Virtual sensing using an adaptive LMS algorithm Manuscript Number 1175G Jacqueline M. MUNN, Ben S. CAZZOLATO and Colin H. HANSEN Active Noise and Vibration Control Group, Department of Mechanical Engineering, University of Adelaide, Adelaide, SA, 5005, Australia. Email:
[email protected] Abstract The aim of virtual error sensing is to project the localised zone of attenuation away from the error sensor, to a location where sound attenuation is desired, such as at an observer’s ear. Forward difference projection is a virtual sensing technique that employs an array of at least two microphones with fixed weights, calculated using either a linear or quadratic prediction. These prediction methods have shown promise in simulations, but in real-time control the prediction accuracy has been compromised by phase and sensitivity mismatches between the sensors, as well as the excitation of higher-order modes driven off-resonance. A possible solution to the problem is to take these sources of error into account when calculating the fixed weights, by using an adaptive LMS algorithm. This done by placing a microphone at the intended location of the zone of quiet and using an LMS algorithm to adapt the weights applied to the signal at each microphone in the prediction array until the optimal weights are determined. This paper will investigate the effect of phase and sensitivity mismatchand the presence of higher-order modes on the prediction accuracy of the fixed weights prediction method and the effectiveness of the LMS algorithm in compensating for these errors. KEYWORDS: active noise control, local control, virtual error sensing
INTRODUCTION The performance of the forward difference virtual microphones has been investigated in a onedimensional waveguide [1–5]. These studies found that the linear prediction algorithm is a more accurate predictor of the pressure at the virtual location than the quadratic prediction algorithm due to the presence of short wavelength extraneous noise. Munn et al [4] also found that accuracy of the pressure prediction was greatly affected by the phase and sensitivity mismatches that exists between microphone elements in the prediction array. The use of the adaptive LMS algorithm to determine the optimal microphone weights should help eliminate these errors. Cazzolato [6] investigated the performance of the LMS algorithm using a simulation of the one-dimensional waveguide in the presence of phase, sensitivity and position errors. This work found that the algorithm was able to compensate for these errors. However, the model only included the first six modes and therefore the effect of higher-order modes was not investigated. The aim of this paper is to investigate the effect of the higher-order modes on the prediction preformance of the fixed weights and the LMS algorithm in the noise free environment and in the presence of errors.
THEORY Open loop The performance of the three microphone array will be investigated in this paper using both the linear and quadratic prediction algorithm. The three microphones are equi-spaced over a distance of . Linear Estimate
! #" #$&'%
(1)
Quadratic Estimate (
" *),+ .
/
0
! #" #$ '% %'
(2)
where is the pressure at the virtual location, 1 , #" and #$ are the measured acoustic pressures, 2# is the distance between the microphone array (3$ ) and the virtual location and is the transducer separation distance (25 mm) . Adaptive LMS [7], 4
The optimal weights were determined using the gradient descent algorithm from 46587 9 465
