光电测量信息中大气折射误差的神经网络建模修正研究
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摘要
大气折射误差的客观性影响了光电测量信息的真实性，大气折射误差的复杂性增加了其修正的难度。传统的修正方法，无论是理论上还是方法上，都没有跳出大气模型及其分层假设这一圈子，它们只适合于标准大气。对非标准大气，传统的非线性建模和数理统计方法往往无法实现高精度修正，而人类大量的光电测量活动都是在非标准大气中进行的。随着光电测量设备的测量精度与人们对光电测量信息要求的不断提高，光电测量信息中大气折射误差的高精度修正已成为高精度光电测量工程中亟待解决的关键问题。
类似大气折射误差这样复杂的非线性对象，神经网络理论具有传统的非线性建模无法媲美的优势。所以，本研究尝试利用神经网络理论中的BPNN模型来研究光电测量信息中的大气折射误差修正。本研究首先对该领域国内外的研究状况进行了分析，对与本研究相关的基础理论与基本方法进行了阐述。在上述基本理论与基本方法的指导下，运用数学基础理论与计算机建模仿真，依托俄罗斯普尔科沃天文台的大气折射实测数据平台、2个变形光电测量工程等提供的相关信息及MATLAB7提供的神经网络工具箱，对光电测量信息中大气折射误差的神经网络建模修正开展了下述独创性的研究：
(1)根据大气折射误差修正的映射函数理论，对10多种映射函数进行了数学理论上的一般化，提出了“高阶分式映射函数”这一新概念。研究完成了基本映射函数的神经网络变换。首次在普尔科沃天文大气折射实测值数据平台上，进行了映射函数、神经网络的计算机建模与拟合比较。结果表明：在拟合精度上，BPNN优于映射函数，是目前修正精度最好的4阶分式映射函数的2倍。证明了映射函数对天文大气折射的模拟精度的确已接近传统非线性建模修正的理论极限。
(2)根据光电测距仪的全室内检测新方法，对光电测距系统的误差及控制进行了分析研究，为高精度空中基线的建立提供了方法指导。提出了“基线神经网络”的新概念。该方法能够实现基线光电测量信息中大气折射误差与其它误差的高精度分离。
(3)根据矩阵的基本性质，巧妙地利用单位矩阵，从数学原理上证明：就神经网络建模效率的实时性而言，样本预处理与神经网络训练算法的优化是等价的。该证明简洁明了，不存在病态分式(分母为0的分式)的约束。提出了简单有效的样本预处理方法——均值比例法，实例建模结果表明：该方法与MATLAB中提供的预处理方法相比，能提高建模效率1～4倍；样本预处理可以减轻网络训练中的高阶逼近负荷，而算法优化可以弥补样本预处理高阶逼近能力的不足。
(4)对反常大气折射的变化规律、光测信息的利用、基线神经网络的建模理论、建模方法及模型的推广应用进行了研究。提出了基于周日信息一致性检验条件下的基线神经网络模型推广应用新方法。实例建模结果表明：该方法修正后，基线日均变形几乎为0。
(5)对某大型变形光电监测工程的应用研究表明：当周日信息一致性强时，基线神经网络模型对基线的日均修正精度可达到10~(-4)mm／km，基线邻边比例的日均修正精度可达到10~(-3)mm／km，周日均值差分的日均修正精度可达到10~(-2)mm／km，气象公式的日均修正精度可达到10~(-1)mm／km。当周日信息一致性不强时，基线神经网络的实时修正效果明显优于气象公式与基线邻边比例修正，略好于周日均值差分修正。提出了下述新观点：光电测量信息中大气折射误差的建模修正，不管采取什么的模型，周日信息一致性强基础上的应用，都有利于修正精度。此新观点将使大气折射误差修正模型在推广应用中出现的修正精度不确定性较大的问题有望得到更好解释。
(6)数学证明和实例研究表明：BPNN神经网络模型对大气折射中高阶信息的挖掘是隐含层神经元完成的，而不是输入层神经元。类似映射函数的非线性高阶构造对BPNN神经网络建模挖掘高阶信息的贡献不显著。在大气折射高阶信息的挖掘能力上，神经网络优于映射函数，尽管二者的挖掘形式不同，但在数学原理上是一致的。较好地解释了学术交流中的一些颇具争议的问题。
(7)本研究发展了光电测量信息中大气折射误差修正理论，丰富了神经网络理论的应用实践。
The atmospheric refraction errors (ARE) are objectivity in the photo-electricity survey information (PESI), the error accurate correction is very difficult for its complexity. Some conventional correction rules are only feasible in the standard atmosphere based on the atmosphere models theory and the foliaceous hypothesis method. The conventional nonlinear modeling and statistics technique can not achieve the high precision correction in the nonstandard atmosphere, but the large numbers of photo-electricity survey works have been achieved in the nonstandard atmosphere. Along with unceasing enhancement of the equipment measuring accuracy and people accuracy requirements, the atmospheric refraction errors correction (AREC) desiderate improving in some high precision photo-electricity survey projects.
The neural network theory has many advantages than the conventional nonlinear modeling and statistics technique to resemble the intricate nonlinear object of AREC, therefore, this research is trying to improve the precision of the AREC by using the back propagation neural network (BPNN) model for the PESI. It firstly presents the inland and overseas actuality and introduces interrelated the basic theory and essential method for the AREC study on this research field. Some original researches were carried out for the AREC with the BPNN model in the PESI. These research based on following foundation: the aforementioned elementary theory and essential method, the list data in the Pulkovo refraction table (PRT) and the correlation information of two distortion photo-electricity survey projects, the mathematics basic theory and the computer modeling simulation by the help of Matlab7 BP toolbox.
(1). It brings forward a new concept of the high degree fraction form mapping function based on the mapping function (MF) principle of the AREC and the generalization expressions of over ten sorts MF function in mathematics, and transforms the basic MF to the BPNN model. It achieves the modeling and fitting of the models on the PRT firstly. Simulation shows that the BPNN is double of the 4-degree fraction form MF in the accuracy of simulation, and proves that correction precision of the MF modeling indeed has approached theoretic precision which the traditional non-linear modeling revises.
(2). It put forward second new concept of the baseline back propagation neural network model (BLBPNNM). It studies the entire laboratory performance test of the photoelectric distance meter and analyzes that the measure errors of radio meteorology parameters to influence precision of the AREC. The BLBPNNM can separate the atmospheric refraction errors from the information of baseline photoelectric distance meter by very high precision.
(3). It gives a new compendious mathematics proof without the ill-conditioned fraction form constraint for that both the sample pretreatment and the optimization training algorithm of BPNN are equivalence in the modeling efficiency by using the identity matrix and the basic character of matrix operation. It provides an efficacious sample pretreatment arithmetic that the value of sample divided by their average. Example shows that the arithmetic is more efficacious than the pretreatment function of MATLAB and the modeling efficiency of BPNN can enhance 1～4 times.
(4). It performs such researches as the abnormity change rules of atmospheric refraction, how use the PESI and modeling principle, steps and application way of the BLBPNNM. It offers a new application method based on the full-day information consistency check between the modeling baseline and the correction line for the BLBPNNM. Example shows that the method is feasible and daily distortion mean value of the baseline is nearly zero and has separated the atmospheric refraction errors from the information of baseline photoelectric distance meter with very high precision.
(5). The application research shows that daily mean correction precision (DMCP) of the baseline can attain 10~(-4)mm/km by using the BLBPNNM, the neighboring baseline length ratio method is 10~(-3)mm/km, the full-day mean value difference expressions is 10~(-2)mm/km, the exact meteorology formula is 10~(-1)mm/km when their full-day information consistency check are better, and the real-time correction effect of BLBPNNM is the best in these methods when the consistency check are not nice. So it presents a new correction viewpoint which all the models can improve the AREC precision in the PESI when their consistency checks are fine. The problem which the correction precision is uncertain by the traditional AREC method will make progress in application, which is hopeful on the new viewpoint.
(6). In the high order information mining effect of atmospheric refraction, the math proof and simulation show that the mining power of the BPNN model excelled the MF, but the mining power comes from the hidden lay nerve cell rather than the input lay as a result of the mining effect of BPNN model is not distinct in a similar way which the MF form add high order items. Although both the BPNN and the MF are different in the mining modality, their fundamental principles are consistent in mathematics.
(7). This research has developed and enriched "the AREC and the BPNN" in both theory and practice, and has attained the anticipative objectives.
类似大气折射误差这样复杂的非线性对象，神经网络理论具有传统的非线性建模无法媲美的优势。所以，本研究尝试利用神经网络理论中的BPNN模型来研究光电测量信息中的大气折射误差修正。本研究首先对该领域国内外的研究状况进行了分析，对与本研究相关的基础理论与基本方法进行了阐述。在上述基本理论与基本方法的指导下，运用数学基础理论与计算机建模仿真，依托俄罗斯普尔科沃天文台的大气折射实测数据平台、2个变形光电测量工程等提供的相关信息及MATLAB7提供的神经网络工具箱，对光电测量信息中大气折射误差的神经网络建模修正开展了下述独创性的研究：
(1)根据大气折射误差修正的映射函数理论，对10多种映射函数进行了数学理论上的一般化，提出了“高阶分式映射函数”这一新概念。研究完成了基本映射函数的神经网络变换。首次在普尔科沃天文大气折射实测值数据平台上，进行了映射函数、神经网络的计算机建模与拟合比较。结果表明：在拟合精度上，BPNN优于映射函数，是目前修正精度最好的4阶分式映射函数的2倍。证明了映射函数对天文大气折射的模拟精度的确已接近传统非线性建模修正的理论极限。
(2)根据光电测距仪的全室内检测新方法，对光电测距系统的误差及控制进行了分析研究，为高精度空中基线的建立提供了方法指导。提出了“基线神经网络”的新概念。该方法能够实现基线光电测量信息中大气折射误差与其它误差的高精度分离。
(3)根据矩阵的基本性质，巧妙地利用单位矩阵，从数学原理上证明：就神经网络建模效率的实时性而言，样本预处理与神经网络训练算法的优化是等价的。该证明简洁明了，不存在病态分式(分母为0的分式)的约束。提出了简单有效的样本预处理方法——均值比例法，实例建模结果表明：该方法与MATLAB中提供的预处理方法相比，能提高建模效率1～4倍；样本预处理可以减轻网络训练中的高阶逼近负荷，而算法优化可以弥补样本预处理高阶逼近能力的不足。
(4)对反常大气折射的变化规律、光测信息的利用、基线神经网络的建模理论、建模方法及模型的推广应用进行了研究。提出了基于周日信息一致性检验条件下的基线神经网络模型推广应用新方法。实例建模结果表明：该方法修正后，基线日均变形几乎为0。
(5)对某大型变形光电监测工程的应用研究表明：当周日信息一致性强时，基线神经网络模型对基线的日均修正精度可达到10~(-4)mm／km，基线邻边比例的日均修正精度可达到10~(-3)mm／km，周日均值差分的日均修正精度可达到10~(-2)mm／km，气象公式的日均修正精度可达到10~(-1)mm／km。当周日信息一致性不强时，基线神经网络的实时修正效果明显优于气象公式与基线邻边比例修正，略好于周日均值差分修正。提出了下述新观点：光电测量信息中大气折射误差的建模修正，不管采取什么的模型，周日信息一致性强基础上的应用，都有利于修正精度。此新观点将使大气折射误差修正模型在推广应用中出现的修正精度不确定性较大的问题有望得到更好解释。
(6)数学证明和实例研究表明：BPNN神经网络模型对大气折射中高阶信息的挖掘是隐含层神经元完成的，而不是输入层神经元。类似映射函数的非线性高阶构造对BPNN神经网络建模挖掘高阶信息的贡献不显著。在大气折射高阶信息的挖掘能力上，神经网络优于映射函数，尽管二者的挖掘形式不同，但在数学原理上是一致的。较好地解释了学术交流中的一些颇具争议的问题。
(7)本研究发展了光电测量信息中大气折射误差修正理论，丰富了神经网络理论的应用实践。
The atmospheric refraction errors (ARE) are objectivity in the photo-electricity survey information (PESI), the error accurate correction is very difficult for its complexity. Some conventional correction rules are only feasible in the standard atmosphere based on the atmosphere models theory and the foliaceous hypothesis method. The conventional nonlinear modeling and statistics technique can not achieve the high precision correction in the nonstandard atmosphere, but the large numbers of photo-electricity survey works have been achieved in the nonstandard atmosphere. Along with unceasing enhancement of the equipment measuring accuracy and people accuracy requirements, the atmospheric refraction errors correction (AREC) desiderate improving in some high precision photo-electricity survey projects.
The neural network theory has many advantages than the conventional nonlinear modeling and statistics technique to resemble the intricate nonlinear object of AREC, therefore, this research is trying to improve the precision of the AREC by using the back propagation neural network (BPNN) model for the PESI. It firstly presents the inland and overseas actuality and introduces interrelated the basic theory and essential method for the AREC study on this research field. Some original researches were carried out for the AREC with the BPNN model in the PESI. These research based on following foundation: the aforementioned elementary theory and essential method, the list data in the Pulkovo refraction table (PRT) and the correlation information of two distortion photo-electricity survey projects, the mathematics basic theory and the computer modeling simulation by the help of Matlab7 BP toolbox.
(1). It brings forward a new concept of the high degree fraction form mapping function based on the mapping function (MF) principle of the AREC and the generalization expressions of over ten sorts MF function in mathematics, and transforms the basic MF to the BPNN model. It achieves the modeling and fitting of the models on the PRT firstly. Simulation shows that the BPNN is double of the 4-degree fraction form MF in the accuracy of simulation, and proves that correction precision of the MF modeling indeed has approached theoretic precision which the traditional non-linear modeling revises.
(2). It put forward second new concept of the baseline back propagation neural network model (BLBPNNM). It studies the entire laboratory performance test of the photoelectric distance meter and analyzes that the measure errors of radio meteorology parameters to influence precision of the AREC. The BLBPNNM can separate the atmospheric refraction errors from the information of baseline photoelectric distance meter by very high precision.
(3). It gives a new compendious mathematics proof without the ill-conditioned fraction form constraint for that both the sample pretreatment and the optimization training algorithm of BPNN are equivalence in the modeling efficiency by using the identity matrix and the basic character of matrix operation. It provides an efficacious sample pretreatment arithmetic that the value of sample divided by their average. Example shows that the arithmetic is more efficacious than the pretreatment function of MATLAB and the modeling efficiency of BPNN can enhance 1～4 times.
(4). It performs such researches as the abnormity change rules of atmospheric refraction, how use the PESI and modeling principle, steps and application way of the BLBPNNM. It offers a new application method based on the full-day information consistency check between the modeling baseline and the correction line for the BLBPNNM. Example shows that the method is feasible and daily distortion mean value of the baseline is nearly zero and has separated the atmospheric refraction errors from the information of baseline photoelectric distance meter with very high precision.
(5). The application research shows that daily mean correction precision (DMCP) of the baseline can attain 10~(-4)mm/km by using the BLBPNNM, the neighboring baseline length ratio method is 10~(-3)mm/km, the full-day mean value difference expressions is 10~(-2)mm/km, the exact meteorology formula is 10~(-1)mm/km when their full-day information consistency check are better, and the real-time correction effect of BLBPNNM is the best in these methods when the consistency check are not nice. So it presents a new correction viewpoint which all the models can improve the AREC precision in the PESI when their consistency checks are fine. The problem which the correction precision is uncertain by the traditional AREC method will make progress in application, which is hopeful on the new viewpoint.
(6). In the high order information mining effect of atmospheric refraction, the math proof and simulation show that the mining power of the BPNN model excelled the MF, but the mining power comes from the hidden lay nerve cell rather than the input lay as a result of the mining effect of BPNN model is not distinct in a similar way which the MF form add high order items. Although both the BPNN and the MF are different in the mining modality, their fundamental principles are consistent in mathematics.
(7). This research has developed and enriched "the AREC and the BPNN" in both theory and practice, and has attained the anticipative objectives.
引文
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