Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes

In actual nonlinear active noise control (NANC) systems, there often exist nonlinear distortions in such cases: the primary path may be nonlinear, the reference noise may exhibit nonlinear distortion, and the secondary path may have nonminimum-phase. To solve the problems of nonlinear distortions, two novel feedback adaptive filters based on the functional link neural network (FLNN) for NANC systems with low computational complexity are proposed in this paper, which are a feedback functional link neural network (FFLNN) and a reduced feedback functional link neural network (RFFLNN), respectively. To train the proposed nonlinear filters for NANC systems, a reduced complexity filtered-s least mean square (FSLMS) algorithm using filter bank approach is developed. The analysis of computational complexity shows that the RFFLNN adaptive filter involves less computation as compared to FFLNN and FLNN adaptive filters. Moreover, it is demonstrated through computer simulations for nonlinear noise processes that the RFFLNN adaptive filter outperforms FLNN and FFLNN in term of convergence speed and steady-state error. Furthermore, it is more effective in reducing nonlinear effects in NANC systems than other filters.