Improvements to the array reduction method for acoustic beamforming array designs

New methods of beamforming array design have been recently proposed, namely the Array Reduction Method (ARM) and its improvement, the Adaptive Array Reduction Method (AARM). For both of these methods, a large grid array design possessing many more microphones than desired is simulated. By calculating the product of the Maximum Sidelobe Level (MSL) and the Main Lobe Width (MLW) (defined as Φ), a microphone is selected that possesses the minimum value of Φ or a variation of Φ. This microphone is removed and the process is then repeated until a desired number of microphones remains. The AARM was derived that factors in the relative change of MSL and MLW with respect to the number of microphones removed, to ensure that the algorithm produced the best overall image source map, rather than simply attempting to minimize Φ. Furthermore, a penalty is introduced during the microphone selection stage that is based on the distortion of the main lobe, such that the final array produces a source image map with a main lobe that is symmetric as possible. In this paper, ARM, AARM and AARM (without factoring in lobe distortion effects) arrays are presented, that were designed for specific acoustic source locations and frequencies. They are numerically tested using a single source at the center and off-center relative to the array center and a dual-source configuration. The experimental conditions were conducted in an anechoic wind tunnel using the same conditions as the numerical simulations, with the exception of airfoil self-noise tests. The AARM is further tested over a challenging irregular array area, such that a typical logarithmic spiral cannot be fitted, revealing the capability of using the AARM in challenging environments.
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