Study of the nonlocal active sound control with preservation of desired field in time domain

In the active sound control, a domain is protected from externally generated noise via constructing secondary sound sources, which are called controls. These controls are applied on the boundary of the shielded domain. Apart from the external noise, a desired sound generated by interior sources should also be retained inside the shielded domain. However, it turns out it is a challenge to preserve the internally generated sound unaffected due to both the reverse effect of the controls on the input data and sparse distribution on the boundary. To take into account the reverse effect, an innovative algorithm based on nonlocal control is implemented in the time domain for the first time. Its real-time practical implementation may include preliminary tuning to the real surrounding conditions. A number of test cases are considered including external broadband noise and internal monochromatic desired sound. A sensitivity analysis is carried out with respect to some key design parameters such as density of sensors and controls as well as respective geometrical displacement from one another determined by the Hausdorff distance. It is demonstrated that the nonlocal control provides the noise attenuation level, which is not very sensitive to the presence of the desired sound.