Nonlinear Active Noise Control System Research Articles

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.

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.

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.

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.

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.

Nonlinear Neural System for Active Noise Controller to Reduce Narrowband Noise

Noise in a dynamic system is practically unavoidable. Today, such noise is commonly reduced using an active noise control (ANC) system with the filtered-x least mean square (FXLMS) algorithm. However, the performance of the ANC system with FXLMS algorithm is significantly impaired in nonlinear systems. Therefore, this paper develops an efficient nonlinear adaptive feedback neural controller (NAFNC) to eliminate narrowband noise for both linear and nonlinear ANC systems. The proposed controller is implemented to update its coefficients without prior offline training by neural network. Hence, the proposed method has rapid convergence rate as confirmed by simulation results. The proposed work also analyzes the stability and convergence of the proposed algorithm. Simulation results verify the effectiveness of the proposed method.

Adaptive nonlinear ANC system based on time-domain signal reconstruction technology

When the primary reference signal obtained by the existing Active noise control (ANC) system is not accurate, the control effect of interior noise will be reduced or even fail. Considering the fault-tolerate and robustness of the system, the study proposes an adaptive nonlinear ANC system for interior noise, which contains noise signal decomposition, multi-network reconstruction model and Variable step-size LMS (VSS-LMS) algorithm. The noise signal decomposition method is used to address the non-stationary of the interior noise; Based on the signal components, the multi-network model for the noise signal reconstruction of passenger ear-sides is designed, which is pre-trained by a restricted Boltzmann machine for improved reconstruction accuracy and realize the adaptive extraction of signal features; And then based on the reconstruction signal components, the controller weights of corresponding components are adaptively updated by the VSS-LMS algorithm to control the passenger ear-sides noise. The effectiveness of the proposed adaptive nonlinear ANC system is validated using noise signal sources collected from a vehicle. Compared with the different ANC systems, the proposed system is superior in terms of fault-tolerant and robustness, which can guarantee stable work of the interior noise control.

A novel acoustic feedback compensation filter for nonlinear active noise control system

The acoustic feedback is widely seen in the active noise control (ANC) system for short acoustic duct such as the intake system of an automobile engine, which severely destabilizes the stability of the original ANC system. The conventional acoustic feedback compensation methods based on IIR filter can only be applied to the linear acoustic path and is not suitable for a nonlinear ANC (NANC) system. To solve this problem, this paper proposes a Volterra recursive even mirror Fourier nonlinear (VREMFN) filter, which can effectively suppress both linear acoustic feedback and nonlinear acoustic feedback in the NANC system. In this paper, we show the solutions for the linear acoustic feedback and nonlinear acoustic feedback of VREMFN and discuss its stability condition. Moreover, a new leaky normalized LMS algorithm is also developed to further improve the performance of NANC system based on VREMFN. Simulated results comparing IIR, Volterra and VREMFN based on parameter adaptive algorithm (PAA), FXLMS and FULMS show that the proposed VREMFN dramatically improves the noise reduction performance of NANC system both in linear acoustic feedback path and nonlinear acoustic feedback path. Furthermore, two experiments with different acoustic feedback paths also demonstrate the effectiveness of the proposed VREMFN.

Flower Pollination Heuristics for Nonlinear Active Noise Control Systems

In this paper, a novel design of the flower pollination algorithm is presented for model identification problems in nonlinear active noise control systems. The recently introduced flower pollination based heuristics is implemented to minimize the mean squared error based merit/cost function representing the scenarios of active noise control system with linear/nonlinear and primary/secondary paths based on the sinusoidal signal, random and complex random signals as noise interferences. The flower pollination heuristics based active noise controllers are formulated through exploitation of nonlinear filtering with Volterra series. The comparative study on statistical observations in terms of accuracy, convergence and complexity measures demonstrates that the proposed meta-heuristic of flower pollination algorithm is reliable, accurate, stable as well as robust for active noise control system. The accuracy of the proposed nature inspired computing of flower pollination is in good agreement with the state of the art counterpart solvers based on variants of genetic algorithms, particle swarm optimization, backtracking search optimization algorithm, fireworks optimization algorithm along with their memetic combination with local search methodologies. Moreover, the central tendency and variation based statistical indices further validate the consistency and reliability of the proposed scheme mimic the mathematical model for the process of flower pollination systems.

BIBO-stable implementation of adaptive function expansion bilinear filter for nonlinear active noise control

The preeminent merit of function expansion bilinear (FEB) filters is their ability to represent nonlinear distributions for active noise control (ANC) systems. Unfortunately, the huge computational burden and bounded input bounded output (BIBO) unstable problem hinder its practical applications. In this paper, we propose a general channel reduced efficient implementation algorithm for FEB filter and two BIBO stable control methods, to further reduce the computational load and overcome the unstable problem. The efficiency of the proposed methods is verified by computational complexity analyses and computer simulations for nonlinear ANC (NANC) systems. The results of computational analysis and computer simulation show the satisfied control performances with significant computational reduction.

Hermite Functional Link Artificial-Neural-Network-Assisted Adaptive Algorithms for IoV Nonlinear Active Noise Control

The Internet of Vehicles (IoV) plays a central role in intelligent transportation systems. Components, such as motor and transmission in the vehicle may produce noise, which seriously affects comfort. Therefore, vehicle manufacturers attach great importance to active noise control (ANC) technology. However, such an ANC system may have some nonlinear distortions in practical, thereby the nonlinear ANC (NANC) system is warranted. Moreover, we consider using IoV for rational resource allocation and record historical data for fault diagnosis, early warning, etc. So far, no work on NANC in the IoV environment is reported. In this article, based on the Hermite polynomial, a class of functional link artificial neural network (FLANN) algorithms is developed for NANC. The first proposed algorithm, called filtered-h least mean ${\mathcal {L}}_{p}$ -norm (FhLMP), incorporates the ${\mathcal {L}}_{p}$ -norm to obtain reliable performance. To further enhance the performance, the recursive FhLMP (RFhLMP) and hyperbolic recursive FhLMP (HRFhLMP) algorithms are designed by formulating two recursive structures. The proposed RFhLMP algorithm takes the filter output as part of the input and is expanded by the Hermite FLANN. The HRFhLMP algorithm activates the output by a hyperbolic tangent function and then recursively returns the activated output to the filter input. Simulations verify the improvement of the proposed algorithms for the NANC system.

Hierarchical partial update generalized functional link artificial neural network filter for nonlinear active noise control

To reduce the computational burden of the generalized FLANN (GFLANN) filter for nonlinear active noise control (NANC), a hierarchical partial update GFLANN (HPU-GFLANN) filter is presented in this paper. Based on the principle of divide and conquer, the proposed HPU-GFLANN divides the complex GFLANN filter (i.e., long memory length and large cross-terms selection parameter) into simple small-scale GFLANN modules and then interconnected in a pipelined form. Since those modules are simultaneously performed in a parallelism fashion, there is a significant improvement in computational efficiency. Besides, a hierarchical learning strategy is used to avoid the coupling effect between the nonlinear and linear part of the pipelined architecture. Data-dependent hierarchical M-Max filtered-error LMS algorithm is derived to selectively update coefficients of the HPU-GFLANN filter, which can further reduce the computational complexity. Moreover, the convergence analysis of the NANC system indicates that the proposed algorithm is stable. Computer simulation results verify that the proposed adaptive HPU-GFLANN filter is more effective in nonlinear ANC systems than the FLANN and GFLANN filters.

Nonlinear active noise control system based on correlated EMD and Chebyshev filter

• A nonlinear ANC system using signal decomposition and Chebyshev filter is proposed. • The non-stationary primary noise is decomposed by the improved correlated EMD. • The Chebyshev nonlinear filter is investigated to expand the decomposed IMFs. • Simulation results indicate that proposed method outperforms conventional methods. Investigations into active noise control (ANC) have been widely conducted with the aim of effective control of low-frequency noise. This paper proposes a novel nonlinear ANC system to control non-stationary noise produced by rotating machinery under nonlinear primary path. A real-time correlated empirical mode decomposition (CEMD) is first presented to decompose non-stationary noise into intrinsic mode functions (IMFs), some of which are chosen by the correlation analysis between IMFs and primary noise. Subsequently, the second-order Chebyshev nonlinear filter is applied to expand selected IMFs that are controlled individually by the filtered-x LMS. The convergence of proposed nonlinear ANC system is also investigated. Simulation results demonstrate that proposed method outperforms the filtered-x LMS, filtered-s LMS and Volterra filtered-x LMS algorithms with respect to noise reduction and convergence rate.

Improved adaptive recursive even mirror Fourier nonlinear filter for nonlinear active noise control

In this paper, we analyze the theoretical mechanism for the effectiveness of recursive filters including both linear and nonlinear feedforward and feedback subsections to accurately approximate nonlinear distributions in the active noise control (ANC) system. As a result, we improve the recursive even mirror Fourier nonlinear (REMFN) filter by adding an additional linear section termed REMFNL filter together with its channel reduced form (CRREMFNL) to explore better control performance. As for the linear feedback section introduced, we have studied the bound-input bound-output (BIBO) stability condition for the REMFNL filter and designed a stable control scheme to guarantee the filter satisfying the stability criteria. The performance of the proposed filters equipped with a filtered-x least mean square (FXLMS) algorithm is validated through analyses of computational complexity and simulations of various nonlinearities for nonlinear ANC (NANC) systems. Simulation results demonstrate that the proposed REMFNL and CRREMFNL filters can achieve better performance over the bilinear, recursive second-order Volterra (RSOV), recursive functional link artificial neural network (RFLANN) and standard REMFN filters based on the FXLMS algorithm, which often outperform the conventional Volterra FXLMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms.

Backtracking search integrated with sequential quadratic programming for nonlinear active noise control systems

In the present work, integrated strength of backtracking search algorithm (BSA) and sequential quadratic programming (SQP) is exploited for nonlinear active noise control (ANC) systems. Legacy of approximation theory in mean squared sense is utilized to construct a cost function for ANC system based on finite impulse response (FIR) and Volterra filtering procedures. Global search efficacy of BSA aided with rapid local refinements with SQP is practiced for effective optimization of fitness function for ANC systems having sinusoidal, random and complex random signals under several variants based on linear/nonlinear and primary/secondary paths. Statistical observations demonstrated the worth of stochastic solvers BSA and BSA-SQP by means of accuracy, convergence and complexity indices.

Functional link artificial neural network filter based on the q-gradient for nonlinear active noise control

As one of the most commonly used nonlinear active noise control (NANC) algorithms, the filtered-s least mean square (FsLMS) algorithm outperforms the conventional filtered-x least mean square (FxLMS) algorithm when the primary path has a quadratic nonlinearity. However, it still suffers from performance degradation under strong interferences. In this paper, two new algorithms, named filtered-s q-least mean p-norm (FsqLMP) and filtered-s q-least mean square (FsqLMS), based on the concept of Jackson's derivative, are proposed. By using new Jackson's derivative method, the proposed algorithms are less sensitive to the interferences in NANC system. Additionally, it is shown that the family of q-least mean square algorithms are special cases of the proposed FsqLMP algorithm. To further improve performance of the FsqLMS algorithm and solve the parameter selection problem, a time varying q scheme is developed. Simulation studies indicate that the proposed algorithms provide superior performance in various noise environments as compared to the existing algorithms.

A generalized exponential functional link artificial neural networks filter with channel-reduced diagonal structure for nonlinear active noise control

The nonlinear adaptive exponential functional link artificial neural networks (E-FLANN) filter has been introduced to improve the noise reduction capability of the functional link artificial neural networks (FLANN) in nonlinear active noise control (NANC) system. It, however, suffers from a heavy computational burden at the nonlinear secondary path (NSP) and poor convergence performance in strong nonlinearity systems. To surmount these shortcomings, a computationally efficient generalized E-FLANN filter with the channel-reduced diagonal structure (GE-FLANN-CRD) for NANC system is developed in this paper. Based on introducing the suitable cross-terms and adaptive exponential factor into the trigonometric functional expansions, the nonlinear processing capability of the filter is enhanced in NANC. Also, by applying the filtered-error least mean square (FELMS) algorithm to the GE-FLANN-CRD, it substantially decreases the computational cost to update the exponential factor. Computer simulations demonstrate that the proposed filter-based the NANC system performs better than the FLANN, E-FLANN and Generalized FLANN (GFLANN) filters-based NANC system in the presence of strong nonlinearity.

Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control

In many practical active noise control systems, the nonlinear secondary path (NSP) model can offer broader applications than the linear secondary path (LSP) model for the widespread existence of nonlinearities in the secondary path. However, the computational burden often limits the application of the NSP algorithms. In this paper, we apply a sparse Volterra model for the LSP and NSP instead of the complete Volterra model, which may be over parameterized for the nonlinear active noise control (NANC) system. The developed new control algorithms greatly result in reduction of computational complexity. We also provide an analysis of the NANC system to show that the noise at the canceling point could be approximated by the function expansion filters when the secondary path is modeled as the second-order Volterra series. In addition, two new function expansion forms, the even mirror Fourier nonlinear filter with a linear finite-impulse response section and the Chebyshev filter, are explored to process the nonlinearities in the NANC system using the filtered-x least mean square and filtered-error least mean square algorithm structures. The computational complexity analysis and the computer simulations validate that the new control algorithms with a sparse Volterra model for the secondary path can significantly reduce computational load without sacrificing the control performance.