Toward Optimized Nonlocal Active Sound Control with Preservation of Desired Sound

In the active sound control problem considered, it is presumed that a bounded domain is protected from external noise via the distribution of active control sources on its perimeter. Moreover, sound generated inside the protected domain is interpreted as desired and supposed to be retained unaffected. We suppose that only the total sound field from all primary and secondary sources is available for measurement at the perimeter of the protected region. The approach based on the nonlocal active sound control has proved to be efficient to tackle this problem. To make this algorithm more feasible for practical implementation, we minimize the number of control units. This problem is reduced to the optimal distribution of nodes in numerical quadratures over surfaces. Such a problem has not still been resolved for arbitrary enough functions. However, in this paper, we compare different well-known integration patterns. Since we consider the distribution of nodes as sparse as possible, any asymptotic estimations of the approximation error are not reliable. Thus, the only possible way for comparison of distribution patterns is an immediate numerical experiment. In our previous work, we considered the question of the optimal distribution of the control elements for monochromatic waves. Another novelty of the paper is related to the nonlocal active control of broadband noise with preservation of broadband desired sound. This task is tackled for the first time.