1. Jiangsu Provincial Engineering Lab of Lake Environment Remote Sensing Technologies, Huaiyin Institute of Technology, Huaian 223003, China;
2. School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
摘要针对前馈管道非线性有源噪声控制系统，提出一种基于通用切比雪夫滤波器的次级通道建模方法和通用切比雪夫滤波x最小均方误差算法（GCFXLMS，general Chebyshev filtered-x least mean square）。通用切比雪夫滤波器由第一类切比雪夫滤波器扩展获得，交叉项部分可通过对角结构实现，根据对角结构的性质，可以采用减少通道信号的实现策略以降低结构复杂度；使用该滤波结构建模次级通道，并给出了稀疏虚拟次级通道模型，基于此模型推导了GCFXLMS算法。该方法性能比较包括计算复杂度对比和控制效果对比。实验结果表明，在非线性有源噪声控制系统中，通用切比雪夫滤波器可达到与Volterra次级通道建模类似的建模效果，相比于传统的前馈滤波器，通用切比雪夫滤波器具有更优的控制性能。
Abstract：Here, for feedforward duct nonlinear active noise control (NANC) systems, a nonlinear secondary path modeling method and the general Chebyshev filtered-x least mean square (GCFXLMS) algorithm based on general Chebyshev filter (GCF) were proposed. The general Chebyshev filter was obtained through extending the first type of Chebyshev filter and realized with diagonal structures. In diagonal structures, some signal channels far from the principle channels were decreased to reduce the structural complexity. The GCF structure was used to do secondary path modeling, and the sparse virtual secondary path model was deduced. The GCFXLMS algorithm was derived based on this model. The performance of the proposed method was verified through contrastive analysis of computational complexity and control effect with this method and other ones for feedforward duct NANC systems. The results showed that for feedforward duct NANC systems, GCF can reach the secondary path modeling effect similar to that obtained with Volterra filter; compared to the traditional feedforward filters, GCF has better control performance.
郭新年1,2，周恒瑞1，赵正敏1，都思丹2. 基于通用切比雪夫滤波器的有源噪声控制研究[J]. 振动与冲击, 2020, 39(1): 223-239.
GUO Xinnian1,2,ZHOU Hengrui1,ZHAO Zhengmin1,DU Sidan2. Active noise control based on general Chebyshev filter. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(1): 223-239.
[1] Kuo S M, Morgan D R. Active Noise Control Systems: Algorithm and DSP Implementations [M]. New York: Wiley, 1996.
[2] 陈克安. 有源噪声控制. 第二版. 北京: 国防工业出版社, 2014.
CHEN Ke-an. Active noise control, second edition. Beijing, National Defense Industry Press, 2014.
[3] 丁少虎, 陈克安, 李双. 水下圆柱壳低频声辐射特性及有源控制[J]. 振动与冲击, 2015, 34(20): 185-190.
DING Shao-hu, CHEN Ke-an, LI Shuang. Low frequencies radiation characteristics of a submerged cylindrical shell and its active control [J]. Journal of vibration and shock, 2015, 34(20): 185-190.
[4] 聂永红, 程军圣, 杨宇,等. 基于经验模态分解的多通道有源噪声控制[J]. 振动与冲击, 2013, 32(20): 189-195.
NIE Yong-hong, Yang Jun-sheng, Yang Yu, et al. A multichannel active noise control system based on empirical mode decomposition [J]. Journal of vibration and shock, 2013, 32(20): 189-195.
[5] Zhang X, Qiu X. Performance of a snoring noise control system based on an active partition [J]. Applied Acoustics, 2017; 116: 283-290.
[6] Tan L, Jiang J. Adaptive Volterra filters for active control of nonlinear noise processes [J]. IEEE Transactions on Signal Processing, 2001; 49(8): 1667-1676.
[7] Zhao H, Zhang J. A novel adaptive nonlinear filter-based pipelined feedforward second-order Volterra architecture [J]. IEEE Transactions on Signal Processing, 2009; 57(1): 237-246.
[8] Danas D P, Panda G. Active mitigation of nonlinear noise Processes using a novel filtered-s LMS algorithm [J]. IEEE Transactions on Speech & Audio Processing, 2004; 12(3): 313-322.
[9] 陈珏, 玉昊昕, 陈克安. 三类有源噪声控制算法性能比较[J]. 噪声与振动控制, 2013; 33(4): 107-113.
CHEN Yu, WANG Hao-xin, CHEN Ke-an. Comparison of performance of three types of active noise control algorithms [J]. Noise and Vibration Control, 2013; 33(4): 107-113.
[10] Zhou D, DeBrunner V. Efficient Adaptive Nonlinear Filters for Nonlinear Active Noise Control[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2007; 54(3): 669-681.
[11] Guo X, Yang L, Jiang J, et al. Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control [J]. IEEE Transactions on Instrumentation and Measurement, 2018; 67(3): 482-496.
[12] Carini A, Sicuranza G L. A study about Chebyshev nonlinear filters [J]. Signal Processing, 2016; 122(C): 24-32.
[13] 郭新年, 周恒瑞. 基于自适应切比雪夫滤波器的非线性有源噪声控制 [J]. 噪声与振动控制, 2017; 37(3): 88-91.
GUO Xin-nian, ZHOU Heng-rui. Adaptive FCLMS algorithm for nonlinear active noise control based on Chebyshev filter [J]. Noise and Vibration Control, 2017; 37(3): 88-91.
[14] Patel V, Gandhi V, Heda S, et al. Design of Adaptive Exponential Functional Link Network-Based Nonlinear Filters [J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2016; 63(9): 1434-1442.
[15] Guo X, Dong C, Tan Li, et al. Adaptive even mirror Fourier filtered error LMS algorithm for multichannel nonlinear active noise control [C]. IEEE Information Technology, Electronics and Mobile Communication Conference, 2016; 1-6.
[16] Zhao H, Zeng X, He Z, et al. Nonlinear adaptive filter-based simplified bilinear model for multichannel active control of nonlinear noise processes [J]. Applied Acoustics, 2013; 74: 1414-1421.
[17] Tan L, Dong C, Du S. On implementation of adaptive bilinear filters for nonlinear active noise control [J]. Applied Acoustic, 2016; 106: 122-128.
[18] Luo L, Sun J. A novel bilinear functional link neural network filter for nonlinear active noise control [J]. Applied Soft Computing, 2018; 68: 636-650.
[19] Carini A, Sicuranza GL. BIBO-stable recursive functional link polynomial filters [J]. IEEE Transactions on Signal Process., 2017; 65(6): 1595-1606.
[20] 马进, 邹海山, 邱小军. 存在声反馈的前馈有源噪声控制系统性能分析 [J]. 声学学报, 2016; 41(5): 686-693.
MA Jin, ZOU Hai-shan, Qiu Xiao-jun. Performance analysis of feedforward active noise control systems with acoustic feedback [J]. ACTA Acoustica, 2016, 41(5): 686-693.
[21] Raz GV, Veen BDV. Baseband Volterra filters for implementing carrier based nonlinearities [J]. IEEE Transactions. Signal Process., 1998; 46: 103–114.
[22] Dong C, Tan L, Guo X, et al. Efficient adaptive bilinear filters for nonlinear active noise control [C]. IEEE International Conference on Signal Processing and Communication Systems., 2017; 1-5.
