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.

中文翻译：

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概率评估在主动噪声控制算法中的最优预测中的应用

摘要 本研究探索了使用贝叶斯推理方法作为预处理方法的改进型主动噪声控制 (ANC) 系统。用现有的控制算法、传统的滤波 x 最小均方 (FxLMS) 算法和通过 FxLMS/F 算法 (C-FxLMS/F) 的新凸结构研究了低频噪声衰减的关键方面，它们结合了具有动态线性模型 (DLM) 的贝叶斯推理。贝叶斯方法和 DLM 的组合包括统计策略和描述性时间序列，这有助于原始信号预处理并同时生成预测信号作为参考信号。对于信号处理，预处理能够确定操作机器的噪声特性及其对控制系统的反馈。这是启用时域控制算法以防止环境干扰和时延效应的重要输入。此外，主动控制理论的使用主要依赖于二次源产生的响应时间。基于先验观测信息和贝叶斯推理的预测信号提供了辅助路径正常成本的替代方案，例如与控制算法中的电声信号转换和计算工作相关的那些。在这项工作中，通过案例研究研究了贝叶斯方法和 FxLMS 算法的组合。为了探索更多的适用性，还研究了 C-FxLMS/F 算法与贝叶斯推理的结合，并提出了收敛性分析。从施工现场声学仪器获得的现场测量数据用于分析。模拟结果通过两个说明性案例呈现。此外，还讨论了贝叶斯推理作用下三种不同信号形式的比较。发现基于DLM的贝叶斯推理方法在ANC系统中是可行的，并且收敛性能优于没有贝叶斯推理的ANC系统。这表明，要实现这样的信号控制系统，最好在 ANC 算法的时域领域提高最终系统性能。需要这种基于特征策略、计算损失低的预处理系统，不仅可以减少时延妥协，还可以防止参考信号的突然干扰。