Acoustic-based modal filtering of orthogonal radiating functions for global error sensing: Part I theory and simulation

Abstract

This is the first of two companion papers which summarise the theoretical and experimental work aimed at developing a generalised, acoustic-based sensing strategy for free and semi free field problems. The aim of the work is the design of practical acoustic sensing systems for active noise control of large complex noise sources, based on data fusion of a large number of sensor signals. A wide breath of literature illustrates several practical advantages to pursuing a sensing system which measures orthogonal functions with respect to a global error, and how a large number of point sensors are required in the filtering process. For this reason we examine modal filtering of orthogonal functions for two-dimensional noise sources and highlight the practicalities of sensing systems which measure the associated constituents. We compare three variations of orthogonally radiating shapes based on structural modes, structural elements and combinations of in-/out-of-phase acoustic monopoles. Comparisons are made based on the number of constituents required to estimate 90% of radiated power; the modal filtering weights frequency dependence; and simulated decompositions of a sound pressure field to radiated power. Of the sensing strategies which are structural specific, we extend them to facilitate the use of acoustic sensors to measure the orthogonal “structural” patterns.