Inverse Source Problems of Active Sound Control for Composite Domains

In the active noise shielding problem, a quite arbitrary domain (bounded or unbounded) is shielded from the field (noise), generated outside, via introducing additional sources. Along with noise, the presence of internal (wanted) sound sources is admitted. Active shielding is achieved by constructing additional (secondary) sources in such a way that the total contribution of all sources leads to the noise attenuation. In contrast to passive control, there is no any mechanical insulation in the system. In practice, active and passive noise control strategies could often be combined, because passive insulation is more efficient for higher frequencies, whereas active shielding is more efficient for lower frequencies. The problem is formulated as an inverse source problem with the secondary sources positioned outside the domain to be shielded. The solution to the problem is obtained in both the frequency and time domains, and based on Calderόn – Ryaben’kii’s surface potentials [1]. A key property of these potentials is that they are projections. The constructed solution to the problem requires only the knowledge of the total field at the perimeter of the shielded domain [1-3]. In practice, usually the total field can only be measured. The methodology automatically differentiates between the wanted and unwanted components of the field. A unique feature of the proposed methodology is its capability to cancel the unwanted noise across the volume and keep the wanted sound unaffected. It is important that the technique requires no detailed information of either the properties of the medium or the noise sources. The technique can also be extended to a composite protected region (multiply connected) [4]. Moreover, the overall domain can arbitrarily be split into a collection of subdomains, and those subdomains are selectively allowed to either communicate freely or otherwise be shielded from their peers. In doing so, no reciprocity is assumed, i.e., for a given pair or subdomains one may be allowed to hear the other, but not vice a versa. Possible applications of this approach to engineering problems such as oil prospecting are discussed.