集对分析在水资源不确定性分析中的应用
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摘要
合理开发、利用、治理、保护、管理水资源是人类作用于自然水系统的理性活动,对水资源进行优化配置是实现水资源在不同区域和用水户的有效公平分配,从而达到水资源可持续利用的重要手段。通过水资源配置可以实现对流域水循环及其影响的自然与社会诸因素进行整体调控。受到众多因素的影响,水文水资源现象(径流、洪水等)变化极其复杂,具有很大的不确定性,在对水资源进行优化配置的全过程,包括系统预测、模拟、评价、推理、决策和调控等内容,都存在大量的不确定性。而集对分析(SPA)是中国学者赵克勤先生于1989年基于哲学中的对立统一和普遍联系的原理提出的一种分析不确定性关系的新颖方法。大量应用实践证明,集对分析在水文水资源不确定性分析中表现出描述不确定性更全面、概念清晰、原理简明、计算方便以及结果直观可靠等优点。论文在详细阐述水资源优化配置及其不确定性的基本概念和理论的基础上,论述了集对分析在水文水资源不确定性分析中的研究进展和应用现状,深入探讨集对分析理论在水文水资源不确定性分析研究中可行性、适用性和具体实现途径,并取得如下主要结果:
(1)集对分析理论为处理确定、不确定系统提供了新的途径,根据集对分析理论建立起来的预测联系数回归模型可以明显改善回归模型的预测精度。对于预测因子结构具有的动态性,运用数理统计中的近邻估计方法,通过计算各个预测因子的变异系数,来判断预测因子在某次预测中处于强势或者弱势,进而动态地选择预报功能大的强势因子,消除对预报起负面作用的弱势因子的作用,这样很好地体现了预测因子结构中具有的动态性,基于此建立了基于近邻估计的年径流预测动态联系数回归模型。
(2)为有效刻画年径流序列的内在分布规律,使区间划分更加合理,应用有序样品聚类方法建立年径流序列丰枯状态的分类标准;针对年径流序列存在相依性、随机性和不确定性的特点,提出基于集对分析原理的集对权重,这比现有的自相关系数权重包含了年径流序列内在的更多不确定性信息,更能合理地表达各滞时步长的马尔可夫链的重要性;基于此建立了基于有序样品聚类的集对权马尔可夫链年径流动态预测模型。
(3)针对区间型多属性决策问题中的模糊性和不确定性,用二元联系数原理直观描述决策问题中确定性和不确定性之间的关系;提出二元联系数相离度定义,计算决策方案各决策属性的总偏差,通过构造单目标最优化问题确定各决策属性的最优权重向量;计算决策方案的区间型决策属性值与各决策属性最理想方案的相离度,进而求得各决策方案与最理想方案的加权综合相离度,实现对决策方案的优劣排序,建立了基于二元联系数的水资源区间型多属性决策模型。
(4)上述研究结果初步表明:深入开展水文水资源不确定性分析的集对分析方法研究,既可进一步挖掘并客观全面的描述水文水资源不确定性的复杂结构,也有助于丰富、完善和发展水文水资源不确定性分析理论,是水文水资源不确定性分析的新发展方向,具有广泛的应用前景。
Optimal allocation of water resources is an important means to achieve water resources and water users in different regions of the effective and equitable distribution, so as to achieve sustainable use of water resources. Water resources allocation can achieve to the overall regulation through the water cycle and its impact on the watershed's natural and social factors. But due to a number of factors, the change of hydrology and water resources phenomenon (runoff, flooding, etc.) is extremely complex, with great uncertainty. There is a lot of uncertainty in the entire process of optimal allocation of water resources, including system prediction, simulation, evaluation, reasoning, decision-making and regulation and so on. The Set Pair Analysis is a new method to analysis of uncertainty relations that was first proposed by China’s scholar Zhao Ke-qin in national system theory and regional planning meetings at Baotou of Inner Mongolia in 1989 years, based on the philosophy of the unity of opposites and the principle of the universal link. Practice has proved that a large number of applications, the uncertainty analysis in hydrology and water resources with Set Pair Analysis had shown a more comprehensive description of the uncertainty, the concept clear and concise principles calculated to facilitate, as well as the results of an intuitive and reliable. In this paper, bases on detail describing the basic concepts and theories of optimal allocation of water resources and its uncertainty, discusses the research progress and application status quo of the uncertainty analysis in hydrology and water resources by Set Pair Analysis, in-depth studies the feasibility, applicability and specific ways to achieve of the uncertainty analysis in hydrology and water resources by Set Pair Analysis, and the major results are summarized as following:
(1) Set pair analysis theory provides a new way for the identified uncertain system, the connection number regression model to forecast that according the set pair analysis theory can significantly improve the prediction accuracy of regression model. For the dynamic of the predictor structure, this paper will use nearest neighbor estimate, by calculating the coefficient of variation of each predictor to determine predictive factors are strong or weak in a certain prediction, then select the strong forecasting function factors dynamically, to eliminate the negative effect from the weak forecasting factors, this reflects well the predictor structure is dynamic. And then a nearest neighbor estimate based dynamic connection number regression model, named NNE-DCNR for short, was established.
(2) To characterize the internal distribution rules of annual runoff sequence effectively, and make a more rational division interval, apply the sequence clustering method to establish the wetness-dryness classification criteria of annual runoff sequence. For the characteristics of annual runoff sequence such as the existence of dependencies, randomness and uncertainty, set pair weight based on set pair analysis is proposed. This contains more inherent uncertainty information of annual runoff sequence than the existing self-correlation coefficient weight, express the importance of the lag time step length of Markov chain more reasonably. And then a set pair weight markov chain model based on sequence clustering method for dynamically predicting annual runoff was established.
(3) For the fuzzy and uncertainty of interval multi-attribute decision problem, using the binary connection number theory to intuitively describe the relationship between certainty and uncertainty of decision problem. Propose the definition of binary connection number deviation degree, and calculate the total deviation of all the decision-making properties about each decision-making program, then by constructing a single-objective optimization problem to determine the optimal weight vector of each decision attribute. Calculate the deviation degree between decision attribute values and the best program of these attribute values, then can obtain the integrated and weighted deviation degree between the decision-making programs and the best program of these decision-making programs. And then can realize the sorts of pros and cons for each decision-making program. According to this, a binary connection number based interval multi-attribute decision model of water resources was established.
(4) The study results show that deeply researching the Set Pair Analysis method in uncertainty analysis of hydrology and water resources, can be further excavated and comprehensively describe the complex structure of hydrology and water resources about uncertainty, but also helped to enrich, improve and develop the theory of hydrology and water resources uncertainty analysis. It is the new developed direction of uncertainty analysis in hydrology and water resources, has a broad application prospects.
(1)集对分析理论为处理确定、不确定系统提供了新的途径,根据集对分析理论建立起来的预测联系数回归模型可以明显改善回归模型的预测精度。对于预测因子结构具有的动态性,运用数理统计中的近邻估计方法,通过计算各个预测因子的变异系数,来判断预测因子在某次预测中处于强势或者弱势,进而动态地选择预报功能大的强势因子,消除对预报起负面作用的弱势因子的作用,这样很好地体现了预测因子结构中具有的动态性,基于此建立了基于近邻估计的年径流预测动态联系数回归模型。
(2)为有效刻画年径流序列的内在分布规律,使区间划分更加合理,应用有序样品聚类方法建立年径流序列丰枯状态的分类标准;针对年径流序列存在相依性、随机性和不确定性的特点,提出基于集对分析原理的集对权重,这比现有的自相关系数权重包含了年径流序列内在的更多不确定性信息,更能合理地表达各滞时步长的马尔可夫链的重要性;基于此建立了基于有序样品聚类的集对权马尔可夫链年径流动态预测模型。
(3)针对区间型多属性决策问题中的模糊性和不确定性,用二元联系数原理直观描述决策问题中确定性和不确定性之间的关系;提出二元联系数相离度定义,计算决策方案各决策属性的总偏差,通过构造单目标最优化问题确定各决策属性的最优权重向量;计算决策方案的区间型决策属性值与各决策属性最理想方案的相离度,进而求得各决策方案与最理想方案的加权综合相离度,实现对决策方案的优劣排序,建立了基于二元联系数的水资源区间型多属性决策模型。
(4)上述研究结果初步表明:深入开展水文水资源不确定性分析的集对分析方法研究,既可进一步挖掘并客观全面的描述水文水资源不确定性的复杂结构,也有助于丰富、完善和发展水文水资源不确定性分析理论,是水文水资源不确定性分析的新发展方向,具有广泛的应用前景。
Optimal allocation of water resources is an important means to achieve water resources and water users in different regions of the effective and equitable distribution, so as to achieve sustainable use of water resources. Water resources allocation can achieve to the overall regulation through the water cycle and its impact on the watershed's natural and social factors. But due to a number of factors, the change of hydrology and water resources phenomenon (runoff, flooding, etc.) is extremely complex, with great uncertainty. There is a lot of uncertainty in the entire process of optimal allocation of water resources, including system prediction, simulation, evaluation, reasoning, decision-making and regulation and so on. The Set Pair Analysis is a new method to analysis of uncertainty relations that was first proposed by China’s scholar Zhao Ke-qin in national system theory and regional planning meetings at Baotou of Inner Mongolia in 1989 years, based on the philosophy of the unity of opposites and the principle of the universal link. Practice has proved that a large number of applications, the uncertainty analysis in hydrology and water resources with Set Pair Analysis had shown a more comprehensive description of the uncertainty, the concept clear and concise principles calculated to facilitate, as well as the results of an intuitive and reliable. In this paper, bases on detail describing the basic concepts and theories of optimal allocation of water resources and its uncertainty, discusses the research progress and application status quo of the uncertainty analysis in hydrology and water resources by Set Pair Analysis, in-depth studies the feasibility, applicability and specific ways to achieve of the uncertainty analysis in hydrology and water resources by Set Pair Analysis, and the major results are summarized as following:
(1) Set pair analysis theory provides a new way for the identified uncertain system, the connection number regression model to forecast that according the set pair analysis theory can significantly improve the prediction accuracy of regression model. For the dynamic of the predictor structure, this paper will use nearest neighbor estimate, by calculating the coefficient of variation of each predictor to determine predictive factors are strong or weak in a certain prediction, then select the strong forecasting function factors dynamically, to eliminate the negative effect from the weak forecasting factors, this reflects well the predictor structure is dynamic. And then a nearest neighbor estimate based dynamic connection number regression model, named NNE-DCNR for short, was established.
(2) To characterize the internal distribution rules of annual runoff sequence effectively, and make a more rational division interval, apply the sequence clustering method to establish the wetness-dryness classification criteria of annual runoff sequence. For the characteristics of annual runoff sequence such as the existence of dependencies, randomness and uncertainty, set pair weight based on set pair analysis is proposed. This contains more inherent uncertainty information of annual runoff sequence than the existing self-correlation coefficient weight, express the importance of the lag time step length of Markov chain more reasonably. And then a set pair weight markov chain model based on sequence clustering method for dynamically predicting annual runoff was established.
(3) For the fuzzy and uncertainty of interval multi-attribute decision problem, using the binary connection number theory to intuitively describe the relationship between certainty and uncertainty of decision problem. Propose the definition of binary connection number deviation degree, and calculate the total deviation of all the decision-making properties about each decision-making program, then by constructing a single-objective optimization problem to determine the optimal weight vector of each decision attribute. Calculate the deviation degree between decision attribute values and the best program of these attribute values, then can obtain the integrated and weighted deviation degree between the decision-making programs and the best program of these decision-making programs. And then can realize the sorts of pros and cons for each decision-making program. According to this, a binary connection number based interval multi-attribute decision model of water resources was established.
(4) The study results show that deeply researching the Set Pair Analysis method in uncertainty analysis of hydrology and water resources, can be further excavated and comprehensively describe the complex structure of hydrology and water resources about uncertainty, but also helped to enrich, improve and develop the theory of hydrology and water resources uncertainty analysis. It is the new developed direction of uncertainty analysis in hydrology and water resources, has a broad application prospects.
引文
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