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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. • Design multi-channel nonlinear active noise control system with functional linked artificial neural networks. • Proposing a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm. • Defining the maximum mixture correntropy criterion. • Deriving a fractional-order gradient ascent filtered-s maximum mixture correntropy criterion algorithm. • Computational complexity analysis of proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract 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. [ABSTRACT FROM AUTHOR]

The filtered-x least mean lp -norm (FxLMP) algorithm is proven to be useful for nonlinear active noise control (NANC) systems. However, its performance deteriorates when the impulsive noises are presented in NANC systems. To surmount this shortcoming, a new nonlinear adaptive algorithm based on Volterra expansion model (VFxlogLMP) is developed in this paper, which is derived by minimizing the lp -norm of logarithmic cost. It is found that the FxLMP and VFxlogLMP require to select an appropriate value of p according to the prior information on noise characteristics, which prohibit their practical applications. Based on VFxlogLMP algorithm, we proposed a continuous lp -norm algorithm with logarithmic cost (VFxlogCLMP), which does not need the parameter selection and thresholds estimation. Benefiting from the various error norms for 1≤ p ≤2, it remains the robustness of VFxlogLMP. Moreover, the convergence behavior of VFxlogCLMP for moving average secondary paths and stochastic input signals is performed. Compared to the existing algorithms, two versions of the proposed algorithms have much better convergence and stability in impulsive noise environments. [ABSTRACT FROM AUTHOR]