Research On Active Noise Control Algorithm Based On Nonlinear Function Extension

Nowadays,two kinds of noise control technique have been developed: one is the active noise control(ANC)technique,the principle of which is to control the noise source and utilizes a loudspeaker to generate an anti-noise source with the same amplitude and opposite phase as the noise source for sound interference cancellation;the other method is the passive noise control(PNC)technique,which employs soundproofing materials to control noise.Active noise control is very effective for low-frequency noise which is difficult to be eliminated by passive noise control.Therefore,there has been increasing researches on the active noise control in recent years.However,due to some limitations of existing active noise control algorithms,such as when the signal transmission channel shares different degrees of nonlinear distortion or has non-minimum phase characteristics,the existing linear active noise control algorithms are even completely ineffective.On the other hand,the tradeoff between convergence speed and noise residue in nonlinear active noise control algorithms have not been addressed.Note that above mentioned limitations lead to the application and development of active noise control technique a long way to go.Considering the nonlinear distortion and non-minimum phase characteristics of the transmission channel and ?-stable noise environment in nature,the specific work of this thesis can be summarized as follows:First,a brief review of the basic ideas of several nonlinear active noise control algorithms with classical functional link artificial neural network(FLANN)control structure is given in this thesis(i.e.the filtered-s least mean square(Fs LMS)algorithm and the robust Fs LMS(RFs LMS)algorithm).After analyzing advantages and disadvantages of the existing algorithms,it is concluded that the traditional Fs LMS and RFs LMS algorithms suffer from performance degradation under the impulsive noise environment.Based on this fact,the main idea of improvement is to control impulsive noise.Additionally,the nonlinear system is modeled by FLANN.Considering the types of impulsive noise,take the special case of Gaussian noise in ?-stable noise as an example,a novel filtered-s least mean square(Fsq LMS)algorithm based on q-gradient descent is proposed.Unlike the traditional gradient descent,such q-gradient descent approach has a faster convergence rate and a smaller noise residue.In order to overcome the difficulty of parameter selection,for convenience,the q parameter in the q-gradient descent is set to a variable value,which makes it adaptively adjustable,at the price of increased computational complexity.Thus,a class of variable q gradient filtered-s least mean square(Fs Vq LMS)algorithm is proposed.Moreover,the general form of ?-stable noise has an infinite variance,and the new cost function is defined by the dispersion criterion,that is,the cost function is the p-order error moment.Using the q gradient descent method,the Fsq LMP algorithm is proposed,which is a more general form of the Fsq LMS algorithm.In order to provide theoretical guidance for the practical application,this thesis analyzes the convergence and computational complexity of the proposed Fsq LMP algorithm.According to the analysis,the step-size convergence range of the proposed Fsq LMP algorithm is obtained.Furthermore,based on the above research,aiming at solving the trade-off contradiction between convergence speed and noise residue,combined with the variable step-size(VSS)strategy,variable step-size Fsq LMP(VFsq LMP)algorithm is proposed.In the initial stage of convergence,the algorithm reaches steady state quickly with a large step-size due to the large error(noise residual);after reaching steady state,the error becomes smaller,and the algorithm obtains small noise residual with a smaller step-size.Thus,the proposed algorithm guarantees both fast convergence rate and small noise residue.Finally,numerical simulations demonstrate the superiority of the proposed nonlinear active noise control algorithms,and the results of this thesis mainly extend the existing theoretical and pratical results for active noise control problems.