Comparison of Performance and Computational Complexity of Nonlinear Active Noise Control Algorithms

Abstract

Research on nonlinear active noise control (NANC) revolves around the investigation of the sources of nonlinearity as well as the performance and computational load of the nonlinear algorithms. The nonlinear sources could originate from the noise process, primary and secondary propagation paths, and actuators consisting of loudspeaker, microphone or amplifier. Several NANCs including Volterra filtered-x least mean square (VFXLMS), bilinear filtered-x least mean square (BFXLMS), and filtereds least mean square (FSLMS) have been utilized to overcome these nonlinearities effects. However, the relative performance and computational complexities of these algorithm in comparison to FXLMS algorithm have not been carefully studied. In this paper, systematic comparisons of the FXLMS against the nonlinear algorithms are evaluated in overcoming various nonlinearity sources. The evaluation of the algorithms performance is standardized in terms of the normalized mean square error while the computational complexity is calculated based on the number of multiplications and additions in a single iteration. Computer simulations show that the performance of the FXLMS is more than 80% of the most effective nonlinear algorithm for each type of nonlinearity sources at the fraction of computational load. The simulation results also suggest that it is more advantageous to use FXLMS for practical implementation of NANC.

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

“…Substituting the gradients in (18)(19)(20) into the general adaptive LMS algorithm in (17) yields the proposed updating equations forŜ,̂and̂.…”

Review of active noise control techniques with emphasis on sound quality enhancement

“…In the United States of America, the detailed study and experiment of noise caused by engine vibration and road surface excitation were conducted by Jerome Couche, and the noise reduction of 6.5 dB was achieved in the range of 40-500 Hz [34]. Several prominent works on the development of ANC technology have been reported in the last three decades, such as the filtered-x least-mean-square (FxLMS) algorithm [35], genetic algorithm (GA) [36], functional link artificial neural network (FLANN) [37], simplified hyper-stable adaptive recursive filter (SHARF) algorithm [38] and frequency selective least-meansquare (FSLMS) algorithm [39].…”

Studies on the Effectiveness of Noise Protection for an Enclosed Industrial Area Using Global Active Noise Reduction Systems

“…The presence of nonlinearities in the ANC system degrades the noise cancelation performance of FxLMS-algorithm [6]. Nonlinearity is a concern in ANC applications where low-cost devices such as amplifiers, sensors and actuators exhibit nonlinear distortion [7]. In those cases solutions such as Volterra FxLMS algorithm, Bilinear FxLMS algorithm, filtered-s LMS algorithm, FLANN family of algorithms (based on artificial neural networks) or convex combination of algorithm, are used [6], [7], [8].…”

“…Nonlinearity is a concern in ANC applications where low-cost devices such as amplifiers, sensors and actuators exhibit nonlinear distortion [7]. In those cases solutions such as Volterra FxLMS algorithm, Bilinear FxLMS algorithm, filtered-s LMS algorithm, FLANN family of algorithms (based on artificial neural networks) or convex combination of algorithm, are used [6], [7], [8]. Such solutions are more computationally demanding than FxLMS and have not been used in the solution presented in this paper.…”

“…Considering that and taking into account possible nonstationarity of noise and its impact on the primary and secondary paths of noise propagation, ANC systems are often implemented as feedback adaptive systems [5], [6], [7], [8].…”