Two inverse extremal problems of sound radiation in regular acoustic waveguides are considered. One problem is to actively minimize the sound (noise) field in a waveguide with the aid of a special radiating system inside the waveguide. The other problem is to maximize the source power radiated to a distant zone. We develop a single method for solving both problems. It is based upon regularizing unstable problems and finding the extrema of functionals dependent on the complex intensities of discrete antenna sources. In case of the minimization problem, the functional is the power of the residual field, which is a sum of the noise field and that of the sought-for antenna system. We introduce a rectangular matrix A whose components are the values of waveguide eigenfunctions at the sites of discrete sources, give the physical interpretation of the singular system of A, and develop a numerical algorithm for its computer implementation. The algorithm includes the high-precision finite-difference solution of the eigenvalue problem for the waveguide, the calculation of the singular system of A with a guaranteed accuracy, and the solution of the corresponding system of linear algebraic equations by using the regularized incomplete singular factorization. In conclusion, we give the results of numerical experiments on the active minimization of sound fields in a three-dimensional waveguide with a sound velocity profile of ocean acoustics. These experiments allow us to investigate the solutions of extremal problems (including the values of suppressed power) as functions of the number and positions of the secondary antenna sources and, besides, to estimate the influence of data perturbations (in particular, the influence of the error in finite-difference discretization of the differential eigenvalue problem) on the solution accuracy.The theory of sound radiation in unbounded media and waveguides has been intensively developed in the past years. One of its important problems is the active minimization of the sound field, or the sound suppression. The problem in its exact formulation was pioneered by Malyuzhinets (see [29,17]). It was studied for unbounded media [22,32] and waveguides [18,31]. Based essentially on the Kirchhoff formula, these works theoretically prove that an arbitrary acoustic field inside (or outside) a closed surface can be completely suppressed by using continuous antennas in a neighbourhood of the surface. Another approach to the solution of this problem is based on the results of Kempton [23] who has shown that the field of a given source can be completely suppressed by a finite number of multipole sources located at a single point. These approaches differ in some details but have a common drawback: they cannot be implemented in practice. This is because they use continuous antennas, which is technically impossible.In practice, Discrete antennas are widely used, in practice; for example, they can be employed for suppressing the sound in unbounded media [21,24] or in waveguides [12,37]. However, the comple...

In this paper, nonlinear inverse extrenrum problems of active minimization of the sound power output generated by a noise source into the far zone of the regular acoustic waveguide with a help of the addition of several secondary point sources, are considered. These problems consist in either Unding of coordinates and complex strengths of the point sources (Problem 3.1) or only point sources coordinates for a given distribution of sources strengths (Problem 3.2) under condition of the minimum power output generated to the waveguide far zone by a given noise source. To solve these problems, the authors have developed two algorithms. The first one is based on using enumeration type technique with respect to coordinate of monopoles on some two-dimensional grid and regularization method of incomplete singular factorization with respect to monopole strengths. The second algorithm is based on the multistart method of global optimization and the modified Newton method for finding local extrema. Results are presented for the minimum power radiated by the combination of a single point primary source and optimal arrangements of point secondary sources. They demonstrate in particular that substantial reductions in a primary source power output can be achieved by the optimal choice of both coordinates of monopoles and their strengths as soon as the number of secondary sources reaches-the number of modes propagating in the waveguide considered.

The paper presents three methods developed to assess rating points of objects and groups of objects with qualitative characteristics. The first method allows to transform the elements of a verbal (order-type) scale into fuzzy numbers instead of traditional scores. The membership functions of these numbers depend on results of qualitative characteristic assessment for this group of objects. So we can make a linguistic scale that can be adjusted for a specific group of objects. The second and third methods allow to obtain rating points for objects and groups of objects with qualitative characteristics based on these linguistic scales.

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