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Research Papers

# A Model Updating Technique Based on the Constitutive Relation Error for In Situ Identification of Admittance Coefficient of Sound Absorbing Materials

[+] Author and Article Information
Aurélie Progneaux

Building, Architecture and
Town Planning Department,
Université Libre de Bruxelles,
Avenue F.D. Roosevelt, 50 CP 194/02,
Bruxelles 1050, Belgium
e-mail: aprognea@ulb.ac.be

Philippe Bouillard

Professor
Building, Architecture
and Town Planning Department,
Université Libre de Bruxelles,
Avenue F.D. Roosevelt, 50 CP 194/02,
Bruxelles 1050, Belgium
School of Engineering,
Nazarbayev University,
Kabanbay Batyr Avenue 53,
Astana 010000, Kazakhstan
e-mail: philippe.bouillard@ulb.ac.be

Arnaud Deraemaeker

Professor
Building, Architecture
and Town Planning Department,
Université Libre de Bruxelles,
Avenue F.D. Roosevelt, 50 CP 194/02,
Bruxelles 1050, Belgium

For i = 1,...,$Nsens$ and $j=1,...,Ntot$ ($Nsens$ is the number of sensors, and $Ntot$ is the number of degrees-of-freedom).

The value of the measurements is multiplied by $(1-β)$, with $β=50%$, at each frequency.

All the estimators are computed on the frequency range.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 30, 2014; final manuscript received May 18, 2015; published online June 15, 2015. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 137(5), 051013 (Oct 01, 2015) (14 pages) Paper No: VIB-14-1031; doi: 10.1115/1.4030662 History: Received January 30, 2014; Revised May 18, 2015; Online June 15, 2015

## Abstract

The development of new absorbing materials and the description of their acoustical properties take an important place in the current acoustical researches. This paper focuses on the identification of the admittance coefficient of sound absorbing material from in situ measurements, using the constitutive relation error (CRE)-based updating technique. This technique consists of a two-stage approach, allowing to regularize the inverse problem. Moreover, the technique allows the detection of faulty sensors and therefore the correction of the erroneous measurements before the updating process. The technique is developed, in a first part of this paper, for acoustical problems with generalized boundary conditions, and illustrated, in a second part, on a numerical and a physical two-dimensional (2D) test case.

## Figures

Fig. 1

Acoustical problem

Fig. 3

2D car cabin mesh

Fig. 2

Schema of a loudspeaker

Fig. 4

Distribution of the local indicator: localization of defective sensors

Fig. 5

Evolution of ξ and η as a function of the weighting parameter r for the initial value of the parameters

Fig. 11

Pressure at the 28th node

Fig. 6

An,1 versus frequency

Fig. 7

An,2 versus frequency

Fig. 8

An,3 versus frequency

Fig. 9

An,4 versus frequency

Fig. 10

v¯n,1 versus frequency

Fig. 12

Kundt's tube

Fig. 15

Mesh of the Kundt's tube

Fig. 16

Measured pressure at x=0.105 m for the foam

Fig. 17

Measured pressure at x=0.205 m for the foam

Fig. 18

Measured pressure at x=0.105 m for the felt

Fig. 19

Measured pressure at x=0.205 m for the felt

Fig. 13

Fig. 14

Fig. 22

Measured transfer function for the foam

Fig. 23

Measured transfer function for the felt

Fig. 24

Fig. 25

Fig. 26

Pressure at x=0.105 m for the foam

Fig. 27

Pressure at x=0.205 m for the foam

Fig. 28

Pressure at x=0.105 m for the felt

Fig. 29

Pressure at x=0.205 m for the felt

Fig. 20

Normal component of the velocity for the foam

Fig. 21

Normal component of the velocity for the felt

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