Patch近场声全息及近场声全息分辨率增强方法
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摘要
近场声全息技术是一种功能强大的噪声源识别、定位及声场可视化技术。由于该技术采用近场测量,测得的全息声压中包含了携有丰富声源细节信息的“倏逝波”(Evanescent Wave)成分,因此近场声全息技术突破了瑞利分辨率判据的限制,其空间分辨率可达分析波长的几十分之一,在机械故障诊断及机械设备噪声治理工程中有着广泛的应用前景。
然而,由于有效孔径造成的窗效应等误差因素的影响,普通近场声全息技术在小全息孔径、局部全息测量和大尺寸声源结构条件下存在较大误差,严重阻碍了近场声全息技术的推广。近年来,为解决小全息孔径条件下的声场重建问题,降低重建误差,Patch NAH技术逐渐兴起,成为国际研究的热点和近场声全息技术未来发展的趋势。本文针对Patch NAH技术中的关键问题——全息声压外推问题进行了深入的研究和探讨。论文首先对普通NAH的算法过程进行了理论研究,阐明了普通NAH过程中计算误差的主要来源及产生机理,并分析了这些误差与全息测量孔径尺寸大小间的关系,从而说明了Patch NAH技术中全息声压外推过程的必要性。在此基础上,提出了基于带限信号恢复算法(PGA)、波叠加(WSA)和正交球面波源(OSW)的全息声压外推方法,初步解决了不同情况下的全息声压外推问题,由此建立了相应的三种不同的Patch NAH技术,并通过仿真和实验证明了这些技术的有效性、正确性以及相对于普通NAH的优越性。同时,将全息声压外推方法用于全息声压的插值过程,提出通过全息声压插值来提高NAH图像的空间分辨率,建立了多种近场声全息分辨率增强方法,在达到相同空间分辨率的前提下,显著降低了所需的全息测量点数,大大节约了测量工作量,具有较大的实用价值。
第一章简要地回顾了近场声全息技术的诞生、发展历史和研究现状,分析了近场声全息技术在应用中存在的一些亟需解决的问题,并提出了解决的途径——Patch NAH技术,随后详细阐述了Patch NAH的技术特点,算法流程和研究现状,并在此基础上确立了本文的主要研究内容。
第二章根据傅立叶声学理论,研究了近场声全息重建过程中存在的主要算法误差以及这些误差的产生机理。通过分析Patch NAH中全息声压近场外推过程对这些算法误差的影响,发现通过外推可以有效抑制这些算法对重建结果的影响,从而证明了Patch NAH技术的有效性。
第三章首先通过理论分析揭示了全息声压的波数域带限特性,紧接着从带限信号恢复的角度在理论上证明了全息声压近场外推的科学性和正确性。然后利用全息声压的波数域带限性质,提出了基于PGA的全息声压近场外推方法,建立了基于带限信号恢复算法的Patch NAH。在此基础上,将PGA用于全息声压插值,建立了基于带限信号恢复算法的近场声全息分辨率增强方法。最后通过固支板声源的全息重建和分辨率增强实验验证了所提出的上述两种方法的有效性,也进一步证明了全息声压的波数域带限特性。
第四章将波叠加法引入Patch NAH,首先给出了声辐射问题的声学基础和定解问题描述,由此导出了波叠加方法的基本公式;在此基础上,提出采用波叠加法进行全息声压的近场外推和插值,建立了基于波叠加法的。Patch NAH以及相应的分辨率增强方法;详细分析了波叠加法中源强密度求解的病态性问题,提出通过优化模型参数来降低传递矩阵的病态程度,以及通过正则化方法来稳定求解过程,并介绍了几种常用的正则化方法和正则化参数的选择方法;最后进行了实验验证。
第五章针对基于波叠加方法中存在的虚源位置确定困难的问题,提出采用一系列相互正交的球面波源来进行声场的拟合,并在此基础上进行全息声压的近场外推与插值,建立了基于正交球面波源的Patch NAH以及相应的分辨率增强方法。
第六章总结了本文的主要研究成果,提出了需要进一步研究和解决的问题。
Nearfield acoustic holography (NAH) is a powerful technique for identifying noise sources and visualizing acoustic field. It has high resolution, because the evanescent waves which contain much detailed information of the acoustic field are utilized in the method. Therefore, it can be wildly used in mechanical equipment fault diagnosis and noise reduction.
While NAH suffers from algorithmic errors, that are caused by finite measurement aperture effects and other factors. These errors would rise rapidly with the reduction of the measurement aperture. Therefore, NAH can not be applied when measurement aperture is small. This limitation is an obstacle to-extensive application of NAH technology. In order to overcome this shortage, a novel acoustic holography technique called as Patch NAH has been proposed in recent years. Compared with NAH technique, there exists a special procedure called as hologram pressure extrapolation in Patch NAH. By this procedure, the pressure measured in small aperture is extended or "continued" into a region which is larger than the original measurement aperture. That is why Patch NAH can sufficiently reduce algorithmic errors and keep the accuracy when the measurement aperture is small. Therefore, the hologram pressure extrapolation procedure is the key of Patch NAH, and the research work of this paper focuses on how to extrapolate hologram pressure. In this paper, three novel methods for extrapolating hologram pressure are proposed. And three kinds of Patch NAH technique based on these methods are also established. The validity of these methods has been verified by numerical simulations and experiments. Meanwhile, it is found that the proposed pressure extrapolation methods can also be used to interpolate the measured pressure for the NAH image spatial resolution enhancement. Therefore, the NAH image spatial resolution enhancing techniques were proposed in this paper. The experiment shows that these techniques can effectively improve the resolution of NAH image without increasing the measurement points. The main contents of the dissertation are shown as follows:
In chapter one, the history of NAH was reviewed briefly. By analyzing the current status of NAH technique, the existing problem was discussed. To deal with this problem, the Patch NAH technique was introduced. By analyzing the research status of Patch NAH, the main research contents of this dissertation were determined. In chapter two, two kinds of the algorithmic errors of NAH were studied in detail. They are finite measurement aperture effects caused by truncating of acoustic field and wrap-around error related to dispersion in wave number domain. By analyzing the generation mechanisms of these errors, it shows that these errors have a close relationship with the measurement aperture size, and can be sufficient reduced by hologram pressure extrapolation. To prove the validity of hologram pressure extrapolation for reducing the algorithmic errors, numerical simulations and experiments were performed.
In chapter three, to extrapolate the hologram pressure efficiently, the property of the hologram pressure was researched firstly. The band-limited property of the hologram pressure was illuminated. According to this property, the theoretical feasibility of hologram pressure extrapolation was proved and a novel hologram pressure extrapolating method based on a band-limited signal restoration method named Papoulis-Gerchberg algorithm (PGA) was proposed. The Patch NAH based on this method was also established. Furthermore, it is theoretically proved that the PGA-based pressure extrapolating method also can be used for hologram pressure interpolation. So that, a new method based on interpolation by using PGA was proposed for enhancing the resolution of the nearfield acoustic holography. The validity of the proposed methods was proved by numerical simulations and experiments.
In chapter four, firstly, the theoretical base of acoustic radiation was reviewed and the basic equation of wave superposition approach (WSA) was deduced. According to the mechanism of WSA, the acoustic fields on and near the measurement surface can be approximated by the fields produced by fictitious sources placed inside the structure. Therefore, the pressure extrapolation can be realized by the superposition of fields generated by these fictitious sources. Based on this, the WSA was employed to realize hologram pressure extrapolation and interpolation. The Patch NAH and NAH image resolution enhancing method based on WSA were established. Then, the numerical stability of WSA was investigated. The model optimization and regularization strategy were proposed to deal with the ill-posed problem in solving the source strengths of fictitious sources.
In chapter five, a new hologram pressure extrapolation method using orthogonal spherical wave source is proposed According to the solution of Helmholtz equation in spherical coordinates, any acoustic field can be approximately expressed as a linear sum of a series of orthogonal spherical wave functions. So that, the acoustic field generated by vibrator can be approximated, by superposing the fields generated by a series of orthogonal spherical wave sources of different orders, and the pressure exploration is realized by radiating process of these spherical wave sources. Because the orthogonal spherical wave sources of different orders are orthogonal with each other, they can be placed at one point inside the vibrator. So there is no need to design the position of all the fictitious sources.
In chapter six, researches in this dissertation are summarized, and the topics which need to be further studied are proposed.
然而,由于有效孔径造成的窗效应等误差因素的影响,普通近场声全息技术在小全息孔径、局部全息测量和大尺寸声源结构条件下存在较大误差,严重阻碍了近场声全息技术的推广。近年来,为解决小全息孔径条件下的声场重建问题,降低重建误差,Patch NAH技术逐渐兴起,成为国际研究的热点和近场声全息技术未来发展的趋势。本文针对Patch NAH技术中的关键问题——全息声压外推问题进行了深入的研究和探讨。论文首先对普通NAH的算法过程进行了理论研究,阐明了普通NAH过程中计算误差的主要来源及产生机理,并分析了这些误差与全息测量孔径尺寸大小间的关系,从而说明了Patch NAH技术中全息声压外推过程的必要性。在此基础上,提出了基于带限信号恢复算法(PGA)、波叠加(WSA)和正交球面波源(OSW)的全息声压外推方法,初步解决了不同情况下的全息声压外推问题,由此建立了相应的三种不同的Patch NAH技术,并通过仿真和实验证明了这些技术的有效性、正确性以及相对于普通NAH的优越性。同时,将全息声压外推方法用于全息声压的插值过程,提出通过全息声压插值来提高NAH图像的空间分辨率,建立了多种近场声全息分辨率增强方法,在达到相同空间分辨率的前提下,显著降低了所需的全息测量点数,大大节约了测量工作量,具有较大的实用价值。
第一章简要地回顾了近场声全息技术的诞生、发展历史和研究现状,分析了近场声全息技术在应用中存在的一些亟需解决的问题,并提出了解决的途径——Patch NAH技术,随后详细阐述了Patch NAH的技术特点,算法流程和研究现状,并在此基础上确立了本文的主要研究内容。
第二章根据傅立叶声学理论,研究了近场声全息重建过程中存在的主要算法误差以及这些误差的产生机理。通过分析Patch NAH中全息声压近场外推过程对这些算法误差的影响,发现通过外推可以有效抑制这些算法对重建结果的影响,从而证明了Patch NAH技术的有效性。
第三章首先通过理论分析揭示了全息声压的波数域带限特性,紧接着从带限信号恢复的角度在理论上证明了全息声压近场外推的科学性和正确性。然后利用全息声压的波数域带限性质,提出了基于PGA的全息声压近场外推方法,建立了基于带限信号恢复算法的Patch NAH。在此基础上,将PGA用于全息声压插值,建立了基于带限信号恢复算法的近场声全息分辨率增强方法。最后通过固支板声源的全息重建和分辨率增强实验验证了所提出的上述两种方法的有效性,也进一步证明了全息声压的波数域带限特性。
第四章将波叠加法引入Patch NAH,首先给出了声辐射问题的声学基础和定解问题描述,由此导出了波叠加方法的基本公式;在此基础上,提出采用波叠加法进行全息声压的近场外推和插值,建立了基于波叠加法的。Patch NAH以及相应的分辨率增强方法;详细分析了波叠加法中源强密度求解的病态性问题,提出通过优化模型参数来降低传递矩阵的病态程度,以及通过正则化方法来稳定求解过程,并介绍了几种常用的正则化方法和正则化参数的选择方法;最后进行了实验验证。
第五章针对基于波叠加方法中存在的虚源位置确定困难的问题,提出采用一系列相互正交的球面波源来进行声场的拟合,并在此基础上进行全息声压的近场外推与插值,建立了基于正交球面波源的Patch NAH以及相应的分辨率增强方法。
第六章总结了本文的主要研究成果,提出了需要进一步研究和解决的问题。
Nearfield acoustic holography (NAH) is a powerful technique for identifying noise sources and visualizing acoustic field. It has high resolution, because the evanescent waves which contain much detailed information of the acoustic field are utilized in the method. Therefore, it can be wildly used in mechanical equipment fault diagnosis and noise reduction.
While NAH suffers from algorithmic errors, that are caused by finite measurement aperture effects and other factors. These errors would rise rapidly with the reduction of the measurement aperture. Therefore, NAH can not be applied when measurement aperture is small. This limitation is an obstacle to-extensive application of NAH technology. In order to overcome this shortage, a novel acoustic holography technique called as Patch NAH has been proposed in recent years. Compared with NAH technique, there exists a special procedure called as hologram pressure extrapolation in Patch NAH. By this procedure, the pressure measured in small aperture is extended or "continued" into a region which is larger than the original measurement aperture. That is why Patch NAH can sufficiently reduce algorithmic errors and keep the accuracy when the measurement aperture is small. Therefore, the hologram pressure extrapolation procedure is the key of Patch NAH, and the research work of this paper focuses on how to extrapolate hologram pressure. In this paper, three novel methods for extrapolating hologram pressure are proposed. And three kinds of Patch NAH technique based on these methods are also established. The validity of these methods has been verified by numerical simulations and experiments. Meanwhile, it is found that the proposed pressure extrapolation methods can also be used to interpolate the measured pressure for the NAH image spatial resolution enhancement. Therefore, the NAH image spatial resolution enhancing techniques were proposed in this paper. The experiment shows that these techniques can effectively improve the resolution of NAH image without increasing the measurement points. The main contents of the dissertation are shown as follows:
In chapter one, the history of NAH was reviewed briefly. By analyzing the current status of NAH technique, the existing problem was discussed. To deal with this problem, the Patch NAH technique was introduced. By analyzing the research status of Patch NAH, the main research contents of this dissertation were determined. In chapter two, two kinds of the algorithmic errors of NAH were studied in detail. They are finite measurement aperture effects caused by truncating of acoustic field and wrap-around error related to dispersion in wave number domain. By analyzing the generation mechanisms of these errors, it shows that these errors have a close relationship with the measurement aperture size, and can be sufficient reduced by hologram pressure extrapolation. To prove the validity of hologram pressure extrapolation for reducing the algorithmic errors, numerical simulations and experiments were performed.
In chapter three, to extrapolate the hologram pressure efficiently, the property of the hologram pressure was researched firstly. The band-limited property of the hologram pressure was illuminated. According to this property, the theoretical feasibility of hologram pressure extrapolation was proved and a novel hologram pressure extrapolating method based on a band-limited signal restoration method named Papoulis-Gerchberg algorithm (PGA) was proposed. The Patch NAH based on this method was also established. Furthermore, it is theoretically proved that the PGA-based pressure extrapolating method also can be used for hologram pressure interpolation. So that, a new method based on interpolation by using PGA was proposed for enhancing the resolution of the nearfield acoustic holography. The validity of the proposed methods was proved by numerical simulations and experiments.
In chapter four, firstly, the theoretical base of acoustic radiation was reviewed and the basic equation of wave superposition approach (WSA) was deduced. According to the mechanism of WSA, the acoustic fields on and near the measurement surface can be approximated by the fields produced by fictitious sources placed inside the structure. Therefore, the pressure extrapolation can be realized by the superposition of fields generated by these fictitious sources. Based on this, the WSA was employed to realize hologram pressure extrapolation and interpolation. The Patch NAH and NAH image resolution enhancing method based on WSA were established. Then, the numerical stability of WSA was investigated. The model optimization and regularization strategy were proposed to deal with the ill-posed problem in solving the source strengths of fictitious sources.
In chapter five, a new hologram pressure extrapolation method using orthogonal spherical wave source is proposed According to the solution of Helmholtz equation in spherical coordinates, any acoustic field can be approximately expressed as a linear sum of a series of orthogonal spherical wave functions. So that, the acoustic field generated by vibrator can be approximated, by superposing the fields generated by a series of orthogonal spherical wave sources of different orders, and the pressure exploration is realized by radiating process of these spherical wave sources. Because the orthogonal spherical wave sources of different orders are orthogonal with each other, they can be placed at one point inside the vibrator. So there is no need to design the position of all the fictitious sources.
In chapter six, researches in this dissertation are summarized, and the topics which need to be further studied are proposed.
引文
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