Optimized nonlocal active sound control in frequency domain. (February 2022) - Hu, N.; Utyuzhnikov, S.
Highlights: We consider active sound control with preservation of desired sound. We apply a recently developed nonlocal control to tackle this problem. We solve the problem of minimization of the number of controls and sensors for the first time. We demonstrate that the optimal nonlocal control is not sensitive to the presence of desired sound. Abstract: In the active sound control problem considered in the paper, a quite arbitrary closed region is acoustically shielded from ambient noise generated outside via implementation of secondary sound sources which are situated at the perimeter of the domain to be protected. It is presumed that the information available for the operation of control is only limited by the acoustic field that can be measured on a closed surface around the shielded region. The problem becomes much more complicated if there are desired sound sources situated inside the shielded region. In this case the input field is determined by contributions from noise, desired sound and controls. It is supposed that only the total acoustic field is available that makes the statement of the problem quite general and realistic. As the output, it is required to attenuate noise while preserving the desired field unaffected. To tackle the problem, a recently developed algorithm based on the nonlocal control is applied. From the point of view of a practical realization, the number of microphones and loudspeakers should be minimized. We propose for the first time some ways to essentially optimize distribution patterns of controls and sensors for the nonlocal control with preservation of desired sound. Numerical experiments are carried out for noise attenuation in a cube to study the trade-off between the level of noise reduction and number of sensors and controls. It is demonstrated that the nonlocal control can be efficiently realized with a reasonable number of sensors and controls. As shown, with only two controls per wavelength the achieved level of noise attenuation exceeds 10 dB. This result matches the optimal local control when any desired sound is absent.