河川径流的混沌特征和预测研究
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摘要
对径流变化规律的研究是水资源合理开发利用的前提和基础。河川径流是一种复杂的非线性时间序列。长期以来,人们一直用传统的确定性方法或随机性方法,或将二者结合的方法来描述径流演变过程,揭示径流演变的规律。根据水文要素变化的非线性特点,本文将混沌理论应用于河川径流演变规律的研究中,并通过和其他方法相结合,以黄河为研究对象,对径流时间序列进行了混沌特征分析和预测,取得的主要研究成果如下：
(1)河川径流时间序列的相空间重构。对黄河干流兰州、三门峡、花园口站的月径流时间序列和三门峡站的日径流时间序列进行了相空间重构,得出：月径流时间序列相空间重构的时间延迟τ为2,嵌入维数m达到12时,具有饱和关联维数；三门峡站日径流时间序列相空间重构的时间延迟τ为12,嵌入维数m达到10时,具有饱和关联维数3.5；同一水文站,天然月径流时间序列比实测序列的饱和关联维数要大,要恰当描述实测月径流序列的变化特征,进行动力系统建模,最少需要4个独立变量,即4种因素,最多需要8个独立变量,要描述天然径流序列则最少需要5-6个独立变量,最多需要12个独立变量；下游的饱和关联维数比上游要稍大,下游径流形成所受到的影响因素会更复杂。
(2)河川径流时间序列的混沌特征识别。通过引入饱和关联维数法、主分量分析法、最大Lyapunov指数等方法对黄河干流主要水文站的月、日径流资料的混沌特征识别,得出：①黄河干流月、日径流序列具有混沌特征；②同一水文站、同一时期的实测月径流序列的混沌特征要强于天然序列；③黄河干流下游的混沌特征要强于上游；④从上世纪五十年代到本世纪初黄河干流月径流序列的混沌特性比上世纪二十年代到上世纪七十年代月径流序列的混沌特性要稍强(即,现在要强于过去)；⑤在同一尺度下,比如月径流,所采用径流时间序列的长、短对混沌特征的识别有影响,序列越长,所表现的混沌特征就越强,序列越短,所表现的混沌特征就相对较弱。
(3)河川径流时间序列的混沌预测。对相空间近邻等距预测模式进行改进,利用改进后的相空间近邻等距法对月平均流量时间序列进行预测时,由于满足T=τ=sδt,消除了相空间时滞τ的变化对提前预测时间尺度T的影响,所以无需考虑对τ的选择问题,不仅简化了预测模式,而且显著提高了预测正确率,延长了预测时效,可以进行提前1月、1a甚至更长时间尺度的预测。
(4)将混沌理论和支持向量机方法相结合,建立了基于混沌理论的最小二乘支持向量机模型(C-LSSVM),并对兰州站月径流序列进行了研究。C-LSSVM模型采用结构风险最小化原则,解决了网络模型的过学习问题,在处理小样本预测问题上具有优越性,适合小样本情况的建模,能够取得较好的预测精度。
(5)提出了克服BP神经网络易陷入局部极小点、避免过度训练、增加模型的外推能力的方法。将混沌理论和神经网络相结合,建立基于混沌理论的神经网络预测模型,利用相空间重构技术充分显露日流量时间序列中蕴藏的信息,揭示传统时间序列方法无法展示的变化规律,利用神经网络巨大的非线性模拟能力进行河川日流量的预测研究,取得了较好的模拟和预测结果。
(6)将非趋势波动分析法引入水文系统,对河川径流的长程相关性进行研究。通过对黄河近80年月径流序列的非趋势波动分析,得出：黄河近80年月径流存在内在的负长程相关性；黄河近80年径流长程幂律相关的标度指数a≌0.39,标度区间为11.3a。因此,分析预测在未来十几年,黄河径流的变化可能会成下降趋势。
Research on the river runoff changing rule is the premise and base of reasonable development water resource. Stream flows are sorts of complicated nonlinear time series. For a long time, people research it by using classical certainty methods, random methods, or union of the methods. The deterministic laws onrunoff changs are disclosure. According to the nonline characteristic of hydrographic features, the article uses chaotic theory and confluenses chaotic theory and other methords to to research stream flow. The yellow river is certification object. The main results of this paper are as follows:
(1) The phase space reconfiguration is completed about month and day runoff of Lanzhou, Sanmenxia, and Huayuankou station in the yellow river. The results are obtaind. The month runoff phase space reconfiguration's dayly time'τ'are 2 and the day runoff are 12. The month runoff embedding dementions are 12, day runoff are 10. The saturation relation demention is 3.5 about day runoff phase space reconfiguration.
(2) The chaotic characteristic of runoff time seris is identified adout month and day stream flow in Lanzhou, Huayuankou, Sanmenxia station by using the saturation relation demention, the most Lyapuno index number and PCA. We obtain these results. The first, the month and day cream flow of main station in the yellow river have chaotic characteristic; the second, the actual measurement month runoff time seris'chotic characteristic is stronger than natural in the same hydraulitic station and during the same time. The third, the chaotic characteristic in lower reaches of yellow river is stronger the upper reachs. The 4th, the chaotic characteristic in the modem is stronger than the past. The 5th, the length of runoff time seris can affect chaotic characteristic. The longer is stronger. The 6th, the month runoff chaotic characteristic is stronger than dayrunoff'chaotic characteristic.
(3) The river runoff predicting is done by chaotic methords. The phase space neighbor isomtric prediction model is improved. When we predict runoff with this model, the problem of selecting'τ'need'nt considered, because of T=τ=s 8t', wich eleminits the effect that 'τ' affect to the time of predicting'T'.So the predicting time is prolonged, the accuracy is improved. We can predict runoff by advancing one month or one year.
(4) Binding the chaotic theory and the support vector machine way, the chaotic predicting model base of least square support vector machine (C-LSSVM) is contructed. By using it in Lanzhou station, we attained the results as follow:the model is fit to predict month runoff, because of using structure risk minimizition principle, solveing the over-fiting problem, fiting to small number.
(5) After the ways of overing the problems are proposed,witch are neural network falling into local very minimum point easily, avoding overtraining, and improving the model's extrapolation ablity, the chaotic network model is builded. The phase space reconstruction reveals the complicated information of day runoff seris and the changing law of classtic ways not revealing. By using it in yellow river, the satisfactory result was got.
(6) By using Detrended Fluctuation Analysis way to hydraulitic system, the long-range power-law correlations were identified. Analysising 80 year's month runoff seris of Lanzhou station, we concluded that the seris has negative long-range power-law correlations, the relation index is 0.39, and the time length is 11.3a. By analysising it, we conclude the runoff will decress in the 10a in yellow river.
(1)河川径流时间序列的相空间重构。对黄河干流兰州、三门峡、花园口站的月径流时间序列和三门峡站的日径流时间序列进行了相空间重构,得出：月径流时间序列相空间重构的时间延迟τ为2,嵌入维数m达到12时,具有饱和关联维数；三门峡站日径流时间序列相空间重构的时间延迟τ为12,嵌入维数m达到10时,具有饱和关联维数3.5；同一水文站,天然月径流时间序列比实测序列的饱和关联维数要大,要恰当描述实测月径流序列的变化特征,进行动力系统建模,最少需要4个独立变量,即4种因素,最多需要8个独立变量,要描述天然径流序列则最少需要5-6个独立变量,最多需要12个独立变量；下游的饱和关联维数比上游要稍大,下游径流形成所受到的影响因素会更复杂。
(2)河川径流时间序列的混沌特征识别。通过引入饱和关联维数法、主分量分析法、最大Lyapunov指数等方法对黄河干流主要水文站的月、日径流资料的混沌特征识别,得出：①黄河干流月、日径流序列具有混沌特征；②同一水文站、同一时期的实测月径流序列的混沌特征要强于天然序列；③黄河干流下游的混沌特征要强于上游；④从上世纪五十年代到本世纪初黄河干流月径流序列的混沌特性比上世纪二十年代到上世纪七十年代月径流序列的混沌特性要稍强(即,现在要强于过去)；⑤在同一尺度下,比如月径流,所采用径流时间序列的长、短对混沌特征的识别有影响,序列越长,所表现的混沌特征就越强,序列越短,所表现的混沌特征就相对较弱。
(3)河川径流时间序列的混沌预测。对相空间近邻等距预测模式进行改进,利用改进后的相空间近邻等距法对月平均流量时间序列进行预测时,由于满足T=τ=sδt,消除了相空间时滞τ的变化对提前预测时间尺度T的影响,所以无需考虑对τ的选择问题,不仅简化了预测模式,而且显著提高了预测正确率,延长了预测时效,可以进行提前1月、1a甚至更长时间尺度的预测。
(4)将混沌理论和支持向量机方法相结合,建立了基于混沌理论的最小二乘支持向量机模型(C-LSSVM),并对兰州站月径流序列进行了研究。C-LSSVM模型采用结构风险最小化原则,解决了网络模型的过学习问题,在处理小样本预测问题上具有优越性,适合小样本情况的建模,能够取得较好的预测精度。
(5)提出了克服BP神经网络易陷入局部极小点、避免过度训练、增加模型的外推能力的方法。将混沌理论和神经网络相结合,建立基于混沌理论的神经网络预测模型,利用相空间重构技术充分显露日流量时间序列中蕴藏的信息,揭示传统时间序列方法无法展示的变化规律,利用神经网络巨大的非线性模拟能力进行河川日流量的预测研究,取得了较好的模拟和预测结果。
(6)将非趋势波动分析法引入水文系统,对河川径流的长程相关性进行研究。通过对黄河近80年月径流序列的非趋势波动分析,得出：黄河近80年月径流存在内在的负长程相关性；黄河近80年径流长程幂律相关的标度指数a≌0.39,标度区间为11.3a。因此,分析预测在未来十几年,黄河径流的变化可能会成下降趋势。
Research on the river runoff changing rule is the premise and base of reasonable development water resource. Stream flows are sorts of complicated nonlinear time series. For a long time, people research it by using classical certainty methods, random methods, or union of the methods. The deterministic laws onrunoff changs are disclosure. According to the nonline characteristic of hydrographic features, the article uses chaotic theory and confluenses chaotic theory and other methords to to research stream flow. The yellow river is certification object. The main results of this paper are as follows:
(1) The phase space reconfiguration is completed about month and day runoff of Lanzhou, Sanmenxia, and Huayuankou station in the yellow river. The results are obtaind. The month runoff phase space reconfiguration's dayly time'τ'are 2 and the day runoff are 12. The month runoff embedding dementions are 12, day runoff are 10. The saturation relation demention is 3.5 about day runoff phase space reconfiguration.
(2) The chaotic characteristic of runoff time seris is identified adout month and day stream flow in Lanzhou, Huayuankou, Sanmenxia station by using the saturation relation demention, the most Lyapuno index number and PCA. We obtain these results. The first, the month and day cream flow of main station in the yellow river have chaotic characteristic; the second, the actual measurement month runoff time seris'chotic characteristic is stronger than natural in the same hydraulitic station and during the same time. The third, the chaotic characteristic in lower reaches of yellow river is stronger the upper reachs. The 4th, the chaotic characteristic in the modem is stronger than the past. The 5th, the length of runoff time seris can affect chaotic characteristic. The longer is stronger. The 6th, the month runoff chaotic characteristic is stronger than dayrunoff'chaotic characteristic.
(3) The river runoff predicting is done by chaotic methords. The phase space neighbor isomtric prediction model is improved. When we predict runoff with this model, the problem of selecting'τ'need'nt considered, because of T=τ=s 8t', wich eleminits the effect that 'τ' affect to the time of predicting'T'.So the predicting time is prolonged, the accuracy is improved. We can predict runoff by advancing one month or one year.
(4) Binding the chaotic theory and the support vector machine way, the chaotic predicting model base of least square support vector machine (C-LSSVM) is contructed. By using it in Lanzhou station, we attained the results as follow:the model is fit to predict month runoff, because of using structure risk minimizition principle, solveing the over-fiting problem, fiting to small number.
(5) After the ways of overing the problems are proposed,witch are neural network falling into local very minimum point easily, avoding overtraining, and improving the model's extrapolation ablity, the chaotic network model is builded. The phase space reconstruction reveals the complicated information of day runoff seris and the changing law of classtic ways not revealing. By using it in yellow river, the satisfactory result was got.
(6) By using Detrended Fluctuation Analysis way to hydraulitic system, the long-range power-law correlations were identified. Analysising 80 year's month runoff seris of Lanzhou station, we concluded that the seris has negative long-range power-law correlations, the relation index is 0.39, and the time length is 11.3a. By analysising it, we conclude the runoff will decress in the 10a in yellow river.
引文
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