【作者】 楼玉；

【导师】 刘国华；

【作者基本信息】 浙江大学 ， 市政工程， 2005， 硕士

【摘要】 自从混沌现象不断地从各个领域被发现以来，混沌系统的研究和应用就倍受关注。混沌系统具有一些特殊的性质，它们给人们带来了两种截然不同的影响。一方面由于它对初值敏感，这使得人们很难充分地认识和了解混沌系统；另一方面，其本身的遍历性、趋向于吸引子等优良特性为传统科学提供了创新研究的契机，必将促进其它科学的进一步发展。 本文主要开展了混沌理论在径流预报中的应用研究。主要研究内容有水文时间序列的混沌特性分析、水文时间序列的混沌加权动态局域预测模型和水文时间序列的混沌局域区间预测模型三部分组成，具体内容和研究成果概括如下： 第一部分主要对水文时间序列的混沌特性进行了分析和研究。首先对混沌识别和混沌分析的基础——相空间重构理论进行了研究，重点讨论了混沌时间序列的特征量，即分数维和最大Lyapunov指数的计算，以及相空间重构参数，即时间延迟、嵌入维数的选取。文中采用G-P关联积分法计算关联维数；Rosenstein小数据量法计算最大Lyapnuov指数；自相关函数法和互信息量法选取重构相空间的延迟时间；伪邻近点法选取重构相空间的最佳嵌入维数。而后在相空间重构基础上，应用多种分析方法进行混沌识别。重点讨论了替代数据法的计算和应用，并首次将其应用到水文领域中。通过对腾龙桥日径流时间序列和兰溪站月径流时间序列的应用研究表明，这两个实际径流时间序列均不同程度的表现出混沌特性，存在着低维的奇异吸引子。 第二部分基于水文序列变化的混沌特性，对水文时间序列的混沌加权动态局域预测模型进行了研究。本文在文献[45]提出的动态局域预测模型(NSCGDF)基础上，进一步采用邻近点权重来定量描述不同邻近点对预测的影响程度，提出了一种新的预测模型——加权动态局域预测模型(NNWGDF)，该模型综合考虑了邻近点权重和广义自由度，给出了确定最优邻域的判定指标，从而使模型每一步预测都可以无额定出一个合理的邻域。上述预测模型采用腾龙桥和兰溪站的径流序列作为实例进行计算分析，计算结果验证了上述模型的有效性。 第三部分主要对水文时间序列的混沌局域区间预测模型进行了研究。针对传统混沌时间序列局域直接预测方法的复杂性，提出了简便的混沌时间序列的局域浙江大学硕士学位论文区间预测方法，该方法具有查询邻近点数据集合的功能，在预测的过程中逐渐建立起了邻近点数据列表，使得遇到同类邻近点集时可以方便从数据列表中取出，而不再需要进行大量的搜索工作;同时，在预测过程中邻近点列表可以不断地更新，并能够补充新类别的邻近点集合，只要历史数据足够多，最终可以得到一个完整的邻近点列表。通过这个邻近点数据列表，可以方便地进行混沌时间序列未来值的预测，省去了在历史数据中反复寻找所有邻近点的过程，提高了预测效率。上述预测模型采用Henon典型混沌序列和兰溪站月径流序列作为算例进行计算分析，计算结果验证了上述模型的有效性。 最后对全文进行总结，对进一步的研究进行了展望。关键词:水文时间序列;混沌;相空间重构;替代数据法;混沌预测;区间预测更多还原

【Abstract】 Since chaotic systems are frequently encountered in various fields, research on chaotic systems thus has great practical significance. Deterministic chaos with some special characters brings two effects on its research, one is that the character of positive Lyapunov exponents is intrinsically associated with a loss of long term predictability, the other is that some good characters of chaotic behaviors provide creative opportunities for conventional science and are helpful to scientific studies in other fields.Chaos theory’s application in hydrology and water resources system is studied in this paper. The paper consists of three parts: the chaotic characteristics of hydrological time series, the weight-dynamic local prediction model for hydrological time series and the local intervals method for hydrological time series. The major contents and research results are as follows:In the first part, the chaotic characteristics of hydrological time series from TengLongQiao and LanXi hydrological stations are researched. First, the theory and method of phase space reconstruction are studied as the basis of chaotic diagnosis and analysis. Emphasis is given on the chaotic characteristics, i.e., fractal dimension and maximal Lyapuonv exponent, and state space parameters, including time delay and reconstruct dimension, were calculated respectively. Fractal dimension was estimated by G-P saturation correlation dimension method, and maximal Lyapuonv exponent was calculated by two methods, namely, Rosenstein method. Time delay was chosen by using autocorrelation function method and mutual information method, while reconstruct dimension was obtained by G-P saturation correlation dimension method and false nearest neighbor percentage method. Then on the basis of phase space reconstruction, the paper applies many methods to chaotic diagnosis. Emphasis is given on the surrogates data method, which is firstly applied to chaotic hydrological time series. The results show there is more or less chaos in these hydrological time series.In the second part, the weight-dynamic local prediction model(NNWGDF) is studied in terms of the chaotic characteristics of hydrological evolution process, which introduces the neighbor’s weight based on the dynamic local prediction model(NSCGDF) of the paper [45]. The NNWGDF model considers the neighbors’ weight and generalized degrees of freedom, and the deciding condition of the optimal neighborhood is proposed. The NNWGDF model can determine the reasonable neighborhood in the each step prediction.In the third part, Based on conventional methods of local predicting chaotic time series, local intervals method is proposed. Here a new concept, interval neighboring points, is defined for building up a data list. The list for finding neighboring points is gradually established in the procedure of forecasting future values. It is convenient that all neighboring points are obtained from the list, instead of searching in history data. Also the method can continually update the list and supply new types of neighboring points for the list.In the end, the research works are summarized. And some further research directions are highlighted.更多还原