声学层析成像反问题求解及温度场重建算法研究
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摘要
声学层析成像（Acoustic computer tomography）温度场检测技术根据多路径声波传播时间数据，推算被测区域的温度分布，属于“由效果反求原因”的逆问题研究，具有非接触不干扰被测温场、测温范围广（0℃～2000℃）、测量对象空间范围大（数十米）、可在线测量等优点。声学高温计是该技术在工业炉温度场监测中的典型应用。而应用该技术监测大气温度分布、深海热液温度分布、仓储粮食温度分布，则是探索中的新的应用领域。本文对声学层析成像反问题求解及温度场重建算法等问题，进行了较深入的理论分析和实验研究，主要完成了以下工作：
分析了影响声学层析成像温度场测量精度的主要原因，针对现有声学层析成像温度场重建算法普遍存在的问题，即：被测区域网格划分数须小于系统可获得的有效声波路径数，原始像素数量有限，重建温度场空间分辨率低。提出一种基于Markov径向基函数与Tikhonov正则化的三维温度场重建算法---3DMTR（Markov radial basic function andTikhonov Regularization）算法。该算法被测区域划分的网格数可远多于声波路径数，更适合复杂温度场重建。
声波收发器阵列设计的合理性，直接影响声学层析成像温度场检测实验系统的测量实时性及温度场重建精度。为实现储粮温度分布声学层析成像法监测，对围绕圆筒形仓布置的声波收发器的数量、布局和有效声波路径选择等参数进行了计算机仿真设计。三种典型的三维模型温度场重建结果表明：剔除仓壁上同一母线上的声波路径，可降低温度场重建误差。增加同一层面上收发器的数目或收发器布置的层数，都能减小重建误差。但若设置过多的声波收发器，会增大系数矩阵的条件数，加大重建误差。通过对声波收发器阵列的仿真设计，可优化收发器阵列各参数，提高声学层析成像温度场检测实验系统的性能和温度场重建精度。
声学层析成像温度场重建是不适定的逆问题。正则化参数的选取对重建精度有重要影响。提出被测区域划分的像素数可远多于声波路径数、正则化参数自适应选取的二维温度场重建算法2DMTR-A（MTR withAdaptive Regularization Parameter）和三维温度场重建算法3DMTR-A。它们采用一种新的、称为最小变化法的正则化参数选取法，自适应地选取正则化参数，兼顾温度场细节重建和噪声抑制。仿真与实验重建结果表明，与常用的L曲线法相比，最小变化法确定的正则化参数对应着更小的温度场重建误差，具有较广泛的适应性。因此2DMTR-A和3DMTR-A算法具有良好的实用性。
声波在非均匀温度场中传播时其路径会因折射而弯曲。尤其对于温度梯度较大的复杂温度场，将声波路径近似为直线会给重建带来较大的误差。为提高非均匀温度场声学层析成像重建精度，提出考虑声波弯曲的二维/三维温度场重建算法。首先用二维/三维重建算法获得一个不考虑声线弯曲的二维/三维重建温度场，然后用打靶--插值法确定本征声线出射角，以三角形/正四面体前向展开法追踪声线，并建立本征声线上声波传播时间与温度分布间的关系，进而实现考虑声线弯曲的二维/三维温度场重建。仿真实验结果表明考虑声线弯曲效应后，能明显提高非均匀温度场重建精度。温度场的温度梯度越大，改善的效果越明显。
采用以虚拟仪器LABVIEW为软件平台的声学层析成像温度场检测实验系统，以本文所提出的温度场重建算法，对空气中的二维温度场、三维温度场和仓储大豆中的二维温度场进行重建，实验验证了本文所提温度场重建算法的有效性和正确性。
Temperature field measurement of acoustic computer tomography calculates temperaturedistributions of the measurement region based on multi-path acoustic travel-times data, whichis classified as the "reverse results into effects" study of inverse problems, has the advantagesof non-contact without interfering temperature fields, wide temperature range (0℃~2000℃),large range of measured object space (dozens of meters) and on-line measurement, etc.Acoustic pyrometer is one of the typical applications of the technique in the furnacetemperature field monitoring. While temperature distribution monitors of atmosphere anddeep-sea hydrothermal and stored grain are new application areas of acoustic computertomography in exploration. In this paper, solution of inverse problem for the acousticcomputer tomography, reconstruction algorithm of temperature field and other issues areanalyzed theoretically and experimental studied deeply, The main work is completed asfollows:
Major causes that affects acoustic computer tomography measurement precision intemperature field are analyzed in this paper. Aiming at those existing problems in acousticcomputer tomography reconstruction algorithm on temperature distribution, i. e.: the gridnumber of measured region division has to be less than number of effective sound wave pathswhich limits the original number of pixels, and results in low spatial resolution of thereconstructed temperature field, a3D temperature field reconstruction algorithm based onMarkov radial basic function and Tikhonov regularization---3DMTR (Markov radial basicfunction and Tikhonov Regularization) is proposed. The number of partition grids in measuredarea can be much greater than number of sound wave paths by using this algorithm, which ismuch more suitable for complex temperature field reconstruction.
The rationality of the sound Transceivers array design directly affects the real-timemeasurement of acoustic computer tomography experimental system and the accuracy oftemperature field reconstruction. In order to monitor temperature distribution in stored grainby the method of acoustic computer tomography, the parameters such as the number of soundtransceivers arranged around the cylindrical granary, the layout and the effective sound pathselection are designed by computer simulation. The temperature field reconstruction results of three typical three-dimensional model show that removal on the silo wall sound paths in thesame bus can reduce the temperature field reconstruction error. Increasing the number of thetransceivers on one layer or the number of the layers transceivers arranged, are able to reducethe reconstruction error. But setting a plethora of sound transceivers may increase thecondition number of the coefficient matrix, and then increase the reconstruction error. Throughthe simulation design of sound transceiver array, transceiver array parameters can beoptimized, and the performance of acoustic computer tomography experimental system can beimproved as well as the reconstruction precision of temperature field.
Temperature field reconstruction by acoustic computer tomography is an ill-posedproblem. The choice of regularization parameter has an important influence on the accuracy ofreconstruction. The temperature field reconstruction algorithm of the2DMTR-A (MTR withAdaptive Regularization Parameter) and the3DMTR-A on measured area raised number ofpixels can be far more sound wave paths, selection of adaptive regularization parameter isproposed. They use a novel adaptive regularization parameter selection method, named asminimum change criterion, to determine a proper regularization parameter, which can make agood compromise between de-noise and detail reconstruction of temperature field. Thereconstruction results of simulation and experimental show that the regularization parametersselected by the minimum change criterion is superior to those selected by the common L-curvemethod because they produce lower reconstruction errors, with a wide range of adaptability.Therefore,2DMTR-A and3DMTR-A algorithm has good practicality.
When sound wave propagates in un-uniform temperature fields, its path is bent due torefraction. Approximately sound wave paths as straight line will cause great errors, especiallyfor temperature field whose temperature gradient is steep. In order to improve thereconstruction accuracy of un-uniform temperature fields by acoustic computer tomography,the2D/3D reconstruction algorithm is proposed in which the bending of sound wave paths isconsidered. Firstly, reconstruct the2D/3D temperature field without considering the bendingof sound wave paths by using2D/3D reconstruction algorithm. Secondly, find the eigenrays inthe reconstruction field by using the triangular/tetrahedron forward deployment method forsound ray tracing after evaluating the emergent angle of eigenrays by usingshooting-interpolation method. Thirdly, establish the relationship between the acoustictravel-times over the eigenrays and the temperature distribution. Lastly, reconstruct the2D/3D temperature field with consideration of sound wave paths bending. The reconstruction resultsshow that the reconstruction accuracy can be improved obviously by considering the bendingof sound wave paths. The larger the temperature gradient of temperature field is the moreobviously the improvement effect.
By adopting acoustic computer tomography experimental system based on virtualinstrument of LABVIEW, temperature field reconstruction algorithm proposed in this paperreconstructs the air2D/3D and stored soybean2D temperature fields, experimental resultverifies the effectiveness and reasonableness of the temperature field reconstruction algorithmpresented in this paper.
分析了影响声学层析成像温度场测量精度的主要原因，针对现有声学层析成像温度场重建算法普遍存在的问题，即：被测区域网格划分数须小于系统可获得的有效声波路径数，原始像素数量有限，重建温度场空间分辨率低。提出一种基于Markov径向基函数与Tikhonov正则化的三维温度场重建算法---3DMTR（Markov radial basic function andTikhonov Regularization）算法。该算法被测区域划分的网格数可远多于声波路径数，更适合复杂温度场重建。
声波收发器阵列设计的合理性，直接影响声学层析成像温度场检测实验系统的测量实时性及温度场重建精度。为实现储粮温度分布声学层析成像法监测，对围绕圆筒形仓布置的声波收发器的数量、布局和有效声波路径选择等参数进行了计算机仿真设计。三种典型的三维模型温度场重建结果表明：剔除仓壁上同一母线上的声波路径，可降低温度场重建误差。增加同一层面上收发器的数目或收发器布置的层数，都能减小重建误差。但若设置过多的声波收发器，会增大系数矩阵的条件数，加大重建误差。通过对声波收发器阵列的仿真设计，可优化收发器阵列各参数，提高声学层析成像温度场检测实验系统的性能和温度场重建精度。
声学层析成像温度场重建是不适定的逆问题。正则化参数的选取对重建精度有重要影响。提出被测区域划分的像素数可远多于声波路径数、正则化参数自适应选取的二维温度场重建算法2DMTR-A（MTR withAdaptive Regularization Parameter）和三维温度场重建算法3DMTR-A。它们采用一种新的、称为最小变化法的正则化参数选取法，自适应地选取正则化参数，兼顾温度场细节重建和噪声抑制。仿真与实验重建结果表明，与常用的L曲线法相比，最小变化法确定的正则化参数对应着更小的温度场重建误差，具有较广泛的适应性。因此2DMTR-A和3DMTR-A算法具有良好的实用性。
声波在非均匀温度场中传播时其路径会因折射而弯曲。尤其对于温度梯度较大的复杂温度场，将声波路径近似为直线会给重建带来较大的误差。为提高非均匀温度场声学层析成像重建精度，提出考虑声波弯曲的二维/三维温度场重建算法。首先用二维/三维重建算法获得一个不考虑声线弯曲的二维/三维重建温度场，然后用打靶--插值法确定本征声线出射角，以三角形/正四面体前向展开法追踪声线，并建立本征声线上声波传播时间与温度分布间的关系，进而实现考虑声线弯曲的二维/三维温度场重建。仿真实验结果表明考虑声线弯曲效应后，能明显提高非均匀温度场重建精度。温度场的温度梯度越大，改善的效果越明显。
采用以虚拟仪器LABVIEW为软件平台的声学层析成像温度场检测实验系统，以本文所提出的温度场重建算法，对空气中的二维温度场、三维温度场和仓储大豆中的二维温度场进行重建，实验验证了本文所提温度场重建算法的有效性和正确性。
Temperature field measurement of acoustic computer tomography calculates temperaturedistributions of the measurement region based on multi-path acoustic travel-times data, whichis classified as the "reverse results into effects" study of inverse problems, has the advantagesof non-contact without interfering temperature fields, wide temperature range (0℃~2000℃),large range of measured object space (dozens of meters) and on-line measurement, etc.Acoustic pyrometer is one of the typical applications of the technique in the furnacetemperature field monitoring. While temperature distribution monitors of atmosphere anddeep-sea hydrothermal and stored grain are new application areas of acoustic computertomography in exploration. In this paper, solution of inverse problem for the acousticcomputer tomography, reconstruction algorithm of temperature field and other issues areanalyzed theoretically and experimental studied deeply, The main work is completed asfollows:
Major causes that affects acoustic computer tomography measurement precision intemperature field are analyzed in this paper. Aiming at those existing problems in acousticcomputer tomography reconstruction algorithm on temperature distribution, i. e.: the gridnumber of measured region division has to be less than number of effective sound wave pathswhich limits the original number of pixels, and results in low spatial resolution of thereconstructed temperature field, a3D temperature field reconstruction algorithm based onMarkov radial basic function and Tikhonov regularization---3DMTR (Markov radial basicfunction and Tikhonov Regularization) is proposed. The number of partition grids in measuredarea can be much greater than number of sound wave paths by using this algorithm, which ismuch more suitable for complex temperature field reconstruction.
The rationality of the sound Transceivers array design directly affects the real-timemeasurement of acoustic computer tomography experimental system and the accuracy oftemperature field reconstruction. In order to monitor temperature distribution in stored grainby the method of acoustic computer tomography, the parameters such as the number of soundtransceivers arranged around the cylindrical granary, the layout and the effective sound pathselection are designed by computer simulation. The temperature field reconstruction results of three typical three-dimensional model show that removal on the silo wall sound paths in thesame bus can reduce the temperature field reconstruction error. Increasing the number of thetransceivers on one layer or the number of the layers transceivers arranged, are able to reducethe reconstruction error. But setting a plethora of sound transceivers may increase thecondition number of the coefficient matrix, and then increase the reconstruction error. Throughthe simulation design of sound transceiver array, transceiver array parameters can beoptimized, and the performance of acoustic computer tomography experimental system can beimproved as well as the reconstruction precision of temperature field.
Temperature field reconstruction by acoustic computer tomography is an ill-posedproblem. The choice of regularization parameter has an important influence on the accuracy ofreconstruction. The temperature field reconstruction algorithm of the2DMTR-A (MTR withAdaptive Regularization Parameter) and the3DMTR-A on measured area raised number ofpixels can be far more sound wave paths, selection of adaptive regularization parameter isproposed. They use a novel adaptive regularization parameter selection method, named asminimum change criterion, to determine a proper regularization parameter, which can make agood compromise between de-noise and detail reconstruction of temperature field. Thereconstruction results of simulation and experimental show that the regularization parametersselected by the minimum change criterion is superior to those selected by the common L-curvemethod because they produce lower reconstruction errors, with a wide range of adaptability.Therefore,2DMTR-A and3DMTR-A algorithm has good practicality.
When sound wave propagates in un-uniform temperature fields, its path is bent due torefraction. Approximately sound wave paths as straight line will cause great errors, especiallyfor temperature field whose temperature gradient is steep. In order to improve thereconstruction accuracy of un-uniform temperature fields by acoustic computer tomography,the2D/3D reconstruction algorithm is proposed in which the bending of sound wave paths isconsidered. Firstly, reconstruct the2D/3D temperature field without considering the bendingof sound wave paths by using2D/3D reconstruction algorithm. Secondly, find the eigenrays inthe reconstruction field by using the triangular/tetrahedron forward deployment method forsound ray tracing after evaluating the emergent angle of eigenrays by usingshooting-interpolation method. Thirdly, establish the relationship between the acoustictravel-times over the eigenrays and the temperature distribution. Lastly, reconstruct the2D/3D temperature field with consideration of sound wave paths bending. The reconstruction resultsshow that the reconstruction accuracy can be improved obviously by considering the bendingof sound wave paths. The larger the temperature gradient of temperature field is the moreobviously the improvement effect.
By adopting acoustic computer tomography experimental system based on virtualinstrument of LABVIEW, temperature field reconstruction algorithm proposed in this paperreconstructs the air2D/3D and stored soybean2D temperature fields, experimental resultverifies the effectiveness and reasonableness of the temperature field reconstruction algorithmpresented in this paper.
引文
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