Acoustical topology optimization for Zwicker’s loudness model- Application to noise barriers
JungHwan Kook(Technical University of Denmark)
Nederland | Computer Methods in Applied Mechanics and Engineer
2011-05-06 | 바로가기
Cited by 40
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Computer Methods in Applied Mechanics and Engineering
Received 6 May 2011, Revised 2 May 2012, Accepted 4 May 2012, Available online 17 May 2012.
Junghwan Kooka, Kunmo Kooa, Jaeyub Hyuna, Jakob S.Jensenb, Semyung Wanga
a School of Mechatronics, Gwangju Institute of Science and Technology
b Department of Mechanical Engineering, Technical University of Denmark
Traditionally, the objective of design optimization of an acoustic system is to reduce physical acoustic properties, i.e., sound pressure and power. However, since these parameters are not sufficient to present the relation of physical sound stimulus with human perceptual judgment, physical acoustic properties may not represent adequate parameters for optimizing acoustic devices. In this paper, we first present a design method for acoustical topology optimization by considering human’s subjective conception of sound. To consider human hearing characteristics, Zwicker’s loudness is calculated according to DIN45631 (ISO 532B). The main objective of this work is to minimize the main specific loudness of a target critical band rate by optimizing the distribution of the reflecting material in a design domain. The Helmholtz equation is used to model acoustic wave propagation and, it is solved using the finite element method. The sensitivity of the main specific loudness is calculated using the adjoint variable method and the chain rule. To demonstrate the effectiveness of the proposed method, various examples of noise barriers are presented with different source and receiver locations. The results obtained, using the optimized noise barriers that consider Zwicker’s loudness, are compared with the results for straight and T-shaped barriers. The results are also compared with topology optimization using 1/3-octave band level as an objective function. The optimized noise barrier using the proposed method shows the best result with respect to a human’s hearing sensation.
We have developed a design method based on acoustical topology optimization by considering human hearing characteristics, and we have used it to design noise barriers with minimum Zwicker’s loudness by optimizing the distribution of reflecting material in a chosen design domain. Minimization of the maximum main specific loudness was considered as the objective function for the optimization of the noise barrier. A finite element model was developed for a 2D outdoor acoustic problem and, it was used to compute Zwicker’s loudness. Analytical sensitivities of the main specific loudness were calculated using the adjoint variable method and the chain rule. The optimization problem was solved using the MMA. Three numerical examples of noise barrier design were presented in order to demonstrate the proposed optimization procedure with different source and receiver locations. The optimized designs obtained by considering the main specific loudness were also compared to designs obtained using the 1/3-octave band as an objective function as well as with straight and T-shape noise barriers. The biggest reduction of the main specific loudness was achieved when the noise barriers were optimized with the main specific loudness.
In all examples the optimized designs looked similar, but with small differences in the structural details. As a general feature, it was seen that lampshade-like material distributions were formed acting as Helmholtz resonators. The main difference between the two optimization formulations that were considered is whether the nonlinear weightings associated with 1/3-octave band level are taken into account or not. Thus, it was revealed that the optimized designs can be different or similar to each other based on the effect of the nonlinear weighting. It was also confirmed, in example 1, that a decrease in dB does not always produce a decrease in loudness. However, in the other two examples a decrease in dB did produce a decrease in loudness. In all examples considered, the optimized designs considering the main specific loudness show the best performance with respect to human hearing sensation compared to the optimized designs obtained by considering the 1/3-octave band, and when compared with the two reference designs.
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