Multimodal-based shape optimization of rectangular horns for improved radiation efficiency and directivity control

Rectangular horns are widely used in professional audio applications, but designing horns with desired radiation efficiency and directivity is time-consuming and often relies on empirical methods. A multimodal-based optimization approach is proposed in this study and can simultaneously improve the radiation efficiency and directivity control of rectangular horns over a wide frequency range. Based on acoustical properties accurately simulated by a discrete model, the terms in the objective function are constructed to measure radiation efficiency, penalize jagged shapes, and improve directivity control. To meet practical requirements, directivity control is achieved through two strategies: maintaining a flat directivity pattern for constant directivity and precisely adjusting coverage. The optimization problem is solved by a gradient-based algorithm, with the gradient derived as algebraic expressions. Numerical studies validate the effectiveness of the optimization method and systematically investigate the individual impacts of each objective function term on the horn's shape and performance. Finally, a rectangular horn exhibiting high radiation efficiency, constant directivity, and different coverage in the horizontal and vertical planes is obtained with moderate weight coefficients. The proposed method enables direct horn shape design based on performance requirements and provides an alternative to conventional design approaches.