Vibration sensing of orthogonal acoustic multipole radiation patterns for active noise control

Abstract

In developing an active noise and vibration control system (ANVC) control system, there are two competing goals [1]: (1) to be able to measure, and so attenuate, an error criterion that is directly related to power or energy, and (2) to minimise the number of input signals that must be processed by the controller. Attempts to develop ANVC systems for large structures have often involved scaling up smaller ANVC systems. This results in a large number of inputs to, and outputs from, the controller, apparently contradicting goal (2) above. To overcome this many researchers have turned to variants of modal filtering [2, 3], where a small number of global quantities (traditionally structural modes) are resolved from a large number of point sensor measurements. When trying to control the noise radiated by a structure, simply minimising the amplitudes of the structural modes per se will not guarantee a reduction in the sound power produced by a structure [4]. Instead, groupings of the structural modes must be minimised to guarantee a reduction in sound power. These groupings, orthogonal in terms of the acosutic power radiated, were called radiation modes [5]. The drawback to the modal filtering approaches based upon structural modes is that the mode shapes must be known. While calculating these mode shapes for a simple structure in a laboratory setting is quite possible, translating this to a practical noise problem, such as radiation from a large electrical sub-station transformer, is often not practical. The impracticality is compounded by the fact that the vibrational characteristics of every one of these structures will be different, requiring a custom modal filtering (sensing) system be designed for every transformer. The aim of the work presented here is to overcome this need for modal information of the structure by basing the sensing system design on quantities that are transferable from structure to structure. The radiation patterns produced by acoustic multipoles will be used here as a basis to describe the radiated acoustic power from the target structure, the multipoles being made up of notional arrays of acoustic monopoles. Acoustic multipoles has been used before in developing secondary acoustic sources [6, 7]. However, the aim here is different in that the radiation patterns produced by multipoles are used in the development of a sensing system. In this paper development of a vibration based modal filtering sensing system that does not require structural mode shape information will be presented. The utility of the approach outlined here will be demonstrated in both simulation and experimental results.