Nonlinear active noise control using adaptive rational functions with second-order poles frames: Simulation and experimental results

An active noise control algorithm is introduced based on adaptive wavelet networks using rationale functions with second-order poles wavelets. A novel network structure is derived using a nonlinear static mapping cascaded with an infinite impulse response filter wherein only input at the current step is needed to generate the output of the next sample. Therefore, incorporating tap delayed line of input-output of the physical system can be eliminated, avoiding the use of multidimensional wavelet networks. Online dynamic back-propagation learning algorithms (based on gradient descent method) are applied to adjust the network parameters. The local convergence of the closed-loop system is proved using discrete Lyapunov function. Simulations are carried out to compare the performance of proposed methods with other nonlinear algorithms (e.g. FxBPNN, Volterra, FLNN, and RFFLNN). Experiments are then conducted to evaluate the developed algorithms. Both simulation and experimental results show the superior performance of proposed method in terms of fast convergence rate and noise attenuation while avoiding curse of dimensionality.