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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. [ABSTRACT FROM AUTHOR]

Highlights • The filtered-x least mean square/fourth (FXLMS/F) algorithm for active noise control. • A convex combination of the FXLMS/F algorithm (C-FXLMS/F) for active noise control. • The stability condition of the proposed algorithm is analyzed, and computational complexity is provided. • Computer simulations demonstrate good convergence speed and noise reduction performance for active noise control. Abstract The filtered-x least mean square (FXLMS) algorithm is widely used for active noise control (ANC) systems. However, due to the fixed step-size of FXLMS algorithm being used, the FXLMS algorithm results in a compromise between noise reduction performance and convergence speed. Therefore, this paper proposes the filtered-x least mean square/fourth (FXLMS/F) algorithm for ANC systems, which can be viewed as a variable step-size FXLMS (VSS-FXLMS) algorithm. In order to further improve the algorithm performance, the convex combination of the FXLMS/F (C-FXLMS/F) algorithm for ANC systems is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXLMS/F and C-FXLMS/F algorithms can achieve better convergence performance as compared to the FXLMS and FXLMF algorithms under various noise input conditions, and the C-FXLMS/F algorithm outperforms the FXLMS/F algorithm. [ABSTRACT FROM AUTHOR]

The standard adaptive filtering algorithm with a single error norm exhibits slow convergence rate and poor noise reduction performance under specific environments. To overcome this drawback, a filtered-x generalized mixed norm (FXGMN) algorithm for active noise control (ANC) system is proposed. The FXGMN algorithm is developed by using a convex mixture of l p and l q norms as the cost function that it can be viewed as a generalized version of the most existing adaptive filtering algorithms, and it will reduce to a specific algorithm by choosing certain parameters. Especially, it can be used to solve the ANC under Gaussian and non-Gaussian noise environments (including impulsive noise with symmetric α -stable ( S α S ) distribution). To further enhance the algorithm performance, namely convergence speed and noise reduction performance, a convex combination of the FXGMN algorithm (C-FXGMN) is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXGMN and C-FXGMN algorithms can achieve better convergence speed and higher noise reduction as compared to other existing algorithms under various noise input conditions, and the C-FXGMN algorithm outperforms the FXGMN. [ABSTRACT FROM AUTHOR]

The active noise control (ANC) based on the principle of superposition is an attractive method to attenuate the noise signals. However, the impulsive noise in the ANC systems will degrade the performance of the controller. In this paper, a filtered-x recursive maximum correntropy (FxRMC) algorithm is proposed based on the maximum correntropy criterion (MCC) to reduce the effect of outliers. The proposed FxRMC algorithm does not requires any priori information of the noise characteristics and outperforms the filtered-x least mean square (FxLMS) algorithm for impulsive noise. Meanwhile, in order to adjust the kernel size of FxRMC algorithm online, a recursive approach is proposed through taking into account the past estimates of error signals over a sliding window. Simulation and experimental results in the context of active impulsive noise control demonstrate that the proposed algorithms achieve much better performance than the existing algorithms in various noise environments. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter. [Copyright &y& Elsevier]