Sound Field Reconstruction from Incomplete Data by Solving Fuzzy Relational Equations

摘要

The approach to solving inverse problems of source identification in acoustics is proposed based on fuzzy relational calculus. The compositional rule of inference connects the real and observed fuzzy acoustic image using the relationship matrix, which reflects the degree of completeness of the microphone array measurement data. The fuzzy model of the acoustic field is based on 3D membership functions, for which the degree of membership decreases in proportion to the square of the distance to the source. The problem of reconstructing the acoustic field is formulated as the problem of inverse logical inference. The method for reconstructing the acoustic field from incomplete data is proposed based on solving fuzzy relational equations. The problem consists in finding such a number of sound sources, their locations and powers, which minimize the difference between the model and observed fuzzy acoustic image. The solutions of the equation system represent the variants of the acoustic field reconstruction in the form of the main acoustic surface and a set of secondary acoustic surfaces. The main acoustic surface is generated by the least number of sources. The set of secondary acoustic surfaces represents the variants of the sound field reconstruction generated by the upper solutions for the number of sources. Since the sources distribution is completely determined by the properties of the solution set, the proposed approach allows avoiding the generation and selection of candidate sources, that provides simplification of the reconstruction process and reduction of time costs. The genetic and neural algorithm provides accurate and fast reconstruction of the acoustic field for an unknown number of sources and their configuration.