Acoustical topology optimization for Zwicker’s loudness model – Application to noise barriers

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.