Multi-channel normalized FxLMS algorithm for active noise control

Kuo S.M., Morgan D.R.

Active noise control (ANC) is achieved by introducing a cancelling "antinoise" wave through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. ANC has application to a wide variety of problems in manufacturing, industrial operations, and consumer products. The emphasis of this paper is on the practical aspects of ANC systems in terms of adaptive signal processing and digital signal processing (DSP) implementation for real-world applications. In this paper, the basic adaptive algorithm for ANC is developed and analyzed based on single-channel broad-band feedforward control. This algorithm is then modified for narrow-band feedforward and adaptive feedback control. In turn, these single-channel ANC algorithms are expanded to multiple-channel cases. Various online secondary-path modeling techniques and special adaptive algorithms, such as lattice, frequency-domain, subband, and recursive-least-squares, are also introduced. Applications of these techniques to actual problems are highlighted by several examples.

Rupp M.

In some applications, like in active noise control, the error signal cannot be obtained directly but only a filtered version of it. A gradient adaptive algorithm that solves the identification problem under this condition is the well known Filtered-x Least-Mean-Squares (FxLMS) algorithm. If only one coefficient of this error-filter function is nonzero, a special case of the FxLMS algorithm, the Delayed-update Least-Mean-Squares (DLMS) algorithm is obtained. The drawback of these algorithms is the increased dynamic order which, in turn, decreases the convergence rate. Recently, some modifications for these algorithms have been proposed, overcoming the drawbacks by additional computations of the same filter order as the filter length M. In this contribution, an improvement is shown yielding reduced complexity if the error path filter order P is much smaller than the filter order M, which is the case for many applications. Especially for the DLMS algorithm a strong saving can be obtained.

Allen J.B., Berkley D.A.

Image methods are commonly used for the analysis of the acoustic properties of enclosures. In this paper we discuss the theoretical and practical use of image techniques for simulating, on a digital computer, the impulse response between two points in a small rectangular room. The resulting impulse response, when convolved with any desired input signal, such as speech, simulates room reverberation of the input signal. This technique is useful in signal processing or psychoacoustic studies. The entire process is carried out on a digital computer so that a wide range of room parameters can be studied with accurate control over the experimental conditions. A fortran implementation of this model has been included.

Chai K., Liu Y.S., Hu B.J.

When vibrations generated by marine machinery propagate through a ship’s hull into the ocean, they produce low-frequency radiated noise with distinct “acoustic fingerprint” characteristics. This noise, characterized by stable and concentrated energy, long transmission distances, and difficulty in elimination, becomes the primary target for enemy sonar detection. Active vibration isolation serves as a critical method for reducing low-frequency vibrations in ships and enhancing their acoustic stealth performance. However, control challenges persist, including multi-frequency excitation, frequency fluctuation, multi-channel coupling, and slow convergence speed. To address these issues, this paper introduced an innovative multi-channel decentralized decoupling filtered-x least mean square (DMFxLMS) algorithm. Firstly, a recursive least squares identification algorithm with a forgetting factor was proposed, taking into account the characteristics of single-input, multi-output and multi-input, and multi-output control systems, effectively enhancing the algorithm’s convergence speed and control accuracy. Secondly, based on the decentralized decoupling control concept, the multi-channel control system was simplified into parallel single-channel control loops. The control weight coefficient updates were only related to adjacent error signals, significantly reducing the algorithm’s computational complexity. Thirdly, an anti-impact link was designed to improve the algorithm’s robustness, considering the interference caused by other mechanical equipment during the control process. The influence of abnormal error signals in the control weight coefficient correction term was suppressed, and a percentage function was introduced to limit the output signal. Finally, the feasibility and effectiveness of the DMFxLMS algorithm were verified through simulations and experiments. The results demonstrated that the DMFxLMS algorithm achieved significant control effects for both constant frequency line spectrum excitation and frequency fluctuating line spectrum excitation, fulfilling the objective of reducing base vibration. The DMFxLMS algorithm exhibited fast convergence and excellent robustness, making it suitable for practical engineering applications.

Zhou Z., Chen S., Zhang Z.

The normalized filtered-x least mean square (NFxLMS) algorithm adopts a normalized step size to improve the convergence and reduce the gradient noise caused by the high-power input signal. However, this normalization would introduce an even larger misadjustment than the FxLMS algorithm when this high-power noise is in a low-frequency range. To improve the performance of the NFxLMS algorithm in such an environment, a novel vector-decomposition-based structure (VDBS) is proposed in the paper. In this study, the filter weight vector is decomposed into two sub-vectors that are updated by different algorithms. The first sub-vector is updated by the NFxLMS algorithm, whereas the second one is updated by the FxLMS algorithm. In this way, the total misadjustment can be minimized by setting relevant parameters appropriately, while a faster convergence rate and smaller round-off errors can also be reached. The stability analysis proves that the proposed structure can enlarge the convergence range of the step size in the first sub-vector. The results of simulations and experiments justify that the VDBS can improve the performance of the NFxLMS algorithm for high-power low-frequency noise. The proposed structure can make the traditional NFxLMS algorithm perform better in a high-power low-frequency noise environment.

Koyama S., Brunnstrom J., Ito H., Ueno N., Saruwatari H.

An active noise control (ANC) method to reduce noise over a region in space based on kernel interpolation of sound field is proposed. Current methods of spatial ANC are largely based on spherical or circular harmonic expansion of the sound field, where the geometry of the error microphone array is restricted to a simple one such as a sphere or circle. We instead apply the kernel interpolation method, which allows for the estimation of a sound field in a continuous region with flexible array configurations. The interpolation scheme is used to derive adaptive filtering algorithms for minimizing the acoustic potential energy inside a target region. A practical time-domain algorithm is also developed together with its computationally efficient block-based equivalent. We conduct experiments to investigate the achievable level of noise reduction in a two-dimensional free space, as well as adaptive broadband noise control in a three-dimensional reverberant space. The experimental results indicated that the proposed method outperforms the multipoint-pressure-control-based method in terms of regional noise reduction.