Optimization Of Acoustic Source Strength In The Problems Of Active Noise Control

Optimization of Acoustic Source Strength in the Problems of Active Noise Control

We consider a problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, that generate the appropriate annihilating acoustic signal (anti-sound). A general solution for the control sources has been obtained previously in both continuous and discrete formulation of the problem. In the current paper, we focus on optimizing the overall absolute acoustic source strength of the control sources. Mathematically, this amounts to the minimization of multi-variable complex-valued functions in the sense of L1 with conical constraints, which are only 'marginally' convex. The corresponding numerical optimization problem appears very challenging even for the most sophisticated state-of-the-art methodologies, and even when the dimension of the grid is small, and the waves are long. Our central result is that the global L1-optimal solution can, in fact, be obtained without solving the numerical optimization problem. This solution is given by a special layer of monopole sources on the perimeter of the protected region. We provide a rigorous proof of the global L1 minimality for both continuous and discrete optimization problems in the one-dimensional case. We also provide numerical evidence that corroborates our result in the two-dimensional case, when the protected domain is a cylinder. Even though we cannot fully justify it, we believe that the same result holds in the general case, i.e., for multi-dimensional settings and domains of arbitrary shape. We formulate it as a conjecture at the end of the paper.

Quadratic Optimization in the Problems of Active Control of Sound

Computational Science and Its Applications - ICCSA 2003

The three-volume set, LNCS 2667, LNCS 2668, and LNCS 2669, constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2003, held in Montreal, Canada, in May 2003.The three volumes present more than 300 papers and span the whole range of computational science from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The proceedings give a unique account of recent results in computational science.