循环平稳声场的非共形面近场声全息理论与实验研究
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摘要
声源识别技术是实现噪声控制的首要步骤,实现噪声源的可视化将会加深对声源的位置以及声场物理本质的理解。在众多的声成像技术中,近场声全息(Near field acoustic holography, NAH)以其极高的分辨率成为分析声场分布的重要选择。NAH方法通过在紧靠声源的全息测量面上测量声压,最大程度地保留了声场信息,从而实现高分辨率的声场重建。NAH技术已经由最初的仅适用于平面、圆柱面和球面等简单外形的声源,发展到适用于任意外形的声源。通过建立源面和全息面之间的空间变换关系,由全息面声压重建源面的声场,实现了声压分布,表面法向振速,声强向量场分布等。NAH技术在汽车NVH,噪声源定位,结构振动模态分析方面有很大的应用。NAH近三十年来深受国内外研究者的关注,发展很快,但是主要围绕平稳声场展开研究,对于非平稳声场的NAH研究鲜有涉及。
在工程中,有一类特殊的非平稳信号——循环平稳(Cyclostationary)信号,例如内燃机、滚动轴承等旋转机械产生的辐射声场具有明显的循环平稳特性。随着对循环平稳信号的认识越来越深入,循环统计量理论已经开始应用于机械设备状态监测和故障诊断领域,目前研究的比较透彻的是二阶循环统计量。循环谱密度具有对循环平稳信号的解调能力,通过非线性变换和循环因子的共同作用,可以获取循环平稳信号中的周期成分,将调制信息直接解调到循环频率轴上。通过循环统计量理论分析,可以将循环平稳信号的信息可以同时表现在以频率和循环频率为变量的循环谱密度三维图上,并可以在合适的循环频率下获取剖面图,这将会提供比普通频谱更多的信息。
用传统NAH技术分析循环平稳声场时,无法充分考虑和利用循环平稳信号的周期时变特征,将不可避免地忽视了某些频率成分上的能量随时间变化方面的信息。目前的研究工作,已将NAH方法应用到循环平稳场的研究,其主要工作成果是提出循环平稳近场声全息概念(CYNAH: Cyclostationary NAH),实现了平面循环平稳声源的全息重建,其全息图显示了声信号中反映系统特性的调制信息的能量分布状况。循环平稳信息的全息重建,对于了解声场形成的机理,揭示声源的物理特性有很大的帮助。在实际工程中,绝大多数的声源都不具有规则外形,为了能将该方法推广到能分析任意外形的声源,势必要结合新的方法使之能适应任意外形声源的要求。
本文在平面CYNAH理论和循环平稳信号处理技术的基础上,结合边界元法、波叠加法和Helmholtz方程最小二乘法,发展了适合于任意外形声源的CYNAH方法。这三种方法使得CYNAH方法扩大了应用的声源范围,使之更加适合于工程实际。本文建立了三种不同类型的循环平稳声场近场声全息的变换理论和方法,研究了影响声场重建误差的主要因素,并进行了相应的实验研究。本文的研究工作得到了国家自然科学基金(批准号:No. 10674096)的资助。本文采用理论建模、数字仿真与实验研究相结合的研究路线,以二阶循环统计量作为声场重建的物理量,研究了适用于循环平稳声场这类特殊的非平稳声场的近场声全息理论,本文的主要内容如下:
(1)综述近场声全息技术在国内外的研究现状及进展,按照NAH方法所基于的不同数值方法分类阐述。对全息面数据采集技术、重建算法研究及工程应用等方面的成果和存在的问题进行了总结。鉴于目前NAH技术多数是对于平稳声场的研究现状,在平面循环平稳近场声全息(Cyclostationary near field acoustic holography, CYNAH)技术上进一步提出适用于任意外形声源的CYNAH方法,并简要阐述了本文的选题背景与研究意义。
(2)提出基于边界元法(BEM: Boundary Element method)的CYNAH方法,详细地推导了适用于循环平稳声源的改进Helmholz方程。和普通的边界元法NAH方法相比较,基于边界元法的CYNAH方法采用声压和法向速度的循环谱密度代替频谱和功率谱密度作为声场重建的物理量,CYNAH全息图反映了声场中各点声压和法向速度的循环谱密度分布;通过数值仿真,详细分析了重建过程中的影响因素,包括背景噪声、声源外形尺寸、全息面形状及其与重建面的相对位置等。
(3)提出基于波叠加法(Wave Superposition Algorithm, WSA)的CYNAH方法,假设外部声场由声源内部的一系列循环平稳等效源激励产生,在获取了等效源和参考源的互循环谱密度后,就可以重建整个声场中任意位置和参考源之间的互循环谱密度,然后根据循环谱理论得到循环谱密度的空间分布。用数值仿真算例,分析了该方法的适用对象和影响重建的因素。
(4)提出基于Helmholtz方程最小二乘法(Helmholtz Equation Least Square, HELS)的CYNAH方法,假设各阶分量的权重系数按循环平稳规律做变化。通过最小二乘法获取最佳的展开项数和权重系数循环谱密度,从而实现在整个声场中的循环谱密度重建,数值仿真算例验证了该方法的正确性并对影响因素作了对比分析。
(5)将三种适用于任意外形声源的CYNAH方法以及影响重建的因素汇总在一起,比较三种方法的优劣,为方法的实际运用提供指导。
(6)实验验证了循环平稳近场声全息技术的有关理论分析。实验在半消声室内完成,实验对象为一个矩形音箱和一个十二面体球声源,用循环平稳信号驱动扬声器发声,形成循环平稳声场。在声源附近布置位置固定的传声器,用二维数控扫描架完成了声压的步进扫描测量,用32通道数据采集系统记录声压信号,然后用三种方法分析同一声源,进行声场重建研究和对比分析,验证理论分析的结果。
Identification of the noise source is the first step of the noise control. Visualizing the acoustic field will offer more information for the location of the source and its physical mechanism. Among the different methods, nearfield acoustic holography (NAH) is one important tool for analyzing sound field due to its high resolution. The high resolution is obtained from the closely measuring that the sound field information is reserved ultimately in the sampling data including the evanescent wave. NAH method is developed to be suitable for the arbitrarily-shaped source from the simple geometries such as plane, cylinder and sphere. The sound field including the pressure, normal velocity and sound power is recon- structed after building the spatial transformation between the source and the hologram. NAH method is widely applied to the industry such as NVH analysis in the auto-mobile industry, locating noise sources, structure modal analysis. The progress of NAH methods attracts researchers’attention in the recent three decades. The most research on the NAH focused on the stationary sound field and the non-stationary sound field is involved less.
In the industry, there is a kind of non-stationary signal named cyclostationary signal whose cyclic statistics is with characteristics to decompose the carrier wave and modulation wave solely. The cyclostationary sound field excited by some machines is often observed in the industry, such as the internal combustion engines and rolling-bearings, especially when they run under ill conditions. The cyclic statistics theory has been utilized to detect machinery faults, and the main parameters are the second-order statistics which are researched deeply and understood relatively clearly. The periodical and modulation components can be decomposed by cyclostationary spectrum density (CSD) by nonlinear transform and cyclic factor. According to the cyclostatinary theories, the 3-dimensional graphics of the cyclostationary signal with the variance of the cyclic frequency and frequency, or its slice at the proper cyclic frequency, will supply the information of the modulation wave and carrier wave. The common spectrum analysis can’t realize the decomposition.
Since the spectrum or PSD distribution of sound pressure displayed in the original NAH hologram can’t show the statistical information of sound energy varying with time, the conventional NAH is not suitable for cyclostationary sound field. The method named cyclostationary nearfield acoustic holography (CYNAN) is developed to analyze the cyclostationary sound field whose hologram shows the energy distribution of the modulation wave components at the appropriate cyclic frequency. The reconstruction of the cyclostation- ary sound by CYNAH will help understand the physical mechanism and sound field characteristics. Because the objects are limited to be planar or close to planar that is impossible for most cases in the industry, it is necessary to modify the planar CYNAH to adapt to the arbitrarily-shaped objects by combining with other numerical methods.
There are three kinds of CYNAH methods are presented in this dissertation, combining with boundary element method (BEM), wave superposition algorithm (WSA) and Helmholtz equation least square (HELS), respectively. The second-order cyclic statistics is used as the variables for reconstruction of sound field in the place of the velocity or pressure in the common NAH. All of three methods can be used to analyze the sources with complicated profiles that are often encountered in practice. In the dissertation, their theories are derived and factors affecting the reconstruction accuracy are analyzed, the experiments are also described in details. The project in present dissertation is aided financially by National Natural Science Foundation of China (granted No. 10674096).
The main contents of dissertation are as follows:
(1) The progress of NAH is reviewed firstly. The NAH methods are described in classes due to their combined numerical methods. The techniques of hologram data sampling, reconstructed algorithm and engineering application are summarized. The non-stationary sound field is less concerned in the former research. CYNAH methods suitable for arbitrarily-shaped objects are advised on the basis of the planar CYNAH for both the academic and engineering viewpoints.
(2) CYNAH method based on BEM is derived where the second-order cyclic statistics take the place of velocity and pressure as the variance. Comparing with the common BEM- based NAH, the reconstruction of the cyclostationary sound field by BEM-based CYNAH shows the velocity or pressure CSD distribution which will help to understand the characteristics of the sound field. The factors affecting the accuracy are analyzed by the numerical simulations.
(3) WSA-based CYNAH is employed to reconstruct the cyclostationary sound field, which is assumed to be generated by a series of cyclostationary virtual sources inside of the objects. After the cross-CSDs between the virtual sources and the rigid reference are determined by an inverse procedure, the CSD at anywhere of the whole sound field can be calculated. Numerical simulations supply some guides for the application of WSA- based CYNAH to the objects such as spatial ratio, regularization, background noise, etc.
(4) The third CYNAH method suitable for the objects with complicated profiles is related with the HELS method. The coefficients of every basis function are supposed to vary cyclostatioinarily with time. The optimal number of the basis functions and relative cross CSD vector between coefficients and rigid reference are obtained by least square method. Then the reconstruction of the CSD can be realized. Some numerical simulations are also done for understanding the HELS-based CYNAH.
(5) The research on the comparison of these three CYNAH methods above whose objects are arbitrarily-shaped is carried out. The advantages and disadvantages of every method are concluded which are beneficial for researchers to choose the right one under different conditions.
(6) The validities of the methods above are illustrated by experiments finished in an semi-anechoic chamber. The experiment objects are a cubic sound box and a dodecahedron loudspeaker. The objects are driven by the cyclostationary signal. A rigid reference microphone is set around the objects at a close distance and the signals on the hologram are scanning-sampled by a scanning equipment. All the three methods are applied to analyze the same objects and the comparison is done.
在工程中,有一类特殊的非平稳信号——循环平稳(Cyclostationary)信号,例如内燃机、滚动轴承等旋转机械产生的辐射声场具有明显的循环平稳特性。随着对循环平稳信号的认识越来越深入,循环统计量理论已经开始应用于机械设备状态监测和故障诊断领域,目前研究的比较透彻的是二阶循环统计量。循环谱密度具有对循环平稳信号的解调能力,通过非线性变换和循环因子的共同作用,可以获取循环平稳信号中的周期成分,将调制信息直接解调到循环频率轴上。通过循环统计量理论分析,可以将循环平稳信号的信息可以同时表现在以频率和循环频率为变量的循环谱密度三维图上,并可以在合适的循环频率下获取剖面图,这将会提供比普通频谱更多的信息。
用传统NAH技术分析循环平稳声场时,无法充分考虑和利用循环平稳信号的周期时变特征,将不可避免地忽视了某些频率成分上的能量随时间变化方面的信息。目前的研究工作,已将NAH方法应用到循环平稳场的研究,其主要工作成果是提出循环平稳近场声全息概念(CYNAH: Cyclostationary NAH),实现了平面循环平稳声源的全息重建,其全息图显示了声信号中反映系统特性的调制信息的能量分布状况。循环平稳信息的全息重建,对于了解声场形成的机理,揭示声源的物理特性有很大的帮助。在实际工程中,绝大多数的声源都不具有规则外形,为了能将该方法推广到能分析任意外形的声源,势必要结合新的方法使之能适应任意外形声源的要求。
本文在平面CYNAH理论和循环平稳信号处理技术的基础上,结合边界元法、波叠加法和Helmholtz方程最小二乘法,发展了适合于任意外形声源的CYNAH方法。这三种方法使得CYNAH方法扩大了应用的声源范围,使之更加适合于工程实际。本文建立了三种不同类型的循环平稳声场近场声全息的变换理论和方法,研究了影响声场重建误差的主要因素,并进行了相应的实验研究。本文的研究工作得到了国家自然科学基金(批准号:No. 10674096)的资助。本文采用理论建模、数字仿真与实验研究相结合的研究路线,以二阶循环统计量作为声场重建的物理量,研究了适用于循环平稳声场这类特殊的非平稳声场的近场声全息理论,本文的主要内容如下:
(1)综述近场声全息技术在国内外的研究现状及进展,按照NAH方法所基于的不同数值方法分类阐述。对全息面数据采集技术、重建算法研究及工程应用等方面的成果和存在的问题进行了总结。鉴于目前NAH技术多数是对于平稳声场的研究现状,在平面循环平稳近场声全息(Cyclostationary near field acoustic holography, CYNAH)技术上进一步提出适用于任意外形声源的CYNAH方法,并简要阐述了本文的选题背景与研究意义。
(2)提出基于边界元法(BEM: Boundary Element method)的CYNAH方法,详细地推导了适用于循环平稳声源的改进Helmholz方程。和普通的边界元法NAH方法相比较,基于边界元法的CYNAH方法采用声压和法向速度的循环谱密度代替频谱和功率谱密度作为声场重建的物理量,CYNAH全息图反映了声场中各点声压和法向速度的循环谱密度分布;通过数值仿真,详细分析了重建过程中的影响因素,包括背景噪声、声源外形尺寸、全息面形状及其与重建面的相对位置等。
(3)提出基于波叠加法(Wave Superposition Algorithm, WSA)的CYNAH方法,假设外部声场由声源内部的一系列循环平稳等效源激励产生,在获取了等效源和参考源的互循环谱密度后,就可以重建整个声场中任意位置和参考源之间的互循环谱密度,然后根据循环谱理论得到循环谱密度的空间分布。用数值仿真算例,分析了该方法的适用对象和影响重建的因素。
(4)提出基于Helmholtz方程最小二乘法(Helmholtz Equation Least Square, HELS)的CYNAH方法,假设各阶分量的权重系数按循环平稳规律做变化。通过最小二乘法获取最佳的展开项数和权重系数循环谱密度,从而实现在整个声场中的循环谱密度重建,数值仿真算例验证了该方法的正确性并对影响因素作了对比分析。
(5)将三种适用于任意外形声源的CYNAH方法以及影响重建的因素汇总在一起,比较三种方法的优劣,为方法的实际运用提供指导。
(6)实验验证了循环平稳近场声全息技术的有关理论分析。实验在半消声室内完成,实验对象为一个矩形音箱和一个十二面体球声源,用循环平稳信号驱动扬声器发声,形成循环平稳声场。在声源附近布置位置固定的传声器,用二维数控扫描架完成了声压的步进扫描测量,用32通道数据采集系统记录声压信号,然后用三种方法分析同一声源,进行声场重建研究和对比分析,验证理论分析的结果。
Identification of the noise source is the first step of the noise control. Visualizing the acoustic field will offer more information for the location of the source and its physical mechanism. Among the different methods, nearfield acoustic holography (NAH) is one important tool for analyzing sound field due to its high resolution. The high resolution is obtained from the closely measuring that the sound field information is reserved ultimately in the sampling data including the evanescent wave. NAH method is developed to be suitable for the arbitrarily-shaped source from the simple geometries such as plane, cylinder and sphere. The sound field including the pressure, normal velocity and sound power is recon- structed after building the spatial transformation between the source and the hologram. NAH method is widely applied to the industry such as NVH analysis in the auto-mobile industry, locating noise sources, structure modal analysis. The progress of NAH methods attracts researchers’attention in the recent three decades. The most research on the NAH focused on the stationary sound field and the non-stationary sound field is involved less.
In the industry, there is a kind of non-stationary signal named cyclostationary signal whose cyclic statistics is with characteristics to decompose the carrier wave and modulation wave solely. The cyclostationary sound field excited by some machines is often observed in the industry, such as the internal combustion engines and rolling-bearings, especially when they run under ill conditions. The cyclic statistics theory has been utilized to detect machinery faults, and the main parameters are the second-order statistics which are researched deeply and understood relatively clearly. The periodical and modulation components can be decomposed by cyclostationary spectrum density (CSD) by nonlinear transform and cyclic factor. According to the cyclostatinary theories, the 3-dimensional graphics of the cyclostationary signal with the variance of the cyclic frequency and frequency, or its slice at the proper cyclic frequency, will supply the information of the modulation wave and carrier wave. The common spectrum analysis can’t realize the decomposition.
Since the spectrum or PSD distribution of sound pressure displayed in the original NAH hologram can’t show the statistical information of sound energy varying with time, the conventional NAH is not suitable for cyclostationary sound field. The method named cyclostationary nearfield acoustic holography (CYNAN) is developed to analyze the cyclostationary sound field whose hologram shows the energy distribution of the modulation wave components at the appropriate cyclic frequency. The reconstruction of the cyclostation- ary sound by CYNAH will help understand the physical mechanism and sound field characteristics. Because the objects are limited to be planar or close to planar that is impossible for most cases in the industry, it is necessary to modify the planar CYNAH to adapt to the arbitrarily-shaped objects by combining with other numerical methods.
There are three kinds of CYNAH methods are presented in this dissertation, combining with boundary element method (BEM), wave superposition algorithm (WSA) and Helmholtz equation least square (HELS), respectively. The second-order cyclic statistics is used as the variables for reconstruction of sound field in the place of the velocity or pressure in the common NAH. All of three methods can be used to analyze the sources with complicated profiles that are often encountered in practice. In the dissertation, their theories are derived and factors affecting the reconstruction accuracy are analyzed, the experiments are also described in details. The project in present dissertation is aided financially by National Natural Science Foundation of China (granted No. 10674096).
The main contents of dissertation are as follows:
(1) The progress of NAH is reviewed firstly. The NAH methods are described in classes due to their combined numerical methods. The techniques of hologram data sampling, reconstructed algorithm and engineering application are summarized. The non-stationary sound field is less concerned in the former research. CYNAH methods suitable for arbitrarily-shaped objects are advised on the basis of the planar CYNAH for both the academic and engineering viewpoints.
(2) CYNAH method based on BEM is derived where the second-order cyclic statistics take the place of velocity and pressure as the variance. Comparing with the common BEM- based NAH, the reconstruction of the cyclostationary sound field by BEM-based CYNAH shows the velocity or pressure CSD distribution which will help to understand the characteristics of the sound field. The factors affecting the accuracy are analyzed by the numerical simulations.
(3) WSA-based CYNAH is employed to reconstruct the cyclostationary sound field, which is assumed to be generated by a series of cyclostationary virtual sources inside of the objects. After the cross-CSDs between the virtual sources and the rigid reference are determined by an inverse procedure, the CSD at anywhere of the whole sound field can be calculated. Numerical simulations supply some guides for the application of WSA- based CYNAH to the objects such as spatial ratio, regularization, background noise, etc.
(4) The third CYNAH method suitable for the objects with complicated profiles is related with the HELS method. The coefficients of every basis function are supposed to vary cyclostatioinarily with time. The optimal number of the basis functions and relative cross CSD vector between coefficients and rigid reference are obtained by least square method. Then the reconstruction of the CSD can be realized. Some numerical simulations are also done for understanding the HELS-based CYNAH.
(5) The research on the comparison of these three CYNAH methods above whose objects are arbitrarily-shaped is carried out. The advantages and disadvantages of every method are concluded which are beneficial for researchers to choose the right one under different conditions.
(6) The validities of the methods above are illustrated by experiments finished in an semi-anechoic chamber. The experiment objects are a cubic sound box and a dodecahedron loudspeaker. The objects are driven by the cyclostationary signal. A rigid reference microphone is set around the objects at a close distance and the signals on the hologram are scanning-sampled by a scanning equipment. All the three methods are applied to analyze the same objects and the comparison is done.
引文
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