集对分析理论及其在水土资源系统分析中的应用
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摘要
水土资源的变化受自然和人为等因素的影响,存在高维、非线性、实测数据信息不完整等特征,已经成为制约区域水土资源可持续利用的关键因子。随着人口的不断增加和经济的迅速发展,人类对水土资源的利用不断加强,对自然资源造成破坏,迫切的需要一种数据处理方法去研究其发展规律,及时的采取措施,综合治理。因此本文建立基于集对分析的水土资源综合评价和预测新模型,能够克服因数据高维、非线性等特征,较好地解决了水土资源中的多元复杂性问题。
本文取得了以下四方面的成果:
1.提出基于投影寻踪的改进集对分析模型。利用最佳投影方向作为指标权重,并通过完善Ⅴ级相邻级别联系度为-1的不足,假设存在Ⅵ级的指标值,从而得出联系度,并应用到实际当中。结果显示:基于投影寻踪的改进集对分析模型,能够客观确定权重,且权重符合实际规律,改进后的模型对等级划分更细致,对检测数据利用率更高,可应用于各种非线性、非正态高维数据评价研究中。
2.针对集对分析中差异不确定系数i的取值不确定问题,分别将差异度与同一度和对立度的关联度作为i的取值,运用灰色理论中的绝对关联度计算方法对i进行求解,并应用到实际评价中,为集对分析中差异系数i的求解提供了新的思路和方法。
3.利用集对分析对传统物元模型进行优化,减少了原模型的复杂度,实现对事物特征不确定性的分析,拓宽了集对物元的应用领域,为解决水土资源的评价问题提供了新方法依据。
4.提出了利用集对分析检验和互相关系数统计假设检验相结合的方法识别影响水资源变化的主要物理因子,用集对分析方法从同、异、反三方面定量刻画水资源历史样本之间的相似性,然后用多个最相似的历史样本的水资源加权平均值作为当前水资源的预测值,进而建立了基于集对分析的水资源相似预测模型(SPA-SF)。利用SPA-SF预测水资源的丰枯变化,物理概念清晰,计算直观,预测精度较高。这套SPA-SF建模方案简便有效,预测技术完备,在历史样本丰富、代表性高的水文时间序列预测中具有应用价值。
基于以上几种模型的建立,本论文实现了理论与实践的有机结合。同时本文将所建立的模型用于水土资源的多元复杂性、非线性研究,取得满意结果,为解决当前某些实际问题提供新技术,为水土资源系统研究提供了新思路。
The changes of soil and water resources were affected by natural and human that has the characteristics multidimensional,nonlinearity and lack of samples. In order to solve the multiple complexities of water and soil resources, the new set pair analysis model has been established in water and soil resources comprehensive evaluation and prediction in this research.
There are four achievements in this research:
1. Improved Set Pair Analysis Model based on Projection Pursuit (RAGAPP-SPA).The relational degree can be obtained by using the optimum projection vector as the index weight and perfected the deficiency that adjacent relational degree ofⅤdegree is -1, and assumed the existence of six degree index. The evaluation results proved that the weight can be determined objectively by using the RAGAPP-SPA and accorded with the actual law. The grade can be divided carefully and the tested data can be utilized greater, and can be applied to research a variety of non-linear and non-normal high-dimensional data.
2. Due to the uncertain value problem of variation coefficient i in Set Pair Analysis, this paper used the correlation degree of variation degree and identical degree and opposite degree as the i value, respectively, to calculate i by using absolute correlation degree calculation method of grey theory, and obtained the satisfactory results. The results showed that it was feasible to calculate i based on absolute correlation degree of the grey theory, and provided a new idea and method for solving variation coefficient i in Set Pair Analysis.
3. Traditional matter-element model was improved by using set pair analysis in order to reduce the complexity of original model and achieve the uncertainty analysis of matters characteristics, and the improved model was used to evaluate and obtained the satisfactory results. Results show that set pair matter-element model was feasible for evaluating and expanding the application areas based on set pair matter-element model and providing a new way for water resources evaluation.
4. Both set pair analysis and statistic test of correlation coefficients can be used to determine the main physics vectors for affecting the changes of water resources. Set pair analysis method can be used to quantificational compute the similarity between the nonce and history main physics vectors from the views of identical, discrepant and contrary sides. The weighted average of the water resources values of the nearest neighbor history samples can be regarded as the predicted value of the nonce water resources, then the set pair analysis was established based on similarity forecast model of water resources change that named SPA-SF. The application results of SPA-SF showed that the statistic and physical concepts of SPA-SF were distinct, its computation method was visual, its precision was high, and the scheme of modeling SPA-SF was simple, effective and perfect. So the SPA-SF can be applied for forecasting different hydrological time series with plenty representative history samples.
In this research, the organic combination between theory and practice was achieved by using the above models. At the same time, the multiple complex and nonlinear study on soil and water resources obtained satisfactory results, and provided new technologies for solving some practical problems currently, and provided new idea for soil and water resources system research.
本文取得了以下四方面的成果:
1.提出基于投影寻踪的改进集对分析模型。利用最佳投影方向作为指标权重,并通过完善Ⅴ级相邻级别联系度为-1的不足,假设存在Ⅵ级的指标值,从而得出联系度,并应用到实际当中。结果显示:基于投影寻踪的改进集对分析模型,能够客观确定权重,且权重符合实际规律,改进后的模型对等级划分更细致,对检测数据利用率更高,可应用于各种非线性、非正态高维数据评价研究中。
2.针对集对分析中差异不确定系数i的取值不确定问题,分别将差异度与同一度和对立度的关联度作为i的取值,运用灰色理论中的绝对关联度计算方法对i进行求解,并应用到实际评价中,为集对分析中差异系数i的求解提供了新的思路和方法。
3.利用集对分析对传统物元模型进行优化,减少了原模型的复杂度,实现对事物特征不确定性的分析,拓宽了集对物元的应用领域,为解决水土资源的评价问题提供了新方法依据。
4.提出了利用集对分析检验和互相关系数统计假设检验相结合的方法识别影响水资源变化的主要物理因子,用集对分析方法从同、异、反三方面定量刻画水资源历史样本之间的相似性,然后用多个最相似的历史样本的水资源加权平均值作为当前水资源的预测值,进而建立了基于集对分析的水资源相似预测模型(SPA-SF)。利用SPA-SF预测水资源的丰枯变化,物理概念清晰,计算直观,预测精度较高。这套SPA-SF建模方案简便有效,预测技术完备,在历史样本丰富、代表性高的水文时间序列预测中具有应用价值。
基于以上几种模型的建立,本论文实现了理论与实践的有机结合。同时本文将所建立的模型用于水土资源的多元复杂性、非线性研究,取得满意结果,为解决当前某些实际问题提供新技术,为水土资源系统研究提供了新思路。
The changes of soil and water resources were affected by natural and human that has the characteristics multidimensional,nonlinearity and lack of samples. In order to solve the multiple complexities of water and soil resources, the new set pair analysis model has been established in water and soil resources comprehensive evaluation and prediction in this research.
There are four achievements in this research:
1. Improved Set Pair Analysis Model based on Projection Pursuit (RAGAPP-SPA).The relational degree can be obtained by using the optimum projection vector as the index weight and perfected the deficiency that adjacent relational degree ofⅤdegree is -1, and assumed the existence of six degree index. The evaluation results proved that the weight can be determined objectively by using the RAGAPP-SPA and accorded with the actual law. The grade can be divided carefully and the tested data can be utilized greater, and can be applied to research a variety of non-linear and non-normal high-dimensional data.
2. Due to the uncertain value problem of variation coefficient i in Set Pair Analysis, this paper used the correlation degree of variation degree and identical degree and opposite degree as the i value, respectively, to calculate i by using absolute correlation degree calculation method of grey theory, and obtained the satisfactory results. The results showed that it was feasible to calculate i based on absolute correlation degree of the grey theory, and provided a new idea and method for solving variation coefficient i in Set Pair Analysis.
3. Traditional matter-element model was improved by using set pair analysis in order to reduce the complexity of original model and achieve the uncertainty analysis of matters characteristics, and the improved model was used to evaluate and obtained the satisfactory results. Results show that set pair matter-element model was feasible for evaluating and expanding the application areas based on set pair matter-element model and providing a new way for water resources evaluation.
4. Both set pair analysis and statistic test of correlation coefficients can be used to determine the main physics vectors for affecting the changes of water resources. Set pair analysis method can be used to quantificational compute the similarity between the nonce and history main physics vectors from the views of identical, discrepant and contrary sides. The weighted average of the water resources values of the nearest neighbor history samples can be regarded as the predicted value of the nonce water resources, then the set pair analysis was established based on similarity forecast model of water resources change that named SPA-SF. The application results of SPA-SF showed that the statistic and physical concepts of SPA-SF were distinct, its computation method was visual, its precision was high, and the scheme of modeling SPA-SF was simple, effective and perfect. So the SPA-SF can be applied for forecasting different hydrological time series with plenty representative history samples.
In this research, the organic combination between theory and practice was achieved by using the above models. At the same time, the multiple complex and nonlinear study on soil and water resources obtained satisfactory results, and provided new technologies for solving some practical problems currently, and provided new idea for soil and water resources system research.
引文
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Franchini M,Galeati G. 1997.Comparing Several Genetic Algorithm Schemes for the Calibration of Conceptual Rainfall-Runoff Models. Hydro. Scien. J,42(3):357-379
Fu Qiang,Liu Jianyu,Wang Likun.2004. Study on the PPE Model Based on RAGA to Classify the County Energy. Journal Systems Science and Information,2(1):73-82
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Zadeh L A.Fuzzy Sets as A basis for Theory of Possibility. Fuzzy Sets and systems,1978
Zadeh L A.Fuzzy Sets. Information and Control,1965,8:338-353
Zhang Lifeng,Zhao Keqin.1998.The Theories Methods and its Applications of Set Pair Analysis,System Science and its Applications. Tianjin:Peoples’Publishing House,61-64