This study investigates the acoustic performance of various porous materials at elevated temperatures, employing Constrained Gaussian Process Regression (CGPR) to model the relationship between specific airflow resistance and the absolute temperature. Experimental data on six fibrous material samples at 600°C are used to develop and compare CGPR models against conventional Power Law Regression (PLR) methods. The developed CGPR incorporates constraints such as boundedness, monotonicity and convexity/concavity derived from the evident relationships and prior knowledge of the specific airflow resistance versus temperature variations. The results of this study prove the outperformance of the developed CGPR over PLR methods in terms of data efficiency, predictive accuracy, uncertainty quantification, overfitting recovery and extrapolation capability. This comparative analysis outlines a significant improvement in the predictive accuracy of CGPR, achieving improved coefficient of determination values compared to PLR. CGPR also furnishes a direct strategy to quantify the uncertainty of predictions which is vital for applications at elevated temperatures. Additionally, CGPR offers valuable insights into sound absorption behaviour, highlighting its applicability in thermal acoustics and materials engineering. Prospective research avenues stem from this research as the developed CGPR technique has the potential to replace various modelling techniques in materials science and acoustic engineering applications.
GanapathyV.Industrial boilers and heat recovery steam generators: design, applications, and calculations. New York, NY: Marcel Dekker Inc, 2003.
3.
SamarasingheT.Airflow resistivity measurement of alkaline earth silicate materials between room temperature and 800°. ; Doctoral Dissertation, The University of Liverpool, UK, 2019.
4.
TangXYanX.Airflow resistance of acoustical fibrous materials: measurements, calculations and applications. J Ind Textiles2020; 49: 981–1010.
5.
CoxTJD’AntonioP.Acoustic absorbers and diffusers: theory, design and application. London: CRC Press, 2009.
6.
ISO 9053-1. Acoustics- determination of airflow resistance. European Committee for Standardization (CEN), Brussels, Standards, 2018.
7.
DelanyMEBazleyEN.Acoustical properties of fibrous absorbent materials. Appl Acoust1970; 3: 105–116.
8.
GaraiMPompoliF.A simple empirical model of polyester fibre materials for acoustical applications. Appl Acoust2005; 66: 1383–1398.
9.
SamarasingheTHopkinsCSeiffertG, et alAirflow resistance measurement of fibrous materials at high temperatures for acoustical applications. Appl Acoust2020; 164: 107255.
10.
ChristieDR.Measurement of the acoustic properties of a sound absorbing material at high temperatures. J Sound Vib1976; 46: 347–355.
11.
OthmaniCTaktakMZeinA, et al, Experimental and theoretical investigation of the acoustic performance of sugarcane wastes based material. Appl Acoust2016; 109: 90–96.
12.
BansodPVMohantyAR.Inverse acoustical characterization of natural jute sound absorbing material by the particle swarm optimization method. Appl Acoust2016; 112: 41–52.
13.
BottermanBde la GréeGDHornikxMC, et alModelling and optimization of the sound absorption of wood-wool cement boards. Appl Acoust2018; 129: 144–154.
BiotMA. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. J Acoust Soc Am1956; 28: 168–178.
17.
NeumanSP.Theoretical derivation of Darcy’s law. Acta Mech1977; 25: 153–170.
18.
SutherlandW.LII. The viscosity of gases and molecular force. Lond Edinb Dublin Philos Mag J Sci1893; 36: 507–531.
19.
MigliettaPNegroESiniF, et alMeasurement of airflow resistivity variation due to temperature and its impact on simulated sound absorption inside a vehicle’s passenger compartment. SAE Int J Passeng Cars Mech Syst2010; 3: 901–915.
20.
ZhangQDaLZhangY, et alIntegrated neural networks based on feature fusion for underwater target recognition. Appl Acoust2021; 182: 108261.
21.
YangJYanSZengD, et alSelf-supervised learning minimax entropy domain adaptation for the underwater target recognition. Appl Acoust2024; 216: 109725.
LyuBXuJGeyerTF, et alExperimental investigation into the acoustical superiority of ogee serrations in reducing leading edge noise. Appl Acoust2024; 216: 109722.
24.
ChoudharyAMishraRKFatimaS, et alMulti-input CNN based vibro-acoustic fusion for accurate fault diagnosis of induction motor. Eng Appl Artif Intell2023; 120: 105872.
25.
TraniLPaganiGAZanettiJPP, et alDeepQuake — an application of CNN for seismo-acoustic event classification in The Netherlands. Comput Geosci2022; 159: 104980.
26.
BiancoMJGerstoftPTraerJ, et alMachine learning in acoustics: Theory and applications. J Acoust Soc Am2019; 146(5): 3590–3628.
27.
AryalNLeeSW.Frequency-based CNN and attention module for acoustic scene classification. Appl Acoust2023; 210: 109411.
28.
LeeYLimSKwakIY.CNN-based acoustic scene classification system. Electronics2021; 10(4): 371.
29.
QuYLiXQinZ, et alAcoustic scene classification based on three-dimensional multi-channel feature-correlated deep learning networks. Sci Rep2022; 12: 1–11.
30.
CiaburroGIannaceGAliM, et alAn artificial neural network approach to modelling absorbent asphalts acoustic properties. J King Saud Eng Sci2021; 33(4): 213–220.
31.
Bader EddinMMénardSBard HagbergD, et alPrediction of sound insulation using artificial neural networks—Part I: lightweight wooden floor structures. Acoustics2022; 4(1): 203–226.
32.
Bader EddinMVardaxisNGMénardS, et alPrediction of sound insulation using artificial neural networks—Part II: lightweight wooden façade structures. Appl Sci2022; 12(14): 6983.
33.
AquinoDJEusebioLFLorescoPJ. ANN-based classification of rain acoustic sensor data using modified Mel frequency cepstral coefficients. In: 2022 IEEE 14th international conference on humanoid, nanotechnology, information technology, communication and control, environment, and management (HNICEM), Boracay Island, Philippines, 1–4January2022, pp.1–6. New York: IEEE.
34.
RasmussenCEWilliamsCKI. Gaussian Processes for Machine Learning. Cambridge: MIT Press, 2006.
35.
HerathSXiaoXCirakF.Computational modeling and data-driven homogenization of knitted membranes. Int J Numer Methods Eng2022; 123(3): 683–704.
36.
HerathS. Multiscale modelling of woven and knitted fabric membranes. PhD Dissertation, University of Cambridge, Cambridge, June2020.
37.
ASTM C522. Standard test method for airflow resistance of acoustical materials. ASTM International, West Conshohocken, Standards, 2016.
38.
BrownRLBoltRH.The measurement of flow resistance of porous acoustic materials. J Acoust Soc Am1942; 13: 337–344.
39.
DragonettiRIannielloCRomanoRA.Measurement of the resistivity of porous materials with an alternating air-flow method. J Acoust Soc Am2011; 129: 753–764.
40.
YanivSL.Impedance tube measurement of propagation constant and characteristic impedance of porous acoustical material. J Acoust Soc Am1973; 54: 1138–1142.
41.
DauchezNSahraouiSAtallaN.Validation of 3-D poroelastic finite element from the impedance measurement of a vibrating foam sample. Can Acoust2000; 28: 94–95.
42.
MendibilX.Medida de la absorción acústica de los materiales poroelásticos. PhD Dissertation, University of Mondragón, Spain, 2004.
43.
StinsonMRDaigleGA.Electronic system for the measurement of flow resistance. J Acoust Soc Am1988; 83: 2422–2428.
44.
BiesDAHansenCH.Flow resistance information for acoustical design. Appl Acoust1980; 13: 357–391.
45.
YoshidaINakamuraTAuSK.Bayesian updating of model parameters using adaptive Gaussian process regression and particle filter. Struct Saf2023; 102: 102328.
46.
SaidaTNishioM.Transfer learning Gaussian process regression surrogate model with explainability for structural reliability analysis under variation in uncertainties. Comput Struct2023; 281: 107014.
47.
LiuSYOuyangZLChenG, et alBlack-box modeling of ship maneuvering motion based on Gaussian process regression with wavelet threshold denoising. Ocean Eng2023; 271: 113765.
48.
FathabadiASeyedianSMMalekianA.Comparison of Bayesian, k-Nearest Neighbor and Gaussian process regression methods for quantifying uncertainty of suspended sediment concentration prediction. Sci Total Environ2022; 818: 151760.
49.
CaoQDMilesSBChoeY.Infrastructure recovery curve estimation using Gaussian process regression on expert elicited data. Reliab Eng System Saf2022; 217: 108054.
50.
BaglaevaIIaparovBZahradníkI, et alAnalysis of noisy transient signals based on Gaussian process regression. Biophys J2023; 122(3): 451–459.
51.
LuPMaYWuY, et alFast evaluation method of post-impact performance of bridges based on dynamic load test data using Gaussian process regression. Eng Appl Artif Intell2024; 127: 107194.
52.
EhteramMNajah AhmedAKhozaniZS, et alGraph convolutional network – long short term memory neural network- multi layer perceptron- Gaussian progress regression model: a new deep learning model for predicting ozone concertation. Atmos Pollut Res2023; 14(6): 101766.
53.
DudekABaranowskiJ.Gaussian processes for signal processing and representation in control engineering. Appl Sci2022; 12(10): 4946.
54.
FuhgJNBouklasN.On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling. Comput Methods Appl Mech Eng2022; 394: 114915.
55.
SwilerLGulianMFrankelA, et alA survey of constrained Gaussian process regression: approaches and implementation challenges. J Mach Learn Model Comput2020; 1(2): 119–156.
56.
LindenLKleinDKKalinaKA, et alNeural networks meet hyperelasticity: a guide to enforcing physics. J Mech Phys Solids2023; 179: 105363.
57.
López-LoperaAFBachocFDurrandeN, et alFinite-dimensional Gaussian approximation with linear inequality constraints. J Uncertain Quantif2018; 6(3): 1224–1255.
58.
Da VeigaSMarrelA. Gaussian process modeling with inequality constraints. Ann Fac Sci Toulouse2012; 21(3): 529–555.
59.
MaatoukHBayX.Gaussian process emulators for computer experiments with inequality constraints. Math Geosci2017; 49(5): 557–582.
60.
JensenBSNielsenJBLarsenJ.Bounded Gaussian process regression. In: 2013 IEEE international workshop on machine learning for signal processing (MLSP), 2013, pp.1–6. New York: IEEE.
61.
GramacyRB. Surrogates: Gaussian process modeling, design, and optimization for the applied sciences. Boca Raton, FL; New York, NY; London, UK: Routledge, 2021.
62.
ForresterAIJSóbesterAKeaneAJ. Engineering design via surrogate modelling: a practical guide. New York, NY: Wiley, 2008.
63.
JiangPZhouQShaoX.Verification methods for surrogate models. Singapore: Springer Singapore, 2020, pp.89–113.
64.
HerathSChakrabortyS.Nonlinear response modelling of material systems using constrained Gaussian processes. Int J Numer Methods Eng2024; 125(14): e7486.
65.
AriyasingheNHerathS.Machine learning techniques for predictive modelling and uncertainty quantification of the mechanical properties of woven carbon fibre composites. Mater Today Commun2024; 40: 109732.
66.
HerathS.Multiscale modelling and material design of woven textiles using Gaussian processes. Acta Mech2022; 233(1): 317–341.
67.
HerathSHaputhanthriU.Nonlinear multiscale modelling and design using Gaussian processes. J Appl Comput Mech2021; 7(3): 1–10.
68.
R Core Team, R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, [Online]. https://www.R-project.org/ (2021, accessed 20 June 2024)
69.
VérILBeranekLL.Noise and vibration control engineering: principles and applications. 2nd ed.Hoboken, NJ: John Wiley and Sons, 2007, pp.1–966.
