Keywords: noise barriers, shape optimization, genetic algorithms, boundary element method, outdoor noise propagation, noise attenuation.

Noise Barriers are a useful tool for abating road traffic noise near residential buildings. They are widely used for environmental protection on the boundaries of high traffic roads near a population nucleus in order to reduce the noise impact. A large body of research has been carried out in the last two decades focussed to the study of the diffraction of sound around barriers, predicting their performance and developing more efficient designs [1]. Different theoretical methods have been proposed. Among these, the use of the boundary element method (BEM) has been investigated to evaluate complex barrier configurations. The main advantages of the BEM over other methods based on a geometrical theory of diffraction approach are its flexibility, arbitrary shapes and surface acoustic properties can be accurately represented, and accuracy. A correct solution of the governing equations of acoustics to any required accuracy can be produced providing a boundary element size with small enough fraction of a wavelength.

Evolutionary algorithms have been widely used for shape design optimization in different engineering fields. The following can be cited: aeronautics, or solid mechanics [2]. The applications of evolutionary algorithms to the shape design in outdoor acoustics are scarce in literature. In this work the authors propose the application of a methodology based in evolutionary algorithms combined with a BE analysis technique to the optimum shape design of complex noise barriers.

The model assumes an infinite, coherent line source of sound, parallel to an infinite noise barrier of uniform cross section and surface covering along its length. In these conditions the model is two-dimensional. The study is carried out in the frequency domain. This problem is constituted by an emitting the source of fixed position, which pulses in a frequency range, and a receptor. Between the source and the receptor a generic shape obstacle (noise barrier) is situated. The shape of this barrier is modified to minimize the measured sound level in the receptor. The sound level is calculated, being known: the source and receptor position, the barrier shape, and the sound frequency. The fitness function (FF) to maximize is the difference between the sound level in the receptor with and without a barrier, respectively (insertion loss IL). In the performed analysis, a maximum limit on the effective height (h) of the barrier is imposed. Because of the critical performance of sound barriers associated to the h, shape optimization is desired for a maximum constant h. This maximum h value originates a trapezoidal search space and a transformed domain is achieved from cartesian barrier domain in order to make the shape design optimization easier. Performing the shape optimum design considering various frequencies is more accurate with respect to the real sound propagation problem. It also avoids possible problems associated with one single frequency optimization, that could guide the solutiona to false IL values resulting from frequencies nearer to eigenfrequencies associated with the BEM evaluation.

Three armed-shape barriers are taken into account to validate this methodology. The BEM elements used are parabolic and only the barrier surface is discretized with these elements, since the used fundamental solution satisfies the boundary conditions on the ground surface. A maximum element length not greater than ( being the wavelength) is necessary to obtain an appropriately accurate solution. A total of five frequencies corresponding to the octave centre band (63, 125, 250, 500 and 1000 Hz.) are taken into account in the fitness function.

First, an inverse problem has been handled; being the reference IL values those belonging to a previously defined barrier. The presented methodology allows the accurate fit of both IL curves (fitness function value of 8e-4), even in terms of one-third octaves spectra (63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800 and 1000 Hz.) and to locate the original barrier shape. Then, shape optimization is accomplished by forcing the IL reference curve to increase its performance, both in 15% and 30%, respectively, and to obtain their corresponding shape design barriers. The greater the search improvement, the worst the FF obtained (harder optimization work). However, the results obtained succeed in accomplishing the imposed requirements with acceptable FF values (0.09 and 1.95 respectively). Results are detailed in terms of IL values and barrier shape designs, numerically and graphically.

A successful methodology based on coupling evolutionary optimization and the boundary element method has been presented for sound attenuation barriers. Concretely, shape optimum design has been carried out for three armed barriers. An inverse problem is solved and successive improved shape barriers are obtained, both for 15% and 30% better performance in terms of IL reference points.

1

T. Ishizuka, K. Fujiwara, "Performance of noise barriers with various edge shapes and acoustical conditions", Applied Acoustics 65, pp. 125-141, 2004. doi:10.1016/j.apacoust.2003.08.006

2

T. Burczynski, A. Osyczka (Eds.), "IUTAM Symposium on Evolutionary Methods in Mechanics", Solid Mechanics and its Applications, 117, Kluwer Academic Publishers, 2004.

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