus and damping 12

Inverse methods 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? Model? Causal factors (sources)? Physical phenomenon Direct problem : causal factors + model = phenomenon Inverse problem: phenomenon + model = causal factors Model characterization: Causal factors + phenomenon = model 13

Inverse methods Source fields reconstruction using acoustic measurements Structural excitation field reconstruction Both! Local identification of Young Modulus and damping 14

Let s imagine a real 3D structure If the structure is excited, it vibrates and makes noise Direct simulation? Compute the radiated pressure knowing the velocity field Source field reconstruction using acoustic measurements (Normal (Pressure velocity field) map) Inverse method? Find the velocity field by measuring the radiated pressure 15 15

In acoustics, the best known techniques are based on Near-field Acoustic Holography (NAH) Source field reconstruction using acoustic measurements 16 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

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 17

Source field reconstruction using acoustic measurements 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! 18

Source field reconstruction using acoustic measurements 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 19

Source field reconstruction using acoustic measurements Choice of arbitrary functions Ψ and Φ For Φ, we want to choose a mode φ n (N) of the virtual cavity Ω. This mode respects the Helmholtz equation: And the boundary conditions are arbitrary! φ n (N) is an orthonormal basis of functions. The real pressure p(n) can be expressed as a summation of these functions: 20

BC : «open» Source field reconstruction using acoustic measurements virtual cavity BC : «blocked» One choice for the BC of the function Φ can be : - Blocked on the vibrating surface Σ - Blocked on the rigid surface Σ - Open on the virtual surface Σ 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: 21 (in a matrix form)

Source field reconstruction using acoustic measurements virtual cavity And by inverting the problem, the patch velocities on surface Σ are: Unknowns Computed measured Computed measured To sum up: Model -1 Finite elements Measurements As usual in inverse problems, the matrix to be inverted is ill-posed and the inversion needs a regularization step 22

Real experimental test Setup Source Source field field reconstruction reconstruction using acoustic measurements using acoustic measurements 23 23 A car engine excited by an electrodynamic shaker Acoustic measurements

Real experimental test Definition of the virtual cavity Source field reconstruction using acoustic measurements We Ok, want maybe to reconstruct that the coarse velocity surface field it on will the be surface ok We have of defined the engine a virtual surface surrounding the source and we have divided it into «patches» and the pressure has been measured 24

Real experimental test Results Inverse reconstruction with real measurements Source field reconstruction using acoustic measurements Direct numerical simulation (frequency response) Bottom view Model updating is possible using results of the inverse approach Top view 25

Inverse methods Source fields reconstruction using acoustic measurements Structural excitation field reconstruction Both! Local identification of Young Modulus and damping 26

Objective : Structural excitation field reconstruction The objective is here to use vibration of the structure to identify the structural excitation field Laser with scanning head The deflection of the plate is driven by the equation of motion : that can be approximated by a finite difference scheme 27 27 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

Structural excitation field reconstruction Source of vibration Defect on the structure 28

Inverse methods Source fields reconstruction using acoustic measurements Force distribution Both! Local identification of Young Modulus and damping 29

Both! 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 F pu probe Microflown 30

Both! Is it possible to combine NAH and Force Analysis Technique? The plate velocity field is reconstructed using NAH (velocity-velocity NAH) The identified veloicty field is used as an input to Force Analysis Technique F FAT NAH 31

Both! Experimental setup Comparison of the classical approach with vibratory measurements and the FAT/NAH approach with acoustic measurements From laser measurements From acoustic measurements 32 1 cm 5 cm

Inverse methods Source fields reconstruction using acoustic measurements Force distribution Both! Local identification of Young Modulus and damping 33

Force Analysis Technique on non-excited zones Locally, in zones where no force applies, the equation of motion should be equal to zero This property can be used to deduced the complex Young Modulus Local identification of Young Modulus and damping Identification of the equivalent complex Young Modulus Real part Imaginary part 34

Thank you for your attention 35

References Structural excitation field reconstruction Source field reconstruction using acoustic measurements Totaro N., Vigoureux D., Leclère Q., Lagneaux J., Guyader J.L., Sound fields separation and reconstruction of irregularly shaped sources, JSV, 336, 2015. 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. Structural excitation field reconstruction Both! 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. Local identification of Young Modulus and damping 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. 36