超宽带电磁法正演模拟及反演成像
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摘要
本文提出用超宽带(UWB)电磁脉冲进行地下目标体探测或穿墙探测的方法，即超宽带电磁法。它结合了瞬态电磁场理论、窄脉冲信号发射技术、高速采样技术、UWB天线和信号处理技术等学科的研究成果，具有模拟精确、无损伤、分辨率高和探测深度大(或穿透能力强)等优点。
本文深入分析了UWB电磁波在地下有耗介质里的传播特征、能量分布特征、分辨率与探测深度、发射电磁脉冲的时宽或频宽与回波中有效信息量的关系等基础理论问题；开展了用超宽带电磁脉冲对地下介质的高分辨率探测研究，使用有限面积的口径天线，馈入大功率、窄脉冲信号，以同时提高探测深度和分辨率；用高阶时域有限差分(FDTD)法对任意复杂地下介质模型和穿墙生命探测的理论模型进行数值模拟，揭示了窄脉冲电磁波在复杂介质里的传播规律和目标的脉冲响应特征；给出了适合UWB电磁法的电导率和介电常数同时重构的反演法和处理方法建议。
论文主要成果如下：
1．将时域卷积完全匹配层(CPML)和高阶时域有限差分法相结合，模拟了有限面积的口径天线辐射的UWB电磁波场，编制了UWB电磁法的三维高阶FDTD模拟软件，能对任意复杂地下有耗介质进行数值模拟。
2．改进了CPML吸收边界条件的迭代公式里的卷积计算方法，提出分段线性卷积完全匹配层(PCPML)吸收边界处理方法，进一步改善了边界吸收效果。
3．分别用频域的解析解法和时域的FDTD解法分析了均匀有耗介质空间里，有限面积口径天线的窄脉冲辐射场的传播特点与能流密度的空间分布特点；首次揭示了电磁导弹能流密度慢衰减的本质原因，客观地评价了电磁导弹在探地方面的应用价值。
4．实现了任意复杂介质的UWB电磁波场模拟。直观显示了UWB电磁波在几种典型地下探测模型和地面上穿墙探测人体模型里的传播过程，解释了电磁波与有耗地下介质的相互作用机理；分析了天线参数和地电参数对辐射场性能的影响，进而讨论了UWB电磁法的分辨率和探测深度等问题，为UWB电磁法的解释和走向实际提供理论指导。
5．研究了适合UWB电磁法特点的电导率和介电常数同时重构的反演方法。使用改进的时域有限内存BFGS拟牛顿约束反演方法和非线性共轭梯度法近似反演方法，同时重构模型的介电参数与电导率，完成了UWB电磁法的双参数反演，编制了相应的反演软件。
6．研究了UWB电磁法的快速成像方法，提出基于时域波形匹配滤波方法的相关概率成像法，成功实现了对单个或多个目标体的概率成像。
In this dissertation, a new detect method was proposed which use ultra-wideband(UWB) electromagnetic pulse to detect underground targets or through-the-walldetection, so it was called UWB electromagnetic method. It combines transientelectromagnetic field theory, very narrow pulse signal transmission technology, high-speed sampling techniques, UWB antenna and signal processing technology andother subjects of research, the result of simulation is accurate, noninvasive, highresolution and penetrating depth etc. Many basic theoretical issues have been studiedin-depth in this dissertation, such as the UWB electromagnetic waves in lossy media, the dissemination of energy distribution, Resolution and penetrating depth, therelationship between pulse width or bandwidth and the Echo of effectivelyinformation and so on. The high-resolution survey research was carried out to detectthe media under the ground with UWB electromagnetic pulse. We used limited-areaof aperture antenna, feed into the high power and very narrow pulses. In this way, wecan improve the penetrating depth and resolution at one time.
The numerical simulation of the theoretical model for arbitrary complex mediaunderground and through the walls to detect life was carried out which used thehigh-order finite-difference time-domain (FDTD) method, the result revealed thelaw of the electromagnetic pulse dissemination and the impulse responsecharacteristics of objectives in complex media. The inversion method of conductivityand permittivity simultaneously reconstructing for UWB electromagnetic method wasproposed in this dissertation.
The main contribution of this dissertation can be summarized as follows:
1. Combined the time domain convolutional PML with high-order FDTD tosimulate the UWB electromagnetic radiation field of limited-area of aperture antenna, developed the 3D electromagnetic simulation of high-order FDTD software which cancarry out numerical simulation for arbitrarily complex of underground lossy media.
2. Improved the convolution method in iterative formula of CPMLabsorption boundary conditions, proposed piecewise linear convolution PML(PCPML) absorption boundary approach, and further improved the absorptioneffect of the boundary.
3. Discussed the narrow radiation pulse of limited area of aperture antennatransmission and energy density characteristic of the spatial distribution in uniformlossy media space with frequency domain analytic method and the time domainFDTD method respectively, revealed the nature law of electromagnetic flux densityslow decay for the first time, and corrected the misunderstand about electromagneticmissile for the moment, evaluated objectively the applied value of electromagneticmissile used in explorating earth
4. Simulated the UWB electromagnetic wave filed of arbitrary complexitymodel, the transmission of UWB electromagnetic wave in several typical undergroundmodel and through the walls to detect the human body model can be shown directly, explained the interaction mechanism of electromagnetic wave in lossy mediaunderground. Analyzed the antenna parameters and electrical parameters on theperformance of the radiation field, and then discussed the resolution and depth ofUWB electromagnetic detection method. It can provide theoretical guidance for thepractical work of UWB electromagnetic method.
5. The inversion method of conductivity and permittivity simultaneouslyreconstructing for UWB electromagnetic method was proposed in this dissertation.Using the improved time-domain limited memory BFGS quasi-Newton constrainedinversion method and nonlinear conjugate gradient method approximate inversionmethod to reconstruct permittivity and conductivity of the model in the same time, and completed the UWB electromagnetic double-parameter inversion and developedthe corresponding inversion software.
6. Studied the rapid imaging methods of UWB electromagnetic detectmethod which based on time-domain waveform matching filter method of probabilityimaging, and achieved the single or multiple objects with the probability imagingsuccessfully.
本文深入分析了UWB电磁波在地下有耗介质里的传播特征、能量分布特征、分辨率与探测深度、发射电磁脉冲的时宽或频宽与回波中有效信息量的关系等基础理论问题；开展了用超宽带电磁脉冲对地下介质的高分辨率探测研究，使用有限面积的口径天线，馈入大功率、窄脉冲信号，以同时提高探测深度和分辨率；用高阶时域有限差分(FDTD)法对任意复杂地下介质模型和穿墙生命探测的理论模型进行数值模拟，揭示了窄脉冲电磁波在复杂介质里的传播规律和目标的脉冲响应特征；给出了适合UWB电磁法的电导率和介电常数同时重构的反演法和处理方法建议。
论文主要成果如下：
1．将时域卷积完全匹配层(CPML)和高阶时域有限差分法相结合，模拟了有限面积的口径天线辐射的UWB电磁波场，编制了UWB电磁法的三维高阶FDTD模拟软件，能对任意复杂地下有耗介质进行数值模拟。
2．改进了CPML吸收边界条件的迭代公式里的卷积计算方法，提出分段线性卷积完全匹配层(PCPML)吸收边界处理方法，进一步改善了边界吸收效果。
3．分别用频域的解析解法和时域的FDTD解法分析了均匀有耗介质空间里，有限面积口径天线的窄脉冲辐射场的传播特点与能流密度的空间分布特点；首次揭示了电磁导弹能流密度慢衰减的本质原因，客观地评价了电磁导弹在探地方面的应用价值。
4．实现了任意复杂介质的UWB电磁波场模拟。直观显示了UWB电磁波在几种典型地下探测模型和地面上穿墙探测人体模型里的传播过程，解释了电磁波与有耗地下介质的相互作用机理；分析了天线参数和地电参数对辐射场性能的影响，进而讨论了UWB电磁法的分辨率和探测深度等问题，为UWB电磁法的解释和走向实际提供理论指导。
5．研究了适合UWB电磁法特点的电导率和介电常数同时重构的反演方法。使用改进的时域有限内存BFGS拟牛顿约束反演方法和非线性共轭梯度法近似反演方法，同时重构模型的介电参数与电导率，完成了UWB电磁法的双参数反演，编制了相应的反演软件。
6．研究了UWB电磁法的快速成像方法，提出基于时域波形匹配滤波方法的相关概率成像法，成功实现了对单个或多个目标体的概率成像。
In this dissertation, a new detect method was proposed which use ultra-wideband(UWB) electromagnetic pulse to detect underground targets or through-the-walldetection, so it was called UWB electromagnetic method. It combines transientelectromagnetic field theory, very narrow pulse signal transmission technology, high-speed sampling techniques, UWB antenna and signal processing technology andother subjects of research, the result of simulation is accurate, noninvasive, highresolution and penetrating depth etc. Many basic theoretical issues have been studiedin-depth in this dissertation, such as the UWB electromagnetic waves in lossy media, the dissemination of energy distribution, Resolution and penetrating depth, therelationship between pulse width or bandwidth and the Echo of effectivelyinformation and so on. The high-resolution survey research was carried out to detectthe media under the ground with UWB electromagnetic pulse. We used limited-areaof aperture antenna, feed into the high power and very narrow pulses. In this way, wecan improve the penetrating depth and resolution at one time.
The numerical simulation of the theoretical model for arbitrary complex mediaunderground and through the walls to detect life was carried out which used thehigh-order finite-difference time-domain (FDTD) method, the result revealed thelaw of the electromagnetic pulse dissemination and the impulse responsecharacteristics of objectives in complex media. The inversion method of conductivityand permittivity simultaneously reconstructing for UWB electromagnetic method wasproposed in this dissertation.
The main contribution of this dissertation can be summarized as follows:
1. Combined the time domain convolutional PML with high-order FDTD tosimulate the UWB electromagnetic radiation field of limited-area of aperture antenna, developed the 3D electromagnetic simulation of high-order FDTD software which cancarry out numerical simulation for arbitrarily complex of underground lossy media.
2. Improved the convolution method in iterative formula of CPMLabsorption boundary conditions, proposed piecewise linear convolution PML(PCPML) absorption boundary approach, and further improved the absorptioneffect of the boundary.
3. Discussed the narrow radiation pulse of limited area of aperture antennatransmission and energy density characteristic of the spatial distribution in uniformlossy media space with frequency domain analytic method and the time domainFDTD method respectively, revealed the nature law of electromagnetic flux densityslow decay for the first time, and corrected the misunderstand about electromagneticmissile for the moment, evaluated objectively the applied value of electromagneticmissile used in explorating earth
4. Simulated the UWB electromagnetic wave filed of arbitrary complexitymodel, the transmission of UWB electromagnetic wave in several typical undergroundmodel and through the walls to detect the human body model can be shown directly, explained the interaction mechanism of electromagnetic wave in lossy mediaunderground. Analyzed the antenna parameters and electrical parameters on theperformance of the radiation field, and then discussed the resolution and depth ofUWB electromagnetic detection method. It can provide theoretical guidance for thepractical work of UWB electromagnetic method.
5. The inversion method of conductivity and permittivity simultaneouslyreconstructing for UWB electromagnetic method was proposed in this dissertation.Using the improved time-domain limited memory BFGS quasi-Newton constrainedinversion method and nonlinear conjugate gradient method approximate inversionmethod to reconstruct permittivity and conductivity of the model in the same time, and completed the UWB electromagnetic double-parameter inversion and developedthe corresponding inversion software.
6. Studied the rapid imaging methods of UWB electromagnetic detectmethod which based on time-domain waveform matching filter method of probabilityimaging, and achieved the single or multiple objects with the probability imagingsuccessfully.
引文
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