基于FXLMS算法的窄带主动噪声控制系统性能分析研究
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摘要
噪声污染已经成为一个全世界都十分关注的环境问题。传统被动噪声控制方法能够在宽范围内对高频噪声进行很好的抑制,高频特性好,但对低频噪声抑制效果不佳甚至无能为力。相对于传统被动噪声控制方法,主动噪声控制(ActiveNoiseControl–ANC)方法具有良好的低频特性,非常适用于控制低频谐波噪声。这类噪声常产生于旋转设备或具有往复运动的装置。谐波噪声其能量集中于有限的频率,是典型、常见的窄带噪声。在ANC领域,将用于控制窄带噪声的系统称之为窄带ANC系统。社会和经济的发展,对工业设备、运输设备等的需求不断增加,由此带来的噪声污染不可忽视。由于在抑制低频窄带噪声方面的有效性,窄带ANC系统备受关注。
对窄带ANC系统性能的深刻理解和掌握,必须建立在对系统性能细致深入的分析基础之上;另一方面,深入的系统性能分析能够为我们提供系统进一步改进的理论依据并指引改进方向。本文以统计最小均方(LMS)理论为分析基础,对基于滤波-X最小均方(Filtered-XLMS:FXLMS)算法的窄带ANC系统展开详尽深入的性能分析。这里所谓的性能分析是指对系统进行随机分析或统计分析,即从统计意义上分析算法的收敛性甚至稳态特性。论文主要创新性研究工作体现在如下几个方面:
(1)对于含次级通道在线辨识的窄带前馈ANC系统,系统自激是一种降低辅助噪声信号对系统性能的影响的有效方法。然而,利用自激提高系统性能的机理并不明确,尚缺乏理论上的说明。本文针对一种利用自激提高性能的含次级通道在线辨识的窄带前馈ANC系统,从其控制滤波器权值估计误差出发,建立控制系统性能的差分方程。利用统计理论和现代信号处理理论解算差分方程,进而对系统展开了详尽深入的性能分析,包括动态性能和稳态性能分析,给出了自激促进系统性能提高的理论说明,同时分析出影响系统性能的关键环节。
(2)在窄带前馈ANC系统中,若非声学传感器或参考信号发生器存在一定的误差,将导致参考信号频率与目标噪声频率失调或不匹配(FrequencyMismatch– FM)。对于线性系统,即使很小的FM也能导致系统无法有效消除目标噪声。考虑实际系统中没有复数运算的物理实现,且噪声频率成分往往比较丰富,本文从实数域和时间域针对存在小量FM的窄带前馈ANC系统进行了统计性分析,并考察了多频率情形。从平均意义上初步探讨了FM对窄带前馈ANC系统性能的影响,同时给出了系统的稳定边界及其与FM的关系。
(3)当反馈ANC系统用于消除窄带噪声时,由于参考信号是通过内部估计产生,不存在FM问题。与前馈系统相比,反馈系统鲁棒性要差。但控制算法相对简单且结构紧凑,反馈系统的应用仍然很广泛。对于反馈系统,反馈结构的存在使得反馈ANC系统性能的分析难以开展。受上述窄带前馈ANC系统性能分析思路和方法的启发,本文从新的角度对用于抑制窄带噪声的反馈ANC系统进行了深入的性能分析。推导出了系统内部各信号离散傅立叶系数(DiscreteFourier Coefficient– DFC)间的内在关系,分析得到了控制滤波器权值稳态解的特性。据此,建立基于控制滤波器权值的差分方程,结合统计理论和现代信号处理理论解算该差分方程,获取了系统动态性能。
(4)为了验证自激在提高窄带前馈ANC系统性能方面的有效性,本文设计了一维管道ANC实验系统,并基于高速数字信号处理器(DSP)对利用自激的窄带前馈ANC系统进行了实现,开展了一些管道内低频窄带噪声主动控制实验。实验内容涵盖单频率通道和双频率通道噪声的控制,实验结果充分说明了利用自激可以有效提高窄带前馈ANC系统抑制噪声的能力。
As an environmental problem, acoustic noise pollution has garnered significant atten-tion worldwide. The traditional passive noise control techniques can effectively suppresshigh-frequency acoustic noises in a wide frequency band, and they have excellent high-frequency characteristics. However, they are ineffective or powerless in suppressing thosenoises with low frequency. In contrast with the passive noise control approaches, activenoise control (ANC) techniques have excellent low-frequency characteristic, which isideal for suppressing low-frequency harmonic acoustic noises. Harmonic acoustic noisesare usually generated by rotating machines and devices with reciprocating motion. Sincethe energy of harmonic acoustic noises concentrates at specific frequencies, they are akind of typical and common narrowband noises. In ANC field, the system used for atten-uating narrowband noises is the so-called narrowband ANC system. The developmentsof society and economy require more industrial, transportation, and other equipments.Such requirement directly results in a more serious noise pollution problem, which can-not be ignored. The narrowband ANC system has garnered significant attention for itseffectiveness in reducing low-frequency narrowband noises.
To obtain insightful expressions that significantly enhance and enrich our understand-ing of the narrowband ANC system behavior, we have to execute in-depth and detailedanalysis on the performance of the system. On the other hand, in-depth and detailed anal-ysis will provide us theoretical foundation and guidance for further modifying the system.On the basis of statistical least mean square (LMS) theory, this dissertation investigatesperformances of narrowband ANC system based on the filtered - X LMS (FXLMS) algo-rithm in detail and in depth. The so-called performance analysis here means statistical orstochastic analysis of the system, that is, we statistically analyze the convergence and evensteady-state performance of the algorithm. The main contributions of this dissertation areconcluded in order as follows:
(1) For a narrowband feedforward ANC system with online secondary-path modeling,system-self-excitation setup is an effective approach to be used to reduce the in?uenceof the auxiliary noise signal on the performance of the system. However, so far, themechanism that leads to a system’s performance improvement using self-excitation is not clear, and the corresponding analytical and theoretical explanations are still missing.With such a system whose performance is improved by using self-excitation being tar-geted, we established the difference equations governing performance of the system interms of estimation errors of the control filter weights. After deriving the difference equa-tions through applying statistics and modern signal processing theories, we analyticallyinvestigated dynamics and steady-state performance of the system in detail and in depth.We finally provided theoretical proofs and explanations for the system’s performance im-provement caused by self-excitation and figured out the key factors which in?uence suchperformance.
(2) In a narrowband feedforward ANC system, the nonacoustic sensor or the referencesignal generator usually contains errors, which will result in frequencies of the referencesignal that are not identical to the frequencies of the primary noise. That is, frequencymismatch (FM) may exist between the reference signal and primary noise. If the FM,even it is very small, exists in the system, the narrowband noises being targeted couldnot be reduced effectively. With the consideration that there is no physical realization ofcomplex operations in real-life applications where multi-tone noise is usually contained,this dissertation provides statistical analysis of the narrowband feedforward ANC systemin presence of small FM as well as containing multi tones in the real and time domains.We preliminary investigated the in?uence of the FM on the performance of the narrow-band feedforward ANC system in the mean sense. Stability bounds and the relationshipsbetween such bounds and the FM were also provided.
(3) When a feedback ANC system is used to cancel narrowband noise, there will beno FM since the reference signal is synthesized internally. The feedback ANC systemis of less robustness in comparison to the feedforward system. However, the feedbacksystem has been applied widely for its relatively simple control algorithm and compactstructure. The feedback structure equipped in a feedback ANC system makes it difficult toinvestigate the performance of the system. With the inspirations obtained from the aboveideas and analytical techniques applied to investigate the narrowband feedforward ANCsystems, this dissertation provides performance analysis of the feedback ANC system fornarrowband noises cancellation in depth from a new viewpoint. We developed the internalrelationships of discrete Fourier coefficients (DFCs) among signals in the system and con-sequently obtained the steady-state characteristics of the control filter weights. With such preliminary analytical results, we established the difference equations based on the con-trol filter weights themselves. Using statistics and modern signal processing theories, werecursively derived the difference equations, and then analytically investigated dynamicsof the feedback ANC system being targeted in detail.
(4) To verify the effectiveness of self-excitation in improving the performance of thefeedforward narrowband ANC system, we designed a one-dimensional tube as the exper-imental system in this dissertation. Based on high-speed digital signal processor (DSP),the narrowband feedforward ANC system with self excitation was implemented and rep-resentative experiments of low-frequency narrowband noises cancellation in the tube wereconducted. Our experiments included single-tone and double-tone noise cancellation.The experimental results proofs the capability of the feedforward narrowband ANC sys-tem in suppressing narrowband noises, and it can be effectively promoted by using self-excitation.
对窄带ANC系统性能的深刻理解和掌握,必须建立在对系统性能细致深入的分析基础之上;另一方面,深入的系统性能分析能够为我们提供系统进一步改进的理论依据并指引改进方向。本文以统计最小均方(LMS)理论为分析基础,对基于滤波-X最小均方(Filtered-XLMS:FXLMS)算法的窄带ANC系统展开详尽深入的性能分析。这里所谓的性能分析是指对系统进行随机分析或统计分析,即从统计意义上分析算法的收敛性甚至稳态特性。论文主要创新性研究工作体现在如下几个方面:
(1)对于含次级通道在线辨识的窄带前馈ANC系统,系统自激是一种降低辅助噪声信号对系统性能的影响的有效方法。然而,利用自激提高系统性能的机理并不明确,尚缺乏理论上的说明。本文针对一种利用自激提高性能的含次级通道在线辨识的窄带前馈ANC系统,从其控制滤波器权值估计误差出发,建立控制系统性能的差分方程。利用统计理论和现代信号处理理论解算差分方程,进而对系统展开了详尽深入的性能分析,包括动态性能和稳态性能分析,给出了自激促进系统性能提高的理论说明,同时分析出影响系统性能的关键环节。
(2)在窄带前馈ANC系统中,若非声学传感器或参考信号发生器存在一定的误差,将导致参考信号频率与目标噪声频率失调或不匹配(FrequencyMismatch– FM)。对于线性系统,即使很小的FM也能导致系统无法有效消除目标噪声。考虑实际系统中没有复数运算的物理实现,且噪声频率成分往往比较丰富,本文从实数域和时间域针对存在小量FM的窄带前馈ANC系统进行了统计性分析,并考察了多频率情形。从平均意义上初步探讨了FM对窄带前馈ANC系统性能的影响,同时给出了系统的稳定边界及其与FM的关系。
(3)当反馈ANC系统用于消除窄带噪声时,由于参考信号是通过内部估计产生,不存在FM问题。与前馈系统相比,反馈系统鲁棒性要差。但控制算法相对简单且结构紧凑,反馈系统的应用仍然很广泛。对于反馈系统,反馈结构的存在使得反馈ANC系统性能的分析难以开展。受上述窄带前馈ANC系统性能分析思路和方法的启发,本文从新的角度对用于抑制窄带噪声的反馈ANC系统进行了深入的性能分析。推导出了系统内部各信号离散傅立叶系数(DiscreteFourier Coefficient– DFC)间的内在关系,分析得到了控制滤波器权值稳态解的特性。据此,建立基于控制滤波器权值的差分方程,结合统计理论和现代信号处理理论解算该差分方程,获取了系统动态性能。
(4)为了验证自激在提高窄带前馈ANC系统性能方面的有效性,本文设计了一维管道ANC实验系统,并基于高速数字信号处理器(DSP)对利用自激的窄带前馈ANC系统进行了实现,开展了一些管道内低频窄带噪声主动控制实验。实验内容涵盖单频率通道和双频率通道噪声的控制,实验结果充分说明了利用自激可以有效提高窄带前馈ANC系统抑制噪声的能力。
As an environmental problem, acoustic noise pollution has garnered significant atten-tion worldwide. The traditional passive noise control techniques can effectively suppresshigh-frequency acoustic noises in a wide frequency band, and they have excellent high-frequency characteristics. However, they are ineffective or powerless in suppressing thosenoises with low frequency. In contrast with the passive noise control approaches, activenoise control (ANC) techniques have excellent low-frequency characteristic, which isideal for suppressing low-frequency harmonic acoustic noises. Harmonic acoustic noisesare usually generated by rotating machines and devices with reciprocating motion. Sincethe energy of harmonic acoustic noises concentrates at specific frequencies, they are akind of typical and common narrowband noises. In ANC field, the system used for atten-uating narrowband noises is the so-called narrowband ANC system. The developmentsof society and economy require more industrial, transportation, and other equipments.Such requirement directly results in a more serious noise pollution problem, which can-not be ignored. The narrowband ANC system has garnered significant attention for itseffectiveness in reducing low-frequency narrowband noises.
To obtain insightful expressions that significantly enhance and enrich our understand-ing of the narrowband ANC system behavior, we have to execute in-depth and detailedanalysis on the performance of the system. On the other hand, in-depth and detailed anal-ysis will provide us theoretical foundation and guidance for further modifying the system.On the basis of statistical least mean square (LMS) theory, this dissertation investigatesperformances of narrowband ANC system based on the filtered - X LMS (FXLMS) algo-rithm in detail and in depth. The so-called performance analysis here means statistical orstochastic analysis of the system, that is, we statistically analyze the convergence and evensteady-state performance of the algorithm. The main contributions of this dissertation areconcluded in order as follows:
(1) For a narrowband feedforward ANC system with online secondary-path modeling,system-self-excitation setup is an effective approach to be used to reduce the in?uenceof the auxiliary noise signal on the performance of the system. However, so far, themechanism that leads to a system’s performance improvement using self-excitation is not clear, and the corresponding analytical and theoretical explanations are still missing.With such a system whose performance is improved by using self-excitation being tar-geted, we established the difference equations governing performance of the system interms of estimation errors of the control filter weights. After deriving the difference equa-tions through applying statistics and modern signal processing theories, we analyticallyinvestigated dynamics and steady-state performance of the system in detail and in depth.We finally provided theoretical proofs and explanations for the system’s performance im-provement caused by self-excitation and figured out the key factors which in?uence suchperformance.
(2) In a narrowband feedforward ANC system, the nonacoustic sensor or the referencesignal generator usually contains errors, which will result in frequencies of the referencesignal that are not identical to the frequencies of the primary noise. That is, frequencymismatch (FM) may exist between the reference signal and primary noise. If the FM,even it is very small, exists in the system, the narrowband noises being targeted couldnot be reduced effectively. With the consideration that there is no physical realization ofcomplex operations in real-life applications where multi-tone noise is usually contained,this dissertation provides statistical analysis of the narrowband feedforward ANC systemin presence of small FM as well as containing multi tones in the real and time domains.We preliminary investigated the in?uence of the FM on the performance of the narrow-band feedforward ANC system in the mean sense. Stability bounds and the relationshipsbetween such bounds and the FM were also provided.
(3) When a feedback ANC system is used to cancel narrowband noise, there will beno FM since the reference signal is synthesized internally. The feedback ANC systemis of less robustness in comparison to the feedforward system. However, the feedbacksystem has been applied widely for its relatively simple control algorithm and compactstructure. The feedback structure equipped in a feedback ANC system makes it difficult toinvestigate the performance of the system. With the inspirations obtained from the aboveideas and analytical techniques applied to investigate the narrowband feedforward ANCsystems, this dissertation provides performance analysis of the feedback ANC system fornarrowband noises cancellation in depth from a new viewpoint. We developed the internalrelationships of discrete Fourier coefficients (DFCs) among signals in the system and con-sequently obtained the steady-state characteristics of the control filter weights. With such preliminary analytical results, we established the difference equations based on the con-trol filter weights themselves. Using statistics and modern signal processing theories, werecursively derived the difference equations, and then analytically investigated dynamicsof the feedback ANC system being targeted in detail.
(4) To verify the effectiveness of self-excitation in improving the performance of thefeedforward narrowband ANC system, we designed a one-dimensional tube as the exper-imental system in this dissertation. Based on high-speed digital signal processor (DSP),the narrowband feedforward ANC system with self excitation was implemented and rep-resentative experiments of low-frequency narrowband noises cancellation in the tube wereconducted. Our experiments included single-tone and double-tone noise cancellation.The experimental results proofs the capability of the feedforward narrowband ANC sys-tem in suppressing narrowband noises, and it can be effectively promoted by using self-excitation.
引文
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