Active control of workspace noise based on ChFxLMS algorithm
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摘要:
为改善滤波x最小均方（Filter-x Least Mean Square，FxLMS）算法不能同时兼顾稳态误差与收敛速度的不足，提出一种基于cosh函数的变步长FxLMS（Cosh-FxLMS，ChFxLMS）算法. 通过cosh函数建立误差信号与步长因子间的联系，使得步长因子按照cosh函数特性实时调整；分析不同参数对ChFxLMS算法性能的影响，为算法参数选取作指导；分别将正弦信号和实测织机信号作为输入信号，对ChFxLMS算法性能进行验证，并与FxLMS算法、基于sigmoid函数的变步长FxLMS（Sigmoid-FxLMS，SFFxLMS）算法进行对比. 仿真结果表明，ChFxLMS算法性能在时域和频域上都取得较好的控制效果. 分析结果表明，该算法能较大地降低稳态误差和提高收敛速度. 该研究成果可为工作空间噪声主动控制提供一种新思路.
Abstract:To improve the deficiency that the traditional filter-x least mean square (FxLMS) algorithm can not take into account the steady-state error and convergence speed, a variable step size FxLMS (Cosh-FxLMS, ChFxLMS) algorithm based on cosh function was proposed. The relationship between the error signal and the step factor was established by using the cosh function, so that step factor could adjust continuously according to the characteristics of the cosh function. The influence of different parameters on the performance of ChFxLMS algorithm was analyzed to provide guidance for the selection of algorithm parameters. And the sinusoidal signal and measured loom signal were used as input signals to verify the performance of ChFxLMS algorithm. It was compared with FxLMS algorithm and variable step size FxLMS algorithm based on sigmoid function (Sigmoid-FXLMS, SFFxLMS algorithm). The simulation results show that the performance of ChFxLMS algorithm has achieved good control results in time domain and frequency domain. Through comparative analysis, the algorithm can greatly reduce the steady-state error and improve the convergence speed. The research results will provide a new idea for active noise control in workspace.
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Key words:
- active noise control /
- ChFxLMS algorithm /
- steady-state error /
- convergence speed
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图 6 正弦信号输入时3种算法误差曲线图
Figure 6. Error curves of three algorithms when sinusoidal signal is input
图 7 正弦信号输入时3种算法均方误差曲线图
Figure 7. Mean square error curves of three algorithms when sinusoidal signal is input
图 10 织机噪声控制3种算法均方误差曲线图
Figure 10. Mean square error curves of three algorithms when loom noise is input
表 1 正弦信号输入时各算法参数值
Table 1. Parameter values of each algorithm when sinusoidal signal is input
参数 SFFxLMS算法 ChFxLMS算法 $ {\alpha _1} $ $ {\beta _1} $ $ {m_1} $ $ \alpha $ $ \beta $ $ m $ 值 4 6 1 40 10 1 
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表 2 织机噪声控制时各算法参数值
Table 2. Parameter values of each algorithm when loom noise is input
参数 SFFxLMS算法 ChFxLMS算法 $ {\alpha _1} $ $ {\beta _1} $ $ {m_1} $ $ \alpha $ $ \beta $ $ m $ 值 4 0.9 1 20 5 1
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