Separation of closely-spaced acoustics sources in an under-determined system with convex optimization

Abstract

The ability to identify acoustical source locations accurately is critical when performing sound field reconstructions. In previous work, a monopole-based, iterative equivalent source method, wideband acoustical holography, has proven able to provide accurate noise source location in complex machines even when the number of measurements was far smaller than the number of parameters that needed to be determined in the model (see: Tongyang Shi, Yangfan Liu and J. Stuart Bolton, “Diesel engine noise source visualization with wideband acoustical holography,” SAE paper 2017-01-1874). However, at some stage, when acoustical sources are too closely spaced, the current algorithm has difficulty in separating them. This is true, especially at low frequencies, in which case current holography methods tend to visualize two closely-spaced acoustics sources as a single large source, thus losing the accuracy of the source location. In the present work, the equivalent sources were still modeled as an array of monopoles, but the source strength parameter estimation and regularization problem was formulated as a convex function and turned into an iterative convex optimization problem that can be solved by an open source code. It will be demonstrated that the new procedure is capable of reconstructing very closely-spaced acoustics sources.