• International Journal of Technology (IJTech)
  • Vol 13, No 3 (2022)

An Empirical Model for Optimizing the Sound Absorption of Single Layer MPP Based on Response Surface Methodology

An Empirical Model for Optimizing the Sound Absorption of Single Layer MPP Based on Response Surface Methodology

Title: An Empirical Model for Optimizing the Sound Absorption of Single Layer MPP Based on Response Surface Methodology
Al-Ameri Esraa, Azma putra, Ali Mosa, Reduan M Dan, Osam H Attia

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Cite this article as:
Esraa, A., Putra, A., Mosa, A., Dan, R.M., Attia, O.H., 2022. An Empirical Model for Optimizing the Sound Absorption of Single Layer MPP Based on Response Surface Methodology. International Journal of Technology. Volume 13(3), pp. 496-507

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Al-Ameri Esraa Fakulti Kejuruteraan Mekanikal, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
Azma putra Centre for Advanced Research on Energy, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
Ali Mosa Department of Mechanical Engineering, Collage of Engineering, University of Baghdad, Jadriyah - Baghdad, Iraq
Reduan M Dan Centre for Advanced Research on Energy, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
Osam H Attia Department of Reconstruction and Projects, University of Baghdad, Jadriyah - Baghdad, Iraq
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Abstract
An Empirical Model for Optimizing the Sound Absorption of Single Layer MPP Based on Response Surface Methodology

Micro-perforated panel (MPP) is a thin panel absorber capable of absorbing sound energy at a targeted frequency range by adjusting the MPP parameters. An analytical model is available, but it is not a direct, convenient method for practitioners to determine the required MPP parameters. This paper presents an optimized empirical model to calculate the sound absorption coefficient of a single-layer MPP.  The response surface methodology is employed for a simple case to generate a second-order polynomial model through a sequence of designing processes to analyze the functional relationships and variation of the outcome performance (sound absorption coefficient) concerning the MPP parameters, namely the panel thickness, hole diameter, perforation ratio, and the depth of the back air layer.  The analysis is carried out for frequencies between 300 to 900 Hz. The predicted data (empirical) is compared with the actual data (analytical), leading to a coefficient of variation of 0.145%. The proposed empirical model can be used as a method to select the suitable MPP parameters according to the targeted frequency bandwidth of absorption with less computational time.

Optimisation; Response Surface Methodology (RSM); Single layer MPP; Sound absorption

Introduction

    The Microperforated panel (MPP) absorber proposed by Maa (1975) has been widely used as a next-generation sound absorbers system (Mosa et al., 2018). It has the advantages of providing a high sound absorption coefficient, ease of installation, fine washability, environmental friendliness, and attractive appearance (Tayong et al., 2018; Yang et al., 2019), as an alternative to porous absorbing materials  (Ahmad & Salih, 2020; Prasetiyo et al., 2020). Aimed for a wide absorption bandwidth; many studies have been presented on a single layer MPP using various techniques. This includes the presents of the MPP model with incompletely partitioned cavities (Huang et al., 2017) broadband MPP model with ultra-MPP (Qian et al., 2014a); thin MPP models (Prasetiyo et al., 2021), inhomogeneous MPP systems with multiple cavity depths (Prasetiyo et al., 2016; Mosa et al., 2019; Kusaka et al., 2021).
    The analysis and optimization of the MPP parameters to enhance the absorption performance have been presented (Qian et al., 2014b; Yu et al., 2016); however, most of these processes are consumed time with convoluted processing steps, especially models of a large structure (Hussein, 2020; El-Basheer et al., 2017). Generally, it should be considered that the potential interactions between model variables could cause incorrect optimum parameters as any modifying parameter at a time. In order to minimize these computational efforts, the approach of the response surface methodology (RSM) has been employed to implement the optimization of the acoustic absorption for numerous noise control applications (Liang et al, 2007; Harahap et al., 2019; Wang et al., 2017; Wahab et al., 2019).
    Box and Wilson (1951) first presented this method to initialize and evolve empirical models and by providing the basic principles framework of RSM, they denote the response process. Randall P. and Terence J. (Niedz & Evens, 2016) attained a review discussing the theoretical aspects and practical applications of RSM literature. Essentially, the RSM involves replacing the complete procedure along with an empirical model by collecting a series of results at several detached points within the design domain. The impression of the second-order functions is because of the low-order processes are powerful, since generating the corresponding response surface is fast and cheap. (Boulandet & Lissek, 2010; Hawashi et al., 2019; Petrus et al., 2021; Saleh et al., 2021).
    Even though several studies have been presented on the absorption performance of MPP using analytical or simulation methods. Still, they are not direct, convenient methods for practitioners to determine the required MPP parameters. Thus, the current study uses a factorial design of experiment software to present a novel empirical model for a single-layer-MPP absorber based on RSM to contribute a straightforward and more accessible model with less computational time. Furthermore, to optimize the relationship between the model parameters (holes diameters and ratio, cavity depth, and panel thickness). The paper structure presents recent studies on the MPP and the RSM, followed by the empirical model theories and generation methodology step. Section 3 summarized the model validation and predicted results. The conclusion of the study is present at the end.

Conclusion

    The optimized empirical model to calculate the sound absorption coefficient of a ?single-layer MPP has been presented in this paper. The model was developed using the response? surface methodology to generate a second-order polynomial model as a function of MPP parameters, namely the hole diameter, the perforation ratio and the depth of the back air layer?. The predicted data is evaluated with the actual data leading to a coefficient of variation ?of about 0.145%. The predicted model is then verified with the analytical model with good agreement. The proposed model in this paper is however, only valid for the frequency range of 300 – 900 Hz. The same method can be used to generate empirical models of a single layer MPP with a different frequency range of interest. In future work, these empirical models can be utilized as the complete set of mathematical tools to calculate the absorption coefficient of MPP conveniently. The work can also be extended with the more complicated configuration of the MPP structure, such as the double-leaf MPP and the multi-cavity MPP.

Acknowledgement

    The authors would like to express their gratitude to Universiti Teknikal Malaysia Melaka (UTeM). Part of this project is supported by the Fundamental Research Grant Scheme ?from the Ministry of Higher Education Malaysia No. FRGS/1/2016/ ?TK03/FTK­CARE/F00323?. The corresponding author would like to express appreciation for the University of Baghdad for its great support.

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