Active noise control at a virtual acoustic energy density sensor in a three-dimensional sound field

A common problem in local active noise control is that the zone of quiet centered at the physical microphone is too small to extend to the desired location of attenuation, such as an observer’s ear. The physical microphone must therefore be placed at the desired location of attenuation, which is often inconvenient. Virtual microphones overcome this by shifting the zone of quiet away from the physical microphone to a desired location of attenuation, referred to as the virtual location. In an effort to extend the zone of quiet generated at the virtual location, a virtual acoustic energy density method is developed in this paper for use in a three-dimensional sound field. This virtual energy density method uses a modified version of the remote microphone technique to estimate the total acoustic energy density at a virtual location. Experimental results of active noise control at a virtual acoustic energy density sensor and a virtual microphone in a three-dimensional sound field are presented for comparison. Minimising the total virtual acoustic energy density with the active noise control system is shown to create a spatially extended zone of quiet at a fixed virtual location compared to virtual pressure control. INTRODUCTION A traditional local active noise control system creates a zone of quiet at a physical microphone by minimising the measured acoustic sound pressure with a single secondary sound source. While noise levels are significantly attenuated at the microphone location, the zone of quiet is generally small and impractically sized. Elliott et al. (1988) demonstrated both analytically and experimentally that the zone of quiet generated at a microphone in a pure tone diffuse sound field is defined by a sinc function, with the primary sound pressure level reduced by 10 dB over a sphere of diameter one tenth of the excitation wavelength, λ/10. In addition to the zone of quiet being small, the sound pressure levels outside of the zone of quiet are likely to be higher than the original disturbance alone. This is shown in Fig. 1 (a), where the zone of quiet located at the physical microphone is too small to extend to the observer’s ear and the observer in fact experiences an increase in the sound pressure level with the active noise control system operating. The zone of quiet generated at the physical sensor location may be enlarged by minimising the acoustic energy density instead of the acoustic sound pressure. Elliott and Garcia-Bonito (1995) investigated the control of both pressure and pressure gradient (equivalent to one-dimensional acoustic energy density (Nelson and Elliott 1992)) in a diffuse sound field with two secondary sources. Minimising both the pressure and pressure gradient along a single axis produced a 10 dB zone of quiet over a distance of λ/2, in the direction of pressure gradient measurement. This is considerably larger than the zone of quiet obtained by minimising pressure alone. Virtual microphones are used in active noise control to shift the zone of quiet away from the physical microphone to a desired location of attenuation. This is shown in Fig. 1 (b), where the zone of quiet is shifted from the physical microphone to a virtual microphone located at the observer’s ear. Using the physical error signal, a virtual sensing algorithm is used to estimate the pressure at the virtual location. Instead of minimising the physical error signal, the estimated pressure is minimised with the active noise control system to generate a zone of quiet at the virtual location. A number of virtual sensing algorithms have been developed in the past to estimate the pressure at a fixed virtual location including the virtual microphone arrangement (Elliott and David 1992), the remote microphone technique (Roure and Albarrazin 1999), the forward difference prediction technique (Cazzolato 1999), the adaptive LMS virtual microphone technique (Cazzolato 2002), the Kalman filtering virtual sensing technique (Petersen et al. 2008) and the Stochastically Optimal Tonal Diffuse Field (SOTDF) virtual sensing method (Moreau et al. 2009b). In an effort to extend the localised zone of quiet generated at a fixed virtual location, one-dimensional virtual acoustic energy density sensors have been developed using the forward difference prediction technique (Kestell et al. 2000) and the SOTDF virtual sensing method (Moreau et al. 2009b). These one-dimensional virtual acoustic energy density sensors estimate the sound pressure and the pressure gradient along one of the three orthogonal axes. Forward difference prediction virtual energy density sensors were shown to produce a broader region of control compared to virtual microphones in numerical simulations and experiments conducted in a free field and a long narrow duct (Kestell et al. 2001a, Kestell 2000, Kestell et al. 2000; 2001b). Active noise control at a stochastically optimal virtual energy density sensor with two secondary sources in a pure tone diffuse sound field generates a zone of quiet with a diameter of approximately λ/2 at the virtual location (Moreau et al. 2009b). This is a five fold increase in the size of the zone of quiet compared to that obtained by cancelling the pressure at a virtual location alone. In many applications, the the virtual location is not spatially fixed. This occurs, for example, when the desired location of attenuation is the ear of a seated observer and the observer moves their head, thereby moving the virtual location. As a result, a number of moving virtual sensing al-