Nonlinear Active Noise Control Research Articles

Quantized information-theoretic learning based Laguerre functional linked neural networks for nonlinear active noise control

Traditional functional linked neural networks (FLNNs) impose a significant computational burden due to their input expansion, primarily stemming from the utilization of digital filters. This paper presents a Laguerre FLNNs filter for nonlinear active noise control (NANC) systems. By employing the truncated Laguerre series, the presented filter achieves effective approximation of long primary paths with a reduced filter length. Moreover, we develop adaptive algorithms rooted in information-theoretic learning (ITL) within the framework of the Laguerre-FLNNs NANC model. Using the ITL criterions, a Laguerre filtered-s maximum correntropy criterion (LFsMCC) algorithm is derived and a Laguerre filtered-s quantized minimum error entropy criterion (LFsQMEE) algorithm is proposed by minimizing Renyi’s quadratic entropy. To reduce the computation cost, an online vector quantization method is utilized to improve the LFsQMEE. This technique selectively quantizes the error vectors, reducing them to a smaller subset of samples within the codebook. Moreover, an enhanced LFsQMEE with a fiducial point is introduced. The steady-state performance and the computational complexity are analyzed. Theoretical analysis is validated through simulations and the control performance of the proposed model and algorithms is tested in experiments with both simulated and real paths.

Nonlinear active noise control with tap-decomposed robust volterra filter

The Volterra filter is proven to be a structurally simple method for nonlinear active noise control (NLANC). However, its wide application is deeply constrained by computational complexity. This paper proposes a tap-decomposed Volterra filter, in which a long-tap Volterra filter is approximated as multiple short-tap filters by the nearest Kronecker decomposition. Since the number of taps of decomposed filters is much less than that of the original counterpart, the proposed method greatly reduces the implementation cost of the Volterra filter. Moreover, for impulsive noise sources in NLANC, decomposed filters are updated using the maximum correntropy criterion derived from information theory. Simulation experiments with different noise source types highlight the noise control performance of the proposed approach.

A collaborative recursive generalized exponential functional link artificial neural network nonlinear filter based on optional parameter entry method

Different types of exponential functional link artificial neural network (EFLN) filters have been proposed for nonlinear active noise control (NANC) systems, but they still suffer from high computational complexity. To address this issue and further improve steady-state performance, this paper presents a collaborative recursive generalized exponential functional link artificial neural network nonlinear filter based on optional parameter entry method (CR-GEFLN-OPEM). A collaborative filtered-error least mean square (CFELMS) algorithm is also proposed. Simulations and an actual noise control trial demonstrate the improved steady-state performance and low computational complexity of the proposed filter in NANC systems.

Spline Adaptive Filtering Algorithm-based Generalized Maximum Correntropy and its Application to Nonlinear Active Noise Control

Spline Adaptive Filtering Algorithm-based Generalized Maximum Correntropy and its Application to Nonlinear Active Noise Control

Robust generalized hyperbolic secant algorithm for nonlinear active noise control

In nonlinear active noise control (ANC) system where the primary noise obeys non-Gaussian distribution, the traditional filter-s least mean square (FsLMS) algorithm is hardly satisfactory. In order to surmount this deficiency, a novel generalized hyperbolic secant function with lp norm (FsGHSFP) algorithm is proposed for nonlinear ANC system, which designs a robust optimization criterion utilizing the generalized hyperbolic secant distribution function. The FsGHSFP algorithm has robust noise attenuation capability for non-Gaussian noise, but suffers from the problem of tuning the parameter. To address this problem, an improved FsGHSFP (IFsGHSFP) algorithm is developed by taking advantage of the fact that continuous mixed norm does not need to adjust norm parameter. Moreover, in order to strike a balance between convergence and misalignment, thereby further enhancing the robustness of the ANC system, a convex combination algorithm of IFsGHSFP is suggested. The robustness mechanism of the proposed algorithms is analyzed, as well as stability conditions and computational complexity. It is verified by simulations that the proposed algorithms accelerate the convergence speed and improve the noise attenuation performance. In addition, the experimental results further validate the effectiveness of the proposed algorithms.

Fractional-order ascent maximum mixture correntropy criterion for FLANNs based multi-channel nonlinear active noise control

The filtered-s maximum correntropy criterion (FsMCC) algorithm was developed for nonlinear active noise control (NANC) in impulsive noise environments with the use of functional linked artificial neural networks (FLANNs) structure. However, the kernel-width of the FsMCC is constant, which is dull and cannot self-regulate to achieve both the fast convergence and low steady-state error performance. For better convergence ability, in this paper, a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm (FGA-FsMCC) is presented for multi-channel NANC system. The fractional lower-order moments supersede the non-existent second-order moments. To come up with a more reliable algorithm, by merging two kernels with complementary width, the fractional-order gradient ascent filtered-s mixture correntropy criterion (FGA-FsMMCC) was presented. The computational complexity and convergence conditions are analyzed. To verify the robustness of proposed algorithms, simulations are carried out to discuss parameters and control effects of algorithms for alpha-stable noise in different nonlinear environments.

Nonlinear autoregressive spline neural filter and its application

A novel recurrent model called nonlinear autoregressive spline neural filter (NARSNF) is introduced in this paper. Due to its unique spline nonlinear output autoregressive structure, NARSNF exhibits better fitting ability than IIR-spline adaptive filter (IIR-SAF) in identifying nonlinear dynamic systems with output autoregression. Correspondingly, the real-time recurrent learning algorithm based on NARSNF is derived and the Lyapunov stability analysis of learning rates is also provided. Moreover, the NARSNF and bilinear NARSNF (BNARSNF) are proposed to handle compensation of acoustic feedback for nonlinear active noise control (NANC). At last, simulation results in the context of nonlinear dynamic system identification and NANC verify the effectiveness of the proposed models.

Interpolated Individual Weighting Subband Volterra Filter for Nonlinear Active Noise Control

Nonlinear active noise control (NLANC) is always a challenge in algorithm design. Most of the NLANC algorithms are based on the linear-in-the-parameters (LIP) filters, and no work is conducted on subband adaptive filter (SAF). In this brief, a novel nonlinear SAF, termed the Volterra filtered-x normalized SAF (VFxNSAF), is proposed for NLANC, whose input vector is obtained according to the size of the analysis filter bank. Moreover, the virtual microphone strategy is applied to VFxNSAF to suppress the noise at a remote location. To mitigate the computational burden, the interpolated IWVFxNSAF with individual weighting (IW) (I-IWVFxNSAF) is proposed, in which the quadratic kernel is obtained by the interpolated filter. Simulation results corroborate the superiority of the VFxNSAF and I-IWVFxNSAF algorithms for NLANC.

Generalized Hyperbolic Tangent Based Random Fourier Conjugate Gradient Filter for Nonlinear Active Noise Control

The filtered-x least mean square (FxLMS) algorithm has been proposed for an active noise control (ANC) system. However, due to the used mean square error (MSE) criterion, FxLMS suffers from performance degeneration for non-Gaussian noises, dramatically. To address this issue, a novel robust generalized hyperbolic tangent (GHT) criterion is first constructed in this paper. Then, the random Fourier features (RFF) method and the conjugate gradient (CG) method are used to address the nonlinearity existing in ANC and solve the quadratic optimization problem induced by the GHT criterion, respectively. Finally, a novel robust random Fourier conjugate gradient filtered-x generalized hyperbolic tangent (RFCGFxGHT) algorithm is proposed for ANC. The theoretical analyses regarding the convergence and computational complexity of RFCGFxGHT are also derived. Simulation experiments on nonlinear ANC systems corrupted by the synthetic logistic chaotic and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable noises, as well as real-world functional magnetic resonance imaging (fMRI) and server room noises, are conducted to confirm the effectiveness, robustness, and desirable nonlinear learning ability of the proposed algorithm.

Fetal ECG extraction using temporal convolutional encoder-decoder network

To extract weak fetal ECG signals from mixed ECG signals recorded from maternal abdominal wall for accurate analysis of fetal heart rate and fetal ECG patterns. By exploiting the superior nonlinear mapping ability of deep convolutional network, we developed a nonlinear adaptive noise cancelling (nonlinear ANC) extraction framework based on a temporal convolutional encoder-decoder network for extracting fetal ECG signals. We first constructed a deep temporal convolutional network (TCED-Net) model for fetal ECG signal extraction, and with the maternal chest ECG signal as the reference signal, the maternal ECG component in the abdominal mixed signal was estimated using this model. The estimated maternal ECG component was subtracted from the mixed abdominal ECG signals to obtain the fetal ECG component. Experimental analyses were performed using synthetic ECG signals (FECGSYNDB) and clinical ECG signals (NIFECGDB, PCDB) to test the performance of the propose method. The results of experiments on the FECGSYNDB dataset showed that the proposed approach achieved good performance in F1-score (98.89%), mean-square-error (MSE; 0.20) and quality signalto-noise ratio (qSNR; 7.84). The F1- score reached 99.1% on the NIFECGDB dataset and 98.61% on the PCDB dataset. The R peak detection accuracy index of the proposed method was higher than the existing best-performing algorithms such as EKF (F1=93.84%), ES-RNN (F1=97.20%) and AECG-DecompNet (F1=95.43%) by 5.05%, 1.9% and 3.18%, respectively. The fetal ECG signals extracted using the proposed method are clearer than those by the existing algorithms, suggesting the potential value this method for effective fetal health monitoring during pregnancy.

Design of delayless multi-sampled subband functional link neural network with application to active noise control

To accelerate the convergence speed of the functional link neural network (FLNN) particularly for colored input signals, this paper proposes a delayless multi-sampled multiband-structured subband FLNN (DMSFLNN) structure. Then, to update the weights of the DMSFLNN, a normalized subband adaptive algorithm is devised. Next, the stability conditions, optimal step size and computational complexity are investigated. Moreover, the proposed method is applied to the nonlinear active noise control, obtaining the delayless multi-sampled multiband-structured filtered-s normalized least mean square (DMSFsNLMS) algorithm. Finally, simulation results demonstrate that the proposed method improves the convergence speed of the FLNN.

Low-complexity even mirror fourier adaptive filter for nonlinear active noise control

The Even Mirror Fourier (EMF) filter is the universal approximation for nonlinear systems, which has been used in active noise control (ANC) applications, especially in scenarios where ANC contains strong nonlinearity. However, the computational burden can impede its implementation in practice. To mitigate this disadvantage, an improved pipelined EMF (IPEMF) filter has been developed and applied for the nonlinear ANC systems, in this paper. The proposed architecture uses simple small-scale EMF modules (i.e., fewer coefficients) nested in a pipelined fashion to replace the complex EMF structure, and hence has got a computational advantage. Moreover, the modules of the IPEMF are designed to update the synaptic weight vector independently, and the output of IPEMF is simplified by the sum of the local estimates of the modules. As a consequence, the nonlinear processing capability is considerably improved and the filtered-error algorithm deduced for the IPEMF controller is less complicated. Simulation results show that the proposed IPEMF controller significantly reduces the computational complexity compared to EMF, while still maintaining control performance is as equivalent as EMF and better than the pipelined EMF (PEMF), pipelined Volterra filter (PVF).

Performance analysis of nonlinear active noise control system using weighted FLANN algorithm

Functional Link Artificial Neural Network is popularly used as controller in nonlinear Active noise control system as it is characterized by simple structure and relatively low computational complexity. Learning capability of the controller is achieved by filter-s least mean square algorithm and its variants. But these class of algorithms are characterized by slow convergence. This paper uses a set of combining weights to expedite the convergence process and the performance of the active noise controller is analyzed by tracking the combining weights. Computer simulation experiments are also conducted and analysis results presented.

Conjugate gradient-based FLANN algorithms in nonlinear active noise control

The conjugate gradient (CG) method exhibits fast convergence speed than the steepest descent, which has received considerable attention. In this work, we propose two CG-based methods for nonlinear active noise control (NLANC). The proposed filtered-s Bessel CG (FsBCG)-I algorithm implements the functional link artificial neural network (FLANN) as a controller, and it is derived from the Matérn kernel to achieve enhanced performance in various environments. On the basis of the FsBCG-I algorithm, we further develop the FsBCG-II algorithm, which utilizes the Bessel function of the first kind to constrain outliers. As an alternative, the FsBCG-II algorithm has reduced computational complexity and similar performance as compared to the FsBCG-I algorithm. Moreover, the convergence property of the algorithms is analyzed. The proposed algorithms are compared with some highly cited previous works. Extensive simulation results demonstrate that the proposed algorithms can achieve robust performance when the noise source is impulsive, Gaussian, logistic, and time-varying.

A novel application of integrated grasshopper optimization heuristics for attenuation of noise interferences

Novel application of integrated swarming intelligence computing paradigm is exploited for reliable treatment of nonlinear active noise control (ANC) systems using global search capacity of grasshopper optimization algorithm (GOA) combined with local search efficacy of sequential quadratic programming (SQP), i.e., GOA-SQP. The designed optimization mechanism GOA-SQP is applied to minimize the cost function of ANC controller incorporating the nonlinear Volterra filtering having linear/nonlinear primary/secondary paths in case of different noise interferences of sinusoidal, random, and complex random type signals. The comparison of the results through statistical observations in terms of accuracy, convergence and complexity indices reveals that the GOA-SQP based ANC controllers are operative, resilient and viable.

Cascaded Random Fourier Filter for Robust Nonlinear Active Noise Control

The random Fourier filter-based filtered-x least mean square (RF-FxLMS) algorithm has been proposed for the nonlinear active noise control (NANC) system to reduce the computational burden of the kernel filter. However, the RF-FxLMS algorithm markedly fluctuates when dealing with impulsive noise. In addition, the computing cost for the RF-FxLMS algorithm is still pricey in practice. In this work, a random Fourier filter based filtered-x generalized hyperbolic secant function (RF-FxGHSF) algorithm is presented to deal with impulsive noise. In virtue of the bilinear scheme, a cascaded random Fourier filter model is designed for concise computations, and the cascaded RF-FxGHSF (CRF-FxGHSF) algorithm is derived. Moreover, the steady-state convergence conditions are analyzed. The calculation complexity of the proposed algorithms is compared, and experiments emphatically analyze the principle for the presented model. Numerical simulations with &#x03B1;-stable noise and real noise carried out in different nonlinear path scenarios verify the convergence ability of proposed algorithms.

Filtered-x Set Membership Algorithm With Time-Varying Error Bound for Nonlinear Active Noise Control

In order to reduce the computational complexity for nonlinear Active Noise Control (ANC) systems, we propose a filter-x set membership with a time-varying error bound (Fx-SM-VEB) algorithm based on the adaptive approximation principle and data-selective update strategy. By introducing the time-varying error bound (VEB) to replace a pre-specified threshold when nonlinearity exists in the components of the ANC system, the performance of the proposed algorithm is significantly improved. Moreover, the VEB is also easily expanded against the impulsive noise that is normally encountered in actual ANC systems. Based on the impulsive-free estimation, we develop a robust Fx-SM-VEB (RFx-SM-VEB) algorithm for the ANC system which is corrupted by impulsive noise in the reference input signal. Besides, we provide analyses of the steady-state behavior, stability conditions, and computational complexity of the proposed algorithms. Many simulation results in different scenarios of the ANC system have shown that the proposed algorithms are efficient under the nonlinear environment and impulsive noise.

Frequency domain exponential functional link network filter: Design and implementation

The exponential functional link network (EFLN) filter has attracted tremendous interest due to its enhanced nonlinear modeling capability. However, the computational complexity will dramatically increase with the dimension growth of the EFLN-based filter. To improve the computational efficiency, we propose a novel frequency domain exponential functional link network (FDEFLN) filter in this paper. The idea is to organize the samples in blocks of expanded input data, transform them from time domain to frequency domain, and thus execute the filtering and adaptation procedures in frequency domain with the overlap-save method. A FDEFLN-based nonlinear active noise control (NANC) system has also been developed to form the frequency domain exponential filtered-s least mean-square (FDEFsLMS) algorithm. Moreover, the stability, steady-state performance and computational complexity of algorithms are analyzed. Finally, several numerical experiments corroborate the proposed FDEFLN-based algorithms in nonlinear system identification, acoustic echo cancellation and NANC implementations, which demonstrate much better computational efficiency.

A Low-Complexity Volterra Filtered-Error LMS Algorithm with a Kronecker Product Decomposition

Nonlinear active control is very important in many practical applications. Many well-known nonlinear active noise control algorithms may suffer from high computational complexity and low convergence speed, especially in the nonlinear secondary path case. Thus, it is still an actively researched topic for reducing complexity and improving the convergence rate. This paper presents a low-complexity Volterra filtered-error least mean square algorithm when taking a decomposable Volterra model into account for active control of nonlinear noise processes, which is referred as DVMFELMS. The computational complexity analysis shows that the proposed DVMFELMS algorithm can significantly reduce the nonlinear active noise control system’s complexity. The simulation results further show that the proposed algorithm can achieve promising performance compared with the Volterra-based FELMS algorithm and other state-of-the-art nonlinear filters, while the decomposable error of the Volterra kernel may be introduced inevitably. Moreover, the proposed DVMFELMS algorithm shows a better convergence rate in the broadband primary noise case due to fewer parameters used in each sub-filter.

A nonlinear active noise control algorithm using the FEWT and channel-reduced recursive Chebyshev filter

Active noise control (ANC) has been widely studied to eliminate low-frequency noise. However, efficiently controlling higher-order distortions of nonlinear primary and secondary path is still a major challenge. To address this, this paper proposes a novel nonlinear ANC algorithm based on the fast empirical wavelet transform and recursive Chebyshev nonlinear filter. In this method, the fast empirical wavelet transform based on order-statistic filtering is first applied to decompose non-stationary noise into empirical mode functions (EMFs) which are more stationary and easy to control. Furthermore, a novel third-order Chebyshev nonlinear filter including the non-recursive subsection and recursive one is proposed to individually expand EMFs for compensating higher-order nonlinear distortions from primary path and secondary path. Moreover, the strategy of channel-reduced diagonal structure is designed to optimise the number of expanded channels, and the computational complexity of proposed algorithm is also investigated. Experimental results demonstrate that proposed method performs the highest noise reduction over the conventional algorithms but also has a fast convergence rate.