Narrowband Active Noise Control System Research Articles

Improved Direct–Parallel Active Noise Control Systems for Narrowband Noise

Narrowband active noise control (NANC) systems are extensively used to cancel narrowband noise. Direct, parallel, and direct–parallel NANC systems use nonacoustic sensors to measure rotational speeds, and a bank of signal generators then produces synchronized sinusoidal waveforms as reference signals corresponding to the fundamental frequency of the undesired noise. The performance of direct NANC systems is based on the frequency difference between two adjacent reference input sinusoids. Parallel NANC systems apply several sinewave generators and two-weight adaptive filters in parallel to attenuate these narrowband components. Conventional direct–parallel NANC systems split these sinusoids into several mutually exclusive sets such that the distance between frequencies within sets is maximized. This paper proposes an improved direct–parallel NANC system in which reference sinusoidal signals are separated by amplitude to enhance efficiency and improve noise reduction performance. Several experiments were conducted using a muffler model to verify the performance of the proposed NANC system.

An error separation module with variable momentum algorithm for narrowband active noise control

Narrowband active noise control (NANC) is effective for stationary low-frequency noise but struggles with non-stationary noise from rotating or reciprocating machinery whose speed changes cause frequency and amplitude variations. This leads to inaccuracies in the reference frequency estimation and reduced NANC performance. This paper introduces an error separation module (ESM) that integrates autoregressive (AR) models with a variable momentum least mean square (VMLMS) algorithm. This combination effectively separates and suppresses the NANC system residual error across frequencies, enhancing the system's ability to track frequencies accurately in non-stationary conditions. The proposed solution has been validated through extensive simulations and real noise reduction experiments, showing improved noise reduction performance, faster convergence, and a decrease in steady-state mean squared error (MSE).

Online secondary path modeling algorithm without auxiliary noise for narrowband active noise control

Online secondary path modeling (SPM) is a practical method for real-time noise reduction in narrowband active noise control (NANC) systems, particularly when addressing variations in the secondary path. However, the common practice of using auxiliary noise for online SPM increases the residual noise power and deteriorates the noise reduction performance. The present study proposes a strategy that does not rely on auxiliary noise for online SPM in NANC systems. The proposed algorithm comprises two stages: Stage A models the primary path, whereas Stage B concurrently engages in online SPM and active noise control. The control signal is used to model the discrete Fourier transform (DFT) coefficients of the secondary path, avoiding the need for an auxiliary noise and significantly reducing the computational complexity. Moreover, the predicted primary path from Stage A is employed to obtain the pure desired signal of the online SPM. This strategy decorrelates the primary noise and the modeling signal, and accelerates the convergence of the algorithm. Simulations of recorded data demonstrate that the proposed algorithm can quickly track variations in both the primary and secondary paths, and maintain the noise reduction performance and stability of the system.

A low-complexity parallel local remote microphone technology for multichannel narrowband active noise control systems

Narrowband active noise control (NANC) systems can effectively eliminate periodic disturbances at its error sensors, but sometimes the error sensors are inconvenient to be placed at target locations for a long period. Remote microphone technology (RMT) can tackle this problem by moving quiet zones to the target areas. Nevertheless, the RMT-NANC system has significantly higher computational complexity than conventional NANC systems, particularly for multichannel systems. This hinders their implementation in real-time systems with limited computational resources. The additional computational burden stems from multiple convolutions involving the estimated global high-order secondary paths and observation filters when estimating the virtual error signals. To address this problem, a low-complexity parallel local RMT is proposed based on the narrowband filtered-x least mean square (PLRMT-NFxLMS) algorithm in this paper. Using a two-step local modeling approach, multiple local modeling low-order filters for both secondary paths and observation filters are constructed during the training stage. In the subsequent control stage, virtual error signals are estimated in parallel for different frequency components using these filters instead of global modeling filters, thereby alleviating the substantial computational cost arising from convolutions between lengthy vectors. Moreover, a filtered-error structure, termed the PLRMT-NFeLMS algorithm, is introduced in the proposed algorithm to further reduce the computational complexity. A comprehensive analysis of computational complexity is provided to demonstrate the superiority of the two proposed algorithms. Extensive simulations and real-time experiments were conducted to validate the feasibility and practicability of these proposed methods.

An intelligent momentum perturbed variable step-size adaptive algorithm for fast converging HNANC systems

The existing methodologies for hybrid narrow-band active noise control (HNANC) systems utilises variants of the FXLMS algorithm, which typically resulted in degraded convergence and steady-state performance. In this paper, a class of variable step size (VSS) adaptive algorithms are explicitly developed for a HNANC system analyses and the convergence as well as the steady-state performance of the proposed framework are evaluated in comparison to the existing state-of-the-art. For an HNANC system designed to operate in a multiple noise environment, the VSS filtered-x LMS (VSSFXLMS) and momentum VSS filtered- x weight accumulated least mean square (MVSS-FXWALMS) algorithms are proposed. The proposed algorithm employs a variable step size that is inspired by the variable momentum factor, and combines these two parameters to drive the FXWALMS algorithm for an HNANC system in order to accomplish maximum noise reduction. In a multiple noise environment setup for an HNANC system, the proposed algorithm surpasses the state-of-the-art in nearly all conventional operating conditions. A detailed performance analysis of the proposed algorithm has been carried out using mean noise reduction ratio, steady-state power spectra at different conditions. The results demonstrate a significant improvement in noise reduction performance compared to the counterparts.

A narrowband active noise control system with coarse frequency estimator and spectrum shifter

The frequency of an internal synthetic reference signal that is inconsistent with that of the noise signal is a serious problem in narrowband active noise control (NANC) system. This is called frequency mismatch (FM), which severely deteriorates the performance of the system. To alleviate this problem, a multichannel feedback NANC system with a coarse frequency estimator and spectrum shifter is proposed in this paper. Rough estimations of multiple tones are provided by a coarse frequency estimator based on discrete Fourier transform (DFT) coefficients and fed into the spectrum shifter. Splitting the noise signal into several individual orthogonal reference signals by the spectrum shifter rather than internal generation can avoid FM problem. Because estimated frequency errors can be tolerated in the spectrum shifter but cannot be compensated by signal generators. Compared with existing methodologies, the proposed method relaxes the demand on the precision of the frequency estimator, and reduces the undesired delay in the frequency estimation by using smaller fast Fourier transform (FFT) blocks. Moreover, a computational complexity analysis of the proposed method indicates that the proposed method is advantageous in terms of computational complexity. Extensive simulations and real-time experiments were conducted to verify the superior noise reduction performance and faster convergence speed of the proposed method under different FM situations.

A New Effective Narrowband Active Noise Control System for Accommodating Frequency Mismatch

Narrowband active noise control (NANC) has shown excellent performance in dealing with the low frequency periodic noise generated by rotating machines, such as fans, engines and power transformers. Accommodating large frequency mismatch (FM) and improving its tracking capability is required for the NANC system. The existence of FM influences the noise cancellation performance. In this paper, a frequency correction algorithm based on least mean p-power (LMP) combined with the autoregressive (AR) model is designed for the NANC system, which is simple and feasible, and has a good performance under a large step size. In the NANC system, the reference signal is handled by a delay unit and AR model, and the coefficients of the AR model are adjusted by the LMP algorithm, which fine-tunes the coefficients and offers the reference signals to the NANC system. The stability bounds for the step size parameter have also been derived in the mean sense. The designed mechanism converges fast and enhances the noise decrement. Extensive simulations are performed to demonstrate the superior performance of the proposed NANC in dealing with periodic noises.

A New Virtual Tracking Sub-Algorithm Based Hybrid Active Control System for Narrowband Noise With Impulsive Interference

Mechanical noise is usually a mixture of narrowband and impulsive noise which needs complex active noise control (ANC) algorithms to improve the de-noising performance. But the ANC algorithm with a high computation load will reduce the real-time performance of an ANC system, thus decreasing the attenuation performance and even leading to divergence. To alleviate this contradiction in narrowband ANC systems, a new virtual filtered-x L0 norm discrete Fourier cancellation (FxL0DFC) based hybrid FxNLMS(filtered-x normalized least mean square)-FxDFC framework is proposed to decrease the total computing load and keep good attenuation performance. For a fast-changing noise, the FxNLMS algorithm is employed. The new virtual FxL0DFC algorithm serves to prepare parameters for steady-state, and when this happens, the FxDFC algorithm with the parameters provided by FxL0DFC is applied. Compared to using the FxNLMS algorithm to attenuate narrowband periodical noise, the FxDFC algorithm has nearly the same tracking performance while having a low computational load. As a result, the FxL0DFC-based FxNLMS-FxDFC algorithm leads to a reduction of the total computational load. Moreover, the proposed method performs excellently in terms of tracking in simulations and experiments on actual data, particularly in environments with rapid power changes and impulsive noise.

An improved parallel narrowband active noise control system with local on-line secondary-path modeling equipped with frequency estimation algorithm

Active noise control technology shows good performance in those low-frequency narrowband noise control applications. Suffering from time-varying frequencies and secondary path, the performance of narrowband active noise control system may deteriorate seriously. In this work, an improved narrowband active noise control system is proposed to improve the noise reduction performance in those time-varying system. In the improved system, a frequency tracker based on the adaptive notch filter is adopted to estimate the frequencies of the noise signal. The result of frequency estimation is used to generate the reference signal and the prior information of the secondary-path modeling process. Then, the local secondary-path modeling can be conducted in the system with unknown fixed tonal noise signal or time-varying tones. Simulations and experiments are conducted to verify the performance of the proposed algorithm, and the results show that the proposed algorithm has good behavior.

Experimental Research on Reducing Flow-Induced Cavity Resonance with a Narrowband Active Noise Control System

In this paper, active control of flow-induced cavity resonance noise is addressed. A hybrid numerical method is presented to predict the resonance frequency and, instead of traditional active flow control, a narrowband active noise control system is utilized to suppress the resonance. A duct system is built up at low Mach numbers and experiments are carried out to validate the proposed methods. The results have shown that the resonance frequency could be predicted with 1.5% errors and the flow-induced narrowband noise could be effectively suppressed at both the fundamental frequency and its first harmonic. More than 10 dB global attenuations could be achieved for the fundamental resonance frequency without noise enhancements at other frequencies. Further, it was also found that the optimal reference frequency of the narrowband active noise control system could be largely biased from the original resonance frequency, which indicates a nonlinear mechanism of the control system.

Statistical analysis of multichannel FxLMS algorithm for narrowband active noise control

This paper analyzes the statistical performance of a multichannel narrowband active noise control (NANC) system based on the filtered-x least mean square (FxLMS) algorithm. The difference equations for the mean and mean square transient convergence behavior of the multichannel NANC system are derived. Steady-state expressions for weight-errors and mean square errors are then developed in closed forms. Stability boundaries for the multichannel FxLMS algorithm in the mean and mean square sense are also derived. When considering the mean square convergence, the coupling between the cross secondary paths and different frequencies is considered skillfully by matrixing and vectorization operations. Extensive simulations verify the accuracy of the theoretical analysis. Our findings deepen the understanding of the transient and steady-state behaviors of the multichannel NANC system and provide guidance for algorithm design, facilitate its improvement, and assist in parameter selection.

A distributed FxLMS algorithm for narrowband active noise control and its convergence analysis

A conventional multichannel narrowband active noise control (MNANC) system can effectively suppress low-frequency periodic noise. However, a large number of secondary sources and error sensors are required in the system, which leads to high computational complexity. To address this problem, a diffusion narrowband filtered-x least-mean-square (DNFxLMS) algorithm is proposed based on distributed acoustic sensor networks. The computational burden is dispersed among the nodes over the networks. A comprehensive statistical analysis of the algorithm is conducted to better understand its convergence properties. Specifically, we investigate the convergence behavior of the weight-error vector in the mean and mean-square sense. Based on this analysis, the stability bound of the system is discussed. The expressions for steady-state mean-square deviation (MSD) and excess mean-square error (EMSE) are derived. Extensive computer simulations are conducted to verify the theoretical analysis and to evaluate the usefulness of the DNFxLMS algorithm.

A narrowband active noise control system with autoregressive model and linear cascaded adaptive notch filter

Active noise control (ANC) system outperforms traditional passive noise control system in suppressing narrowband noise with low frequency. To reach a superior control quality, an accurate frequency of reference signal is required for the narrowband ANC (NANC) system. The existence of frequency mismatch (FM) degrades the performance of the system. In this paper, a frequency estimation algorithm based on linear cascaded adaptive notch filter (LCANF) combined with the autoregressive (AR) model is designed for the NANC system, which is simple and feasible as well as has an extremely low computational load. In the new NANC system, the rough estimations of multiple tones are given by the LCANF algorithm. Then the results are fed into the AR models, which fine-tune the estimated frequencies and offers the reference signals to the NANC system. The designed new mechanism effectively cuts down the computational load. Extensive simulations were conducted and the results demonstrate that the proposed system converges fast and has prominent noise reducing performance when it deals with periodic noises.

A Novel Narrowband Active Noise Control System with Online Secondary Path Modeling Based on Factor Decomposition and Application in Open Space

Due to the complexity of the coupling between the active noise control (ANC) controller and secondary path estimator, performance analysis of the system becomes particularly difficult. At present, the performance analysis of the system is often based on the fact that the secondary path tends to be stable, and the secondary path fitting error is minimal. However, in the early stage of system operation, or when the secondary path changes suddenly, the secondary path fitting error is significant, which easily causes divergence of the system control. It is still unable to guarantee the step-size bounds of convergence stability. Therefore, factor decomposition was used to analyze the mean weight behavior in this study. This strategy emphasizes the influence of secondary path modeling (SPM) error. The mean square behavior was evaluated using the energy conservation relationship. According to the established theoretical model, the convergence condition of the system was derived and the upper bound of step size suitable for all stages of system operation was obtained. The simulation and experimental results show that the ANC system is quite stable and robust under extreme conditions and has an obvious noise reduction effect in a specific range of open space, which can reach about 20 dB noise reduction.

Modified narrowband active noise control system with frequency mismatch tolerance

A common system used for canceling sinusoidal noise caused by revolving equipment such as machines, propellers and motors is the narrowband active noise control (NANC). In NANC, the frequency mismatch (FM) between a reference signal and the primary noise influences the noise reduction performance. The impact of the FM is eliminated by estimating frequency and changing the step size. The conventional method changes the step size by hand, which includes a significant expense and is not unreliabl. In this paper, a step size optimization algorithm with golden section search (GSS) and virtual system was proposed, which can automatically find the most suitable step size. The optimal step size was obtained by comparing the mean square errors at the golden section points. The virtual system was utilized to isolate the noise reduction system and the step size optimization system. Along these lines, the proposed method enhanced the noise decrement of the existing NANC system. Simulations were undertaken to evaluate the performance of the proposed algorithm.

Steady-State Performance Analysis of the Distributed FxLMS Algorithm for Narrowband ANC System With Frequency Mismatch

Distributed narrowband active noise control (NANC) systems using diffusion filtered-x least mean square (FxLMS) algorithm can effectively suppress the low-frequency periodic noise generated by rotating machinery. The computational burden is dispersed among the nodes over the acoustic sensor networks. The frequency of the reference signal is usually identified by a non-acoustic sensor in a NANC system. However, the frequency of the reference signal will be different from the primary noise frequency due to inevitable aging and fatigue accumulation and the control performance of NANC degrades considerably. This phenomenon is referred to as frequency mismatch (FM). In this letter, we analyze the performance degradation of the diffusion FxLMS algorithm due to FM in an NANC system. A theoretical model of the diffusion FxLMS algorithm in the presence of FM is derived based on the equivalent transfer function approach. Extensive simulations are performed to confirm the validity of the theoretical analysis.

Analysis of the Frequency Interference in the Narrowband Active Noise Control System

The narrowband active noise control (ANC) algorithm works well in the multi-tone noise reduction system. However, the performance of this algorithm degenerates significantly when the noisy frequencies become very close (e. g. frequency gap is 3Hz where the sampling frequency is 5000Hz), which can be seen as frequency interference effects. Up to now, however, this effect has not been researched in detail. In this work, the frequency interference effects are analyzed and discussed. The convergence process, the noise reduction value, the stability condition and the optimum step size are obtained by extensive math formulation derivation, provided two frequencies are close and fixed. Theoretical results show that, tones with large frequency difference can be approximated to independent convergence while the system with close frequencies suffers from poor convergence rate. The value of step size plays an important role in convergence, but the interference effects could never be eliminated by adjusting step size. Simulations are conducted to verify the analysis and the results match well with the analysis.

Novel Adaptive Fuzzy Feedback Neural Network Controller for Narrowband Active Noise Control System

With the development of science and technology in recent years, many operating machines have become sources of noise affecting quality of life. Hence, the topic of noise diminution using an active noise control (ANC) system has attracted many researchers. This paper develops a new adaptive fuzzy feedback neural network controller (AFFNNC) to improve the performance for narrowband active noise control (NANC) systems. The proposed controller combines fuzzy inference and adaptive feedback neural network controllers that are based on the filtered-s least mean square (FSLMS) algorithm. The AFFNNC comprises five network layers, in which the output layer of the controller uses an adaptive algorithm to tune directly the parameters of filters without prior training. The computational complexity, convergence and stability of the AFFNNC are analyzed. Evaluations are performed on both linear and nonlinear NANC systems with a recorded noise signal that was obtained from a transformer. Numerical simulations confirm the efficiency of the proposed controller compared with other ANC controllers.

Multichannel narrowband active noise control system with a frequency estimator based on DFT coefficients

The narrowband active noise control system (NANC) is an active control system that cancels periodic noise. The ability of the system to suppress noise is affected by the accuracy of the frequency estimator. The frequency estimator in the existing narrowband system has difficulty balancing the estimation accuracy and computational complexity. In this paper, a filtered-x discrete Fourier transform coefficients estimator least mean square (Fx-DFTCE-LMS) algorithm is proposed to enhance the noise reduction capability of multichannel NANC system. This system can handle any degree of frequency mismatch without increasing the complexity. Compared with most existing estimation methods, the proposed method does not need set initial frequency or estimator step size. Numerous simulations demonstrate that the proposed NANC system can track multiple frequencies more quickly and accurately, and effectively reduce noise.

Development and experimental verification of a new computationally efficient parallel narrowband active noise control system

The filtered-x least mean square based narrowband active noise control (FX-NANC) system with a parallel structure is typically used to cancel low-frequency multi-tonal noise. The computational efficiency and system performance may, however, be greatly degraded due to an increase in the number of controlled frequencies or the length of estimated secondary path. To alleviate this problem, a cost-saving FE-NANC system has been recently proposed, but the system suffers from slow convergence. This paper presents a local secondary path estimation based filtered-error least mean square (LFELMS) algorithm and applies it to a narrowband active noise control (NANC) system. By filtering a single error signal with a set of low-order local secondary path (LSP) models to obtain filtered signals for weight updating, the proposed LFELMS based NANC (LFE-NANC) system requires significantly less computational cost compared to the FX-NANC system and has considerably faster convergence speed than the FE-NANC system. Two new LSP modeling methods are also proposed. In addition, a computational complexity analysis of some typical NANC systems and the proposed LFE-NANC system is provided. Numerical simulations are performed to investigate the accuracy of the LSP modeling methods and compare the performance of the proposed system with other NANC systems. Finally, real-time experiments are conducted to confirm the effectiveness of the proposed system in single-tone, multi-tone and non-stationary situations.