Noise Source Identification in an Under-Determined System by Convex Optimization

It was shown that the iterative optimization procedure Wideband Acoustical Holography (WBH) is can efficiently identify noise sources in under-determined systems: i.e., when the number of measurements is less than the number of equivalent source parameters that need to be determined. However, experience suggests that the WBH method also has its limitations. First, when sound sources are closely spaced, WBH has difficulty in separating them, especially at low frequencies. Secondly the solution obtained from the WBH is often highly localized: that is, the WBH solution develops around the strongest source, thus tending to under-estimate the level of nearby weaker sources. To alleviate these issues, the equivalent source strength estimation has been re-formulated as a convex problem thus making it possible to balance source sparsity and reconstruction accuracy in a systematic way and, at least in ideal circumstances, to guarantee an optimal solution. In the present work, measurements of radiation from a loudspeaker were conducted with a limited number of microphones. The sound field reconstruction results obtained using convex optimization were compared with WBH results, and it was typically found that convex optimization did allow relatively weak sources to be successfully identified in the presence of a nearby stronger sources.