拱坝变形分析与监控的小波和神经网络方法研究
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摘要
拱坝的变形受到多方面因素的影响，变形与各影响因子之间的关系是复杂
的，高度非线性的映射关系。传统方法只能近似地描述变形与各影响因子之间的
关系。而小波变换技术和神经网络理论能行之有效地解决这类问题。
本文在对拱坝变形的影响因子进行系统分析的基础上，采用多分辨分析的方
法对影响拱坝变形的温度、水位特征进行了分析。详细地分析了温度的周期特征，
水位的一般特征。同时，对温度、水位的分解结果进行去噪，去除其高频噪声，
然后重构提取温度、水位的典型特征结果，为大坝变形的预测监控做准备。采用
最优正交小波基分解拱坝的变形资料，然后去除其高频噪声的影响，重构变形结
果，并详尽地分析了拱坝变形的一般规律。
本文抓住影响拱坝变形的主要影响因子——气温和水位，以及实测变形之间
的间接关系，利用小波变换提取的信息和大坝变形信息作为输入，实测变形值作
为输出，通过对模型的合理优化和有效的数据处理，成功建立了拱坝变形的 BP
网络监控预测分析模型。通过模型的运算，得出了满意的结果，并且模型的预测
精度较高。
本文研究结果表明，小波变换技术是对大坝原型观测资料进行分析的有效手
段；神经网络通过对问题的隐性描述，能有效地实现变形与各影响因子之间的复
杂的高度非线性映射关系。因此，小波变换技术和神经网络理论在大坝的原型观
测资料分析方面具有较强的工程适用性和较好的应用前景。
Arch dam deformation is effected by multi-factors, and their relations, high
nonlinear mapping relation, are very complex. Conventional method can only
approximately describe the relationship of the deformation and its impacting factors.
However, Wavelet Transform technique and Artificial Neural Net Work method can
effectively solve it.
On the basis of systematic analysis the impact factors of arch dam deformation,
the characteristics of temperature and water level of dam are analyzed by adopt the
Multi-resolution analysis method. The characteristic of temperature and the general
characteristic of water level are detailedly analyzed. At the same time, the
high-frequency noise of the decomposed result of temperature and water level are
removed. Then, their representative characteristics are composed, which is prepared
for forecasting and monitoring the dam deformation. The optimum orthogonal
wavelet bases decompose the datum of arch dam deformation. Removing the
high-frequency noise, the result of deformation is composed. Then, the general rules
of dam deformation are detailedly analyzed.
In this paper, the main impact factor, i.e. temperature and water level that effect
the arch dam deformation, and the indirect relationship of adjacent actual
measurement of deformation, are grasped by qualitative analysis. The
Back-Propagation Net-work monitor-forecasting analysis model, whose input is
information getting from Wavelet transformation and actual measurement of dam
deformation, is successfully founded though properly optimized the model and
effectively datum processing. Calculating with this model, the satisfactory resolution
is got. Results show that the forecasting precision of this model is high.
The study resolution shows that Wavelet Transform technique is an effective
analysis method in analyzing prototype measurement of dam, and that Artificial
Neural Net Work can effectively realize complex and high nonlinear mapping
relationship between deformation and each impact factor through recessive
description way. Therefore, Wavelet Transform technique and Artificial Neural Net
Work method will find its way in analyzing prototype measurement of dam, worthy of
propagation in hydraulic engineering practice.
的，高度非线性的映射关系。传统方法只能近似地描述变形与各影响因子之间的
关系。而小波变换技术和神经网络理论能行之有效地解决这类问题。
本文在对拱坝变形的影响因子进行系统分析的基础上，采用多分辨分析的方
法对影响拱坝变形的温度、水位特征进行了分析。详细地分析了温度的周期特征，
水位的一般特征。同时，对温度、水位的分解结果进行去噪，去除其高频噪声，
然后重构提取温度、水位的典型特征结果，为大坝变形的预测监控做准备。采用
最优正交小波基分解拱坝的变形资料，然后去除其高频噪声的影响，重构变形结
果，并详尽地分析了拱坝变形的一般规律。
本文抓住影响拱坝变形的主要影响因子——气温和水位，以及实测变形之间
的间接关系，利用小波变换提取的信息和大坝变形信息作为输入，实测变形值作
为输出，通过对模型的合理优化和有效的数据处理，成功建立了拱坝变形的 BP
网络监控预测分析模型。通过模型的运算，得出了满意的结果，并且模型的预测
精度较高。
本文研究结果表明，小波变换技术是对大坝原型观测资料进行分析的有效手
段；神经网络通过对问题的隐性描述，能有效地实现变形与各影响因子之间的复
杂的高度非线性映射关系。因此，小波变换技术和神经网络理论在大坝的原型观
测资料分析方面具有较强的工程适用性和较好的应用前景。
Arch dam deformation is effected by multi-factors, and their relations, high
nonlinear mapping relation, are very complex. Conventional method can only
approximately describe the relationship of the deformation and its impacting factors.
However, Wavelet Transform technique and Artificial Neural Net Work method can
effectively solve it.
On the basis of systematic analysis the impact factors of arch dam deformation,
the characteristics of temperature and water level of dam are analyzed by adopt the
Multi-resolution analysis method. The characteristic of temperature and the general
characteristic of water level are detailedly analyzed. At the same time, the
high-frequency noise of the decomposed result of temperature and water level are
removed. Then, their representative characteristics are composed, which is prepared
for forecasting and monitoring the dam deformation. The optimum orthogonal
wavelet bases decompose the datum of arch dam deformation. Removing the
high-frequency noise, the result of deformation is composed. Then, the general rules
of dam deformation are detailedly analyzed.
In this paper, the main impact factor, i.e. temperature and water level that effect
the arch dam deformation, and the indirect relationship of adjacent actual
measurement of deformation, are grasped by qualitative analysis. The
Back-Propagation Net-work monitor-forecasting analysis model, whose input is
information getting from Wavelet transformation and actual measurement of dam
deformation, is successfully founded though properly optimized the model and
effectively datum processing. Calculating with this model, the satisfactory resolution
is got. Results show that the forecasting precision of this model is high.
The study resolution shows that Wavelet Transform technique is an effective
analysis method in analyzing prototype measurement of dam, and that Artificial
Neural Net Work can effectively realize complex and high nonlinear mapping
relationship between deformation and each impact factor through recessive
description way. Therefore, Wavelet Transform technique and Artificial Neural Net
Work method will find its way in analyzing prototype measurement of dam, worthy of
propagation in hydraulic engineering practice.
引文
参考文献
[1]李瓒，陈兴华等，混凝土拱坝设计，北京：中国电力出版社，2000 年 9 月
[2]朱伯芳，中国拱坝建设的成就，水力发电，1999（10）：38~41
[3]陈久宇，林见，观测数据的数学处理，上海：上海交通大学出版社，1990 年
8 月
[4]黄铭，李珍照，大坝监测空间位移统计模型研究，武汉水利电力大学学报，
1999，32（3）：19~22
[5]吴中如等，水工建筑物安全监控理论及其应用，南京：河海大学出版社，1990
年 8 月
[6]Giusepptti G., Basic Theory Underlying the Computation of Influence
Coefficient, Ismes, 1986
[7]李步娟，刘新平等，拱坝变形监测预报模型研究，水利水电技术，1996（7）：
10~15
[8]吴中如，顾冲时等，大坝观测资料的综合分析法，河海大学学报，1993，21
（1）：71~76
[9]Wu Zhongru, Wang Zhanrui, Dynamic Monitoring Model of Space
Displacement Field of Concrete Dam, International Symposium on
Monitoring Technology of Dam Safety, 1992.10
[10]蓝悦明，王新洲，灰色预测用于大坝水平变形预测的研究，武汉测绘科技大
学学报，1996，21（4）：350~354
[11]岳东杰，雷伟纲等，灰关联模型 GM（1，N）及其在安全监测中的应用，河
海大学学报，2000，25（2）：10~12
[12]苏怀智，吴中如等，基于模糊神经元网络及遗传算法的大坝安全监控模型，
大坝观测与土木测试，2001，22（1）：28~30
[13]赵斌，吴中如等，神经网络在大坝安全评判专家系统中的应用，大坝观测与
土木测试，1998，22（2）：16~20
[14]赵斌，吴中如等，BP 模型在大坝安全监测预报中的应用，大坝观测与土木
测试，1999，23（6）：1~4
[15]马远华，遗传算法在建立大坝变形监控模型中的应用，天津大学硕士学位论
文，2002 年 12 月
[16]包约翰，自适应模式识别与神经网络，北京：科学出版社，1992
[17]吴中如，沈长松等. 水工建筑物安全监控理论及其应用. 南京: 河海大学出
版社, 1990
[18]Townsend, C.L., Control of Cracking in Mass Concrete Structrues,
Engineering Monograph No.34, Bureau of Reclamation, 1965
[19]黎展眉，拱坝，水利电力出版社，北京：1982
[20]彭玉华，小波变换与工程应用，北京：科学出版社，2002
[21]A.Haar, Zur theorie der orthogonalen funktionensysteme, Math. Annal.,
61
参考文献
1910, 69:331-371
[22]D.Gabor, Theory of communication, J. Inst. Elect. Eng., 1946,
93(3):429-457
[23]Stromberg O., A Modified Harr System and Higher Order Spline Systems,
Math. Series, 1981, 2:475-493
[24]Grossmann A., Morlet J., Decomposition of Hardy Function into Square
Integrable Wavelets of Constant shape, SIAN J. Math. Anal.,
1984:723-726
[25]Grossmann A., Morlet J., Cycle-Octave and Related Transforms in
Seismic Signals Analysis, Geoexploration, 1985, 23:85-102
[26]Y.Meyer, Principe d’incertitude, bases hilbertiennes et algebras
d’operateurs, In Seminaire bourkaki, Paris, 1986, volume 662
[27]G.Battle, A Block spin construction of ondelletes, Part I: lemarie
functions, Comm. Math. Phys., 1987, 110:601-615
[28]P.G.Lemarie, Les Ondelettes en 1989, Lecture Notes in Mathematics
No.1438, Springer-Verlag, Berlin, 1990
[29]S.G.Mallat, A Theory for Multiresolution Signal Decomposition: The
Wavelet Representation, IEEE. Trans. On Pattern Analysis and Machine
Intelligence, 1989, 11(7)
[30]S.G.Mallat, Multiresolution Approximations and Wavelet Orthonormal
Bases of L2(R), Transaction of the American Mathematical Society,
1989, 351(1)
[31]I.Daubechies, Orthonormal Bases of Compactly Supported Wavelets,
Communications on Pure and Applied Math., 1988 41:909-996
[32]C. K.Chui, J. Z.Wang, Computational and Algorithmic Aspects of
Cardinal Spline Wavelet, CAT Report #235, Texas A&M Univ., 1990.
[33]C. K.Chui, J. Z.Wang, A Cardinal Spline Approach to Wavelets, Pro.
Amer. Math. Sco., 1991, 113:785-793
[34]C. K.Chui, An Introduction to Wavelets, New York: Academic Press, 1992,
31-43, 64-68
[35]R.R.Coifman and, Y.Meyer and M.V.Wickerhauser, Wavelet analysis and
signal processing, In Wavelets and their Applications, 1990, 153-178
[36]M.V.Wickerhauser, Lectures on Wavelet Packet Algorithms, 第三次中
法小波会议论文集，1992
[37]M.V.Wickerhauser, High-resolution Still Picture Compression, 第三
次中法小波会议论文集，1992
[38]冉启文，谭立英，小波分析与分数傅里叶变换及应用，北京：国防工业出版
社，2002
[39]郑治真，沈萍等，小波变换及其 MATLAB 工具的应用，北京：地震出版社，
2001
[40]赵松年，熊小芸，子波变换与子波分析，北京：电子工业出版社，1997
62
参考文献
[41]国家电力公司西北勘测设计研究院，初期蓄水大坝及基础安全监测资料综合
分析报告，2001 年 6 月，西安
[42]施妙根，顾丽珍，科学和工程计算基础，北京：清华大学出版社，2002 年 7
月
[43]Fritsch F. N. and R. E. Carlson, Monotone Piecewise Cubic
Interpolation, SIAM J. Numerical Analysis, Vol. 17, 1980, 238-246
[44]吴中如,朱伯芳,三峡水工建筑物安全监测与反馈设计,北京:中国水利水电
出版社,1999 年 4 月
[45]W.W.McCulloch & W.Pits, A logic calculus of the ideas imminent in
neurons activity, Bulletin of Math.Bio., 1943, No.5: 115-133
[46]D.O.Hebb, The Organization of Behavior, Willey, New York, 1949
[47]F.Rosenblatt, Principles of Neurodynamics, New York, Spartan
Book,1962
[48]B.Widrow & M.E.Hoff, Adaptive Switching circuits,1960 IRE WESCON
Convention Record:part4, Computers:Man-Machine System, Los Angeles,
1960
[49]M.L.Minsky & S.A.Papert, Perception, The MIT Press, Cambridge,
MA,1969
[50]J.J.Hopfield, Neural networks and physical systems with emergent
collective computational abilities. Proc. Acad. Sci., USA, 1982,
Vol.79, 2554-2558
[51]J.J.Hopfield, Neurons with graded lake those of two-state neurons.
Proc., Natl. Acad. Sci., 1984, Vol.81, 3088-3092
[52]J.J.Hopfield & D.W.Tank, Neural computation of decisions
Optimization problem. Bid. Cybern., 1985,Vol.52, 141-152
[53]D.E.Rumelhart & J.L.McClelland, Parallel Distributed Processing, MIT
Press, 1986
[54]闻新等，MATLAB 神经网络应用设计，北京：科学出版社，2000
[55]孙增圻等，智能控制理论与技术，北京：清华大学出版社，1997
[56]戚蓝，初始地应力场分析理论与方法研究，天津大学博士学位论文，2002
年 12 月
[57]焦李成著，神经网络系统理论，西安：西安电子科技大学出版社，1990
[58]胡守仁主编，神经网络应用技术，长沙：国防科技大学出版社，1993
[59]罗四维，人工神经网络建造，北京：中国铁道出版社，1998
[1]李瓒，陈兴华等，混凝土拱坝设计，北京：中国电力出版社，2000 年 9 月
[2]朱伯芳，中国拱坝建设的成就，水力发电，1999（10）：38~41
[3]陈久宇，林见，观测数据的数学处理，上海：上海交通大学出版社，1990 年
8 月
[4]黄铭，李珍照，大坝监测空间位移统计模型研究，武汉水利电力大学学报，
1999，32（3）：19~22
[5]吴中如等，水工建筑物安全监控理论及其应用，南京：河海大学出版社，1990
年 8 月
[6]Giusepptti G., Basic Theory Underlying the Computation of Influence
Coefficient, Ismes, 1986
[7]李步娟，刘新平等，拱坝变形监测预报模型研究，水利水电技术，1996（7）：
10~15
[8]吴中如，顾冲时等，大坝观测资料的综合分析法，河海大学学报，1993，21
（1）：71~76
[9]Wu Zhongru, Wang Zhanrui, Dynamic Monitoring Model of Space
Displacement Field of Concrete Dam, International Symposium on
Monitoring Technology of Dam Safety, 1992.10
[10]蓝悦明，王新洲，灰色预测用于大坝水平变形预测的研究，武汉测绘科技大
学学报，1996，21（4）：350~354
[11]岳东杰，雷伟纲等，灰关联模型 GM（1，N）及其在安全监测中的应用，河
海大学学报，2000，25（2）：10~12
[12]苏怀智，吴中如等，基于模糊神经元网络及遗传算法的大坝安全监控模型，
大坝观测与土木测试，2001，22（1）：28~30
[13]赵斌，吴中如等，神经网络在大坝安全评判专家系统中的应用，大坝观测与
土木测试，1998，22（2）：16~20
[14]赵斌，吴中如等，BP 模型在大坝安全监测预报中的应用，大坝观测与土木
测试，1999，23（6）：1~4
[15]马远华，遗传算法在建立大坝变形监控模型中的应用，天津大学硕士学位论
文，2002 年 12 月
[16]包约翰，自适应模式识别与神经网络，北京：科学出版社，1992
[17]吴中如，沈长松等. 水工建筑物安全监控理论及其应用. 南京: 河海大学出
版社, 1990
[18]Townsend, C.L., Control of Cracking in Mass Concrete Structrues,
Engineering Monograph No.34, Bureau of Reclamation, 1965
[19]黎展眉，拱坝，水利电力出版社，北京：1982
[20]彭玉华，小波变换与工程应用，北京：科学出版社，2002
[21]A.Haar, Zur theorie der orthogonalen funktionensysteme, Math. Annal.,
61
参考文献
1910, 69:331-371
[22]D.Gabor, Theory of communication, J. Inst. Elect. Eng., 1946,
93(3):429-457
[23]Stromberg O., A Modified Harr System and Higher Order Spline Systems,
Math. Series, 1981, 2:475-493
[24]Grossmann A., Morlet J., Decomposition of Hardy Function into Square
Integrable Wavelets of Constant shape, SIAN J. Math. Anal.,
1984:723-726
[25]Grossmann A., Morlet J., Cycle-Octave and Related Transforms in
Seismic Signals Analysis, Geoexploration, 1985, 23:85-102
[26]Y.Meyer, Principe d’incertitude, bases hilbertiennes et algebras
d’operateurs, In Seminaire bourkaki, Paris, 1986, volume 662
[27]G.Battle, A Block spin construction of ondelletes, Part I: lemarie
functions, Comm. Math. Phys., 1987, 110:601-615
[28]P.G.Lemarie, Les Ondelettes en 1989, Lecture Notes in Mathematics
No.1438, Springer-Verlag, Berlin, 1990
[29]S.G.Mallat, A Theory for Multiresolution Signal Decomposition: The
Wavelet Representation, IEEE. Trans. On Pattern Analysis and Machine
Intelligence, 1989, 11(7)
[30]S.G.Mallat, Multiresolution Approximations and Wavelet Orthonormal
Bases of L2(R), Transaction of the American Mathematical Society,
1989, 351(1)
[31]I.Daubechies, Orthonormal Bases of Compactly Supported Wavelets,
Communications on Pure and Applied Math., 1988 41:909-996
[32]C. K.Chui, J. Z.Wang, Computational and Algorithmic Aspects of
Cardinal Spline Wavelet, CAT Report #235, Texas A&M Univ., 1990.
[33]C. K.Chui, J. Z.Wang, A Cardinal Spline Approach to Wavelets, Pro.
Amer. Math. Sco., 1991, 113:785-793
[34]C. K.Chui, An Introduction to Wavelets, New York: Academic Press, 1992,
31-43, 64-68
[35]R.R.Coifman and, Y.Meyer and M.V.Wickerhauser, Wavelet analysis and
signal processing, In Wavelets and their Applications, 1990, 153-178
[36]M.V.Wickerhauser, Lectures on Wavelet Packet Algorithms, 第三次中
法小波会议论文集，1992
[37]M.V.Wickerhauser, High-resolution Still Picture Compression, 第三
次中法小波会议论文集，1992
[38]冉启文，谭立英，小波分析与分数傅里叶变换及应用，北京：国防工业出版
社，2002
[39]郑治真，沈萍等，小波变换及其 MATLAB 工具的应用，北京：地震出版社，
2001
[40]赵松年，熊小芸，子波变换与子波分析，北京：电子工业出版社，1997
62
参考文献
[41]国家电力公司西北勘测设计研究院，初期蓄水大坝及基础安全监测资料综合
分析报告，2001 年 6 月，西安
[42]施妙根，顾丽珍，科学和工程计算基础，北京：清华大学出版社，2002 年 7
月
[43]Fritsch F. N. and R. E. Carlson, Monotone Piecewise Cubic
Interpolation, SIAM J. Numerical Analysis, Vol. 17, 1980, 238-246
[44]吴中如,朱伯芳,三峡水工建筑物安全监测与反馈设计,北京:中国水利水电
出版社,1999 年 4 月
[45]W.W.McCulloch & W.Pits, A logic calculus of the ideas imminent in
neurons activity, Bulletin of Math.Bio., 1943, No.5: 115-133
[46]D.O.Hebb, The Organization of Behavior, Willey, New York, 1949
[47]F.Rosenblatt, Principles of Neurodynamics, New York, Spartan
Book,1962
[48]B.Widrow & M.E.Hoff, Adaptive Switching circuits,1960 IRE WESCON
Convention Record:part4, Computers:Man-Machine System, Los Angeles,
1960
[49]M.L.Minsky & S.A.Papert, Perception, The MIT Press, Cambridge,
MA,1969
[50]J.J.Hopfield, Neural networks and physical systems with emergent
collective computational abilities. Proc. Acad. Sci., USA, 1982,
Vol.79, 2554-2558
[51]J.J.Hopfield, Neurons with graded lake those of two-state neurons.
Proc., Natl. Acad. Sci., 1984, Vol.81, 3088-3092
[52]J.J.Hopfield & D.W.Tank, Neural computation of decisions
Optimization problem. Bid. Cybern., 1985,Vol.52, 141-152
[53]D.E.Rumelhart & J.L.McClelland, Parallel Distributed Processing, MIT
Press, 1986
[54]闻新等，MATLAB 神经网络应用设计，北京：科学出版社，2000
[55]孙增圻等，智能控制理论与技术，北京：清华大学出版社，1997
[56]戚蓝，初始地应力场分析理论与方法研究，天津大学博士学位论文，2002
年 12 月
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