Genetic Algorithm in the Optimization of the Acoustic Attenuation System

[EN] It is well known that Genetic Algorithms (GA) is an optimization method which can be used in problems where the traditional optimization techniques are difficult to be applied. Sonic Crystals (SC) are periodic structures that present ranges of sound frequencies related with the periodicity of the structure, where the sound propagation is forbidden. This means that in the acoustic spectrum there are ranges of frequencies with high acoustic attenuation. This attenuation can be improved producing vacancies in the structure. In this paper we use a parallel implementation of a GA to optimize those structures, by means of the creation of vacancies in a starting SC, in order to obtain the best acoustic attenuation in a predetermined range of frequencies. The cost function used in GA is based on the Multiple Scattering Theory (MST), which is a self consistent method for calculating acoustic pressure in SCs. As a final result we achieve a quasi ordered structures that presents a high acoustic attenuation in a predetermined range of frequencies, independent of the periodicity of the SC.The authors acknowledge financial support provided by the Spanish MEC (Project No. MAT2006-03097) and by the Generalitat Valenciana (Spain) under Grant No. GV/2007/191. This work also has been partially supported by MEC (Spanish government) and FEDER funds: projects DPI2005-07835, DPI2004- 8383-C03-02 and GVA-026.Romero García, V.; Fuster García, E.; Sánchez Pérez, JV.; García Raffi, LM.; Blasco, X.; Herrero Durá, JM.; Sanchís Saez, J. (2007). Genetic Algorithm in the Optimization of the Acoustic Attenuation System. Lecture Notes in Computer Science. 4507:614-621. https://doi.org/10.1007/978-3-540-73007-1_74S6146214507Martínez-Sala, R., Sancho, J., Sánchez Pérez, J.V., Llinares, J., Meseguer, F.: Sound attenuation by sculpture. Nature (London) 387, 241 (1995)Hushwaha, M.S., Halevi, P., Martínez, G., Dobrynski, L., Djafari-Rouhani, B.: Theory of acoustic band structure of periodic elastic composites. Phys. Rev. B 49(4), 2313–2322 (1994)Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Xhan, C.T., Sheng, P.: Locally resonatn sonic materials. Science 289, 1734 (2000)Hu, X., Chan, C.T., Zi, J.: Two dimensional sonic crystals with Helmholtz resonators. Phys. Rev. E 71, 055601 (2005)Umnova, O., Attenborough, K., Linton, C.M.: Effects of porous covering on sound attenuation by poriodi arrays of cylinders. J. Acoust. Soc. Am. 119, 278 (2006)Caballero, D., Sánchez-Dehesa, J., Martínez-Sala, R., Rubio, C., Sánchez Pérez, J.V.S., Sanchis, L., Meseguer, F.: Suzuki phase in two-dimensional sonic crystals. Phys. Rev. B 64, 064303 (2001)Hakansson, A., Sánchez-Dehesa, J., Sanchis, L.: Acoustic lens design by genetic algorithms. Phys. Rev. B 70, 214302 (2004)Romero-García, V., Fuster, E., García-Raffi, L.M., Sánchez-Pérez, E.A., Sopena, M., Llinares, J., Sánchez-Pérez, J.V.: Band gap creation using quasiordered strutures based on sonic crystals. Appl. Phys. Lett. 88, 174104-1 174104-3 (2006)Chen, Y.Y., Ye, Z.: Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays. Phys. Rev. E 64, 036616 (2001)Economou, E.N., Sigalas, M.M.: Classical wave propagation in periodic structures: Cermet versus network topology. Phys. Rev. B 48(18), 13434 (1993)Sigalas, M.M., Economou, E.N., Kafesaki, M.: Spectral gaps for electromagnietic and scalar waves: Possible explanation for certain differences. Phys. Rev. B 50(5), 3393 (1994)Goldberg, D.E.: Genetic Algorithms in search, optimization and machine learning. Addison-Wesley, London (1989)Bäck, T.: Evolutionaty Algorithms in theory and practice. Oxford University Press, New York (1996)Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proc. Second International Conference on Genetic Algorithms (1987)Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization. Evolutionary Computation 1(1) (1993)Cantú-Paz, E.: A summary of resaearch on parallel genetic algorithms. Technical Report 95007, Illinois Genetic Algorithms Laboratory. IlliGAL (1995

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