Application of probabilistic assessment for optimal prediction in active noise control algorithms

Abstract

Abstract This study explores a modified active noise control (ANC) system using a Bayesian inference approach as a pre-processing method. The key aspect of low-frequency noise attenuation is investigated with the existing control algorithms, the conventional filtered-x least mean square (FxLMS) algorithm and a new convex structure via an FxLMS/F algorithm (C-FxLMS/F), that combine Bayesian inference with a dynamic linear model (DLM). The combination of a Bayesian approach and a DLM comprises the statistic strategy and a descriptive time series, which is conductive to raw signal pre-processing and concurrently generating a predicted signal as a reference signal. For signal processing, pretreatment enables the determination of the noise characteristics of the operating machine and its feedback to the control system. This is an important input to enable the time domain control algorithm to prevent environmental disturbance and time-delay effects. In addition, the use of active control theory mainly relies on the response time of secondary source generation. The predicted signals based on prior observational information and Bayesian inference afford an alternative to the normal costs of the secondary path, such as those associated with electro-acoustic signal conversion and computation efforts in the control algorithm. In this work, the combination of a Bayesian approach and an FxLMS algorithm is studied via a case study. To explore more applicability, the combination of a C-FxLMS/F algorithm with Bayesian inference is also investigated, and a convergence analysis is presented. The in-situ measurement data obtained from a construction site acoustic apparatus is used for analysis. The simulation results are presented via two illustrative cases. In addition, a comparison for three different signal forms under the effect of Bayesian inference is also discussed. It is found that a Bayesian inference approach based on DLM is workable in the ANC system, and the convergence performance is superior to that of an ANC system without Bayesian inference. This suggests that to implement such a system for signal control, it is better to enhance the final system performance in the time-domain field of ANC algorithms. This pre-processing system based on a characteristic strategy and having a low computational loss is needed not only to reduce the time-delay compromise, but also to prevent the sudden disturbance of the reference signal.