This study presents a detailed investigation of the acoustic performance of roller shutter boxes in the extended position, comprising porous and heavy mass layers. Such configurations are of particular relevance, as roller shutter boxes often represent weak points in the façade sound insulation of residential and office buildings. The Finite Transfer Matrix Method (FTMM) is first employed to model the system, providing a robust description of its acoustic properties, with numerical predictions validated against laboratory measurements. A two-step global sensitivity analysis is then performed to identify the dominant parameters. The Morris method is initially applied to screen mechanical, acoustic, and geometric variables, followed by the computation of Sobol indices to quantify the influence and interactions of the retained parameters. Given the high computational cost of Sobol analysis for complex models, several metamodeling techniques are evaluated, including Polynomial Chaos Expansion, Kriging, and Polynomial Chaos Kriging (PCK). Among these, PCK is shown to provide the most accurate and efficient framework for estimating sensitivity indices. Finally, an optimization procedure based on a genetic algorithm is conducted on the micro-macro model of polyurethane foams, focusing on controllable material parameters. The results emphasize the critical role of the reticulation rate in enhancing the sound transmission loss of extended roller shutter boxes.
SoussiCAucejoMLarbiW, et al. Numerical analyses of the sound transmission at low frequencies of a calibrated insulating glazing unit. Appl Acoust2021; 179: 108065.
2.
PuigJAucejoMDeüJ-F, et al. A hybrid sub-structuring method for prediction of air inlet sound transmission. J Sound Vib2024; 569: 117994.
3.
BakhoucheSLarbiWDeüJ-F, et al. Numerical and experimental investigation of sound transmission through roller shutter boxes. Appl Acoust2023; 214: 109679.
4.
Manguan ChimenoM. Vibro-acoustic analysis of spacecraft structures with thin air layers. Universidad Politécnica de Madrid, 2014.
5.
BakloutiADammakKEl HamiA.Uncertainty analysis based on Kriging meta-model for acoustic-structural problems. Appl Sci2022; 12(3): 1503.
6.
PannetonRAtallaN.Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials. J Acoust Soc Am1996; 100(1): 346–354.
7.
SoussiCAucejoMLarbiW, et al. Numerical analyses of the sound transmission at low frequencies of a calibrated domestic wooden window. Proc IMechE, Part C: J Mechanical Engineering Science2021; 235(14): 2637–2650.
8.
BakhoucheSLarbiWAlouiR, et al. Global sensitivity analysis of sound attenuation in double-wall system with porous layer. Mech Adv Mater Struct2024; 31: 8417–8429.
9.
RhaziDAtallaN.Transfer matrix modeling of the vibroacoustic response of multi-materials structures under mechanical excitation. J Sound Vib2010; 329(13): 2532–2546.
10.
CampolinaBAtallaNDauchezN.Assessment of the validity of statistical energy analysis and transfer matrix method for the prediction of sound transmission loss through aircraft double-walls, Proceedings of the Acoustics 2012 Nantes Conference, Nantes, France, 2012.
11.
CherifRWareingAAtallaN.Sound transmission paths through a statistical energy analysis model of mechanically linked aircraft double-walls. Noise Control Eng J2021; 69(5): 411–421.
12.
RhaziDAtallaN.A simple method to account for size effects in the transfer matrix method. J Acoust Soc Am2010; 127(2): EL30–EL36.
13.
VerdièreKPannetonRElkounS, et al. Transfer matrix method applied to the parallel assembly of sound absorbing materials. J Acoust Soc Am2013; 134(6): 4648–4658.
14.
MorrisMD.Factorial sampling plans for preliminary computational experiments. Technometrics1991; 33(2): 161–174.
15.
Sobol′IM.Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul2001; 55(1–3): 271–280.
16.
BlatmanGSudretB.An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab Eng Mech2010; 25(2): 183–197.
17.
WienerN.The homogeneous chaos. Am J Math1938; 60(4): 897.
KrigeDG.A statistical approach to some basic mine valuation problems on the Witwatersrand. J South Afr Inst Min Met1951; 6(52): 119–139.
20.
MatheronG.Principles of geostatistics. Econ Geol1963; 58(8): 1246–1266.
21.
SacksJSchillerSBWelchWJ.Designs for computer experiments. Technometrics1989; 31(1): 41–47.
22.
SchobiRSudretBWiartJ.Polynomial-chaos-based kriging. Int J Uncertain Quantif2015; 5(2): 171–193.
23.
ChristenJLIchchouMTrocletB, et al. Global sensitivity analysis of acoustic transmission models. In: Presented at the 43rd international congress on noise control engineering, Melbourne, Australia, 16–19 November 2014.
24.
DoutresOAtallaNDongK.A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams. J Appl Phys2013; 113: 054901.
25.
GholamiMSDoutresOAtallaN.Effect of variability in microgeometry of polyurethane foams on their macroscopic acoustic performance. In: Presented at revolution in noise control, Providence, RI, USA, 12–15 June 2016.
26.
CardinaleNRospiGCardinaleT.Numerical and experimental thermal analysis for the improvement of various types of windows frames and rolling-shutter boxes. Int J Energy Environ Eng2015; 6: 101–110.
27.
PatrícioJBragançaL.The contribution of roller shutters to noise insulation of façades. Build Acoust2004; 11(4): 309–324.
28.
DíazCPedreroA.An experimental study on the effect of rolling shutters and shutter boxes on the airborne sound insulation of windows. Appl Acoust2009; 70(2): 369–377.
29.
ISO 10140 — Acoustics — Laboratory measurement of sound insulation of building elements — Part 2: Measurement of airborne sound insulation, 2021.
30.
AllardJFAtallaN.Propagation of sound in porous media: modelling sound absorbing materials. 2nd ed. Wiley, 2009.
31.
GhinetSAtallaN.Vibro-acoustic behavior of multi-layer orthotropic panels. Can Acoust2002; 30(3): 72–73.
32.
AtallaNSgardFAmedinCK.On the modeling of sound radiation from poroelastic materials. J Acoust Soc Am2006; 120(4): 1990–1995.
33.
AlouiRLarbiWChouchaneM.Global sensitivity analysis of piezoelectric energy harvesters. Compos Struct2019; 228: 111317.
34.
CampolongoFCariboniJSaltelliA.An effective screening design for sensitivity analysis of large models. Environ Model Softw2007; 22(10): 1509–1518.
35.
SaltelliA (ed). Global sensitivity analysis: the primer. John Wiley & Sons, 2008.
36.
SaltelliAAnnoniPAzziniI, et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun2010; 181(2): 259–270.
37.
BlatmanG.Chaos polynomial creux et adaptatif pour la propagation d’incertitudes et l’analyse de sensibilité. Université Blaise Pascal - Clermont II, Clermont-Ferrand, 2009.
38.
MarelliSLüthenNSudretB.UQLab user manual – polynomial chaos expansions. Report UQLab-V2.0-104, Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Switzerland, 2022.
39.
XiuDEm KarniadakisG.Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput Methods Appl Mech Eng2002; 191(43): 4927–4948.
40.
BerveillerMSudretBLemaireM.Stochastic finite element: a non intrusive approach by regression. Eur J Comput Mech2006; 15(1–3): 81–92.
41.
HamzaSAnstett-CollinFKiebreR, et al. Analyse de sensibilité basée sur les polynômes du chaos pour des modèles de type boîte noire. In: Presented at Conférence Internationale Francophone d’Automatique (CIFA 2012), Grenoble, France, 04–06 July 2012.
42.
DréauJ.Développements numériques pour la conception robuste d’aubes de turbomachines. Master Calcul Scientifique et Modélisation, 2018.
43.
MohammadiH.Kriging-based black-box global optimization: analysis and new algorithms. Ecole Nationale Supérieure des Mines de Saint-Etienne, 2016.
44.
HuangC.Kriging-assisted evolution strategy for optimization and application in material parameters identification. Normandie Université, 2017.
LataniotisCWicaksonoDMarelliS, et al. UQLab user manual – Kriging (Gaussian process modeling). Report UQLab-V2.0-105, Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Switzerland, 2022.
47.
DubourgV.Adaptive surrogate models for reliability analysis and reliability-based design optimization. Université Blaise Pascal - Clermont II, Clermont-Ferrand, France, 2011.
48.
PavlackBPaixãoJda SilvaS, et al. Polynomial chaos-kriging metamodel for quantification of the debonding area in large wind turbine blades. Struct Health Monit2022; 21(2): 666–682.
49.
BakhoucheSLarbiWMacquartP, et al. Vibro-acoustic analysis of foam-coated plates: modeling and a comparative study of biot-allard and equivalent fluid models. In: Presented at the 16th congress of mechanics, Marrakech, Morocco, 21–24May2024.
