Active Noise Control with Virtual Reference Signals in an FXLMS Algorithm

Abstract: Noise pollution from road traffic is one of the greatest environmental issues in modern day, and the social cost for road traffic noise was estimated to over 16 billion SEK per year in Sweden in2014. Passive or active control methods can be used to reduce the noise. Active control methods or active noise control is more suitable for attenuating noise in lower frequencies. Active noise control reduces noise by eliminating the noise with a secondary source. There are different control strategies to construct an active noise control system, where the update of the secondary sourceis controlled by an algorithm. There are several different algorithms that are possible to use, and one option is to use a Feedforward Filtered-X Least-Mean-Square (FXLMS) algorithm. It uses control positions where the noise is meant to be reduced and reference signals that measure the noise upstream prior the secondary source. FXLMS also uses a model of the secondary source path to the control position in order to ensure convergence of the algorithm. Although the use of multiple reference signals increases the accuracy of the algorithm, it also increases the convergence time and the practical cost of such an installation. Unfortunately, it can require many reference signals to obtain a sufficient noise reduction when the unwanted noise source is complex and has multiple propagation paths.This study investigates the possibility of producing a new, reduced set of reference signals with a linear combination of the original reference signals that still contain the majority of information needed for suficient noise reduction. This new set of reference signals are sometimes called virtual reference signals. Three different methods of virtual reference signals are analysed; first a constant method using singular-value decomposition on the covariance of the reference signals, second another constant method using singular-value decomposition on the covariance of response estimate from each corresponding reference signal, third an adaptive algorithm updating the linear combination to adapt for incoming data. The different strategies are tested on road test measurements at three different constant speeds, 40km=h; 80km=h and 120km=h, and on data generated from a numerical vehicle model in COMSOL.The results from the analysis indicates that the virtual reference signals could sufficiently reproduce information from the original reference signals to obtain a similar noise reduction with fewer reference signals. However, the virtual reference signals with the adaptive algorithm could not manage to track a transient system where the signal amplitudes are varying over time. Further work is needed to analyse the limits and requirements to obtain virtual reference signals that can represent and track a system even for transient events.