Reconstruction of Acoustic Surfaces Incomplete Data as an Identification Problem Based on Fuzzy Relations

Abstract

The model of the acoustic surface in the form of the system of fuzzy relational equations (SFRE) is proposed. The relationship matrix connects fuzzy locations of sources or their groups and sound energy levels. The problem of acoustic surface reconstruction from incomplete data is reduced to the problem of identifying the matrix of fuzzy relations by solving the composite SFRE. Properties of the solution set allow avoiding the generation and selection of the source distribution parameters. The method for reconstructing acoustic surfaces by solving the composite SFRE is proposed. To reconstruct the set of solutions in the form of fuzzy if-then rules, the genetic-gradient algorithm is used. The reconstruction process is simplified due to ability to parallelize the process of numerical solution of the composite SFRE, that allows to increase the frequency of reconstruction when processing acoustic data streams. To minimize processing time, the number of microphones is limited, provided that the risk of incorrect reconstruction remains acceptable. For the testing set of acoustic images, the risk of incorrect reconstruction is evaluated by the comparison of the extracted rules and the rules which describe the real acoustic surface. The risk of incorrect reconstruction of the acoustic level is defined as the ratio of the number of rules from the contiguous and remote power classes to the total number of rules in the actual power class. The risk of incorrect reconstruction of the acoustic surface is defined as the average risk of incorrect reconstruction over all sound energy levels.