Optimized nonlocal active sound control

Abstract

In the active sound control problem, the secondary sound sources, known as controls, are set around the perimeter of an acoustically protected domain. The external noise is attenuated in the protected domain thanks to the secondary sound field generated by controls. This leads to an inverse source problem. Such problem can be solved by algorithms based on the Calderon surface potential. If the primary field on the boundary of the protected domain is presumed to be available, the potential-based local control algorithm can be implemented. However, when the internal desired sound sources exist, the primary field is unavailable in the real-time regime due to the reverse effect. The reverse effect of controls on the input data doubles the desired sound outside the protected domain. Even if the desired sound is absent, the reverse effect still occurs with a sparse grid of controls as the projection property is not fully realized. In this case, the unwanted secondary field is involved, which makes the primary field cannot be measured directly. Thus, the application of this local control method is limited. To overcome this problem, the nonlocal active sound control technique is provided. Compared to local control, nonlocal control only requires the total acoustic field on the boundary of the protected domain. Based on the projection property of the Calderon surface potential, the noise can be eliminated automatically while the desired sound remains in the protected domain. Another main advantage of nonlocal control is that, in case desired sound is absent, it can provide stable noise attenuation even in sparse grids of sensors and controls. The main aim of the thesis is to optimize the current nonlocal active sound control technique in different aspects. The minimum-maximum problem between sensors and controls and the level of noise attenuation is investigated based on different distribution patterns of nodes. In addition, the minimum number of controls per wavelength for essential noise attenuation is studied. Moreover, the feasibility of extending nonlocal active sound control to composite domains with both separate and common boundaries is validated. A practical example based on local active noise control is investigated as well. It demonstrates that the Nyquist limitation can be broken in some cases with symmetry that provides a guideline for further research on nonlocal active sound control. In this thesis, first, we propose the optimal distributions for sensors and controls for different density of grid with local and nonlocal control. Both monochromatic and broadband noise and desired sound are considered. Then, the nonlocal active sound control method is extended to composite domains. Three different sound propagation patterns are designed to meet different demands for noise reduction. Afterwards, the nonlocal control approach for subdomains with common boundaries is studied. The same set of controls at the common boundary can be shared to provide sufficient noise attenuation for both sides. Finally, a practical case of a finite pipe generating broadband noise is taken into account. It demonstrates that even less than two controls per wavelength can provide essential noise cancellation with the uniform acoustic field on the surface of the protected domain.

Date of Award	12 Nov 2024
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Sergey Utyuzhnikov (Main Supervisor) & Dominique Laurence (Co Supervisor)