基于降维思想的水资源脆弱性非线性评估模型及其应用

发布时间：2018-05-09 08:08

本文选题：降维 + 拉格朗日函数　；参考：《工程科学与技术》2017年03期

【摘要】：利用微分方程建模技术构建一种通用的水资源脆弱性非线性评估模型,在对指标进行降维的基础上,研究水资源脆弱性和指标之间的非线性关系。首先,基于投影寻踪技术建立降维模型,对多维指标进行降维处理,然后采用拉格朗日函数法求解最优投影方向;其次根据评估函数具备的性质和特点建立水资源脆弱性微分方程模型;最后求解方程估计未知参数,模拟水资源脆弱性与指标之间的非线性函数模型。利用所建模型定量研究北京市1979—2012年的水资源脆弱性变化规律,筛选影响北京市水资源脆弱性的敏感因子,研究结果符合北京市实际情形,说明模型的适用性。在水资源供需平衡分析的基础上,对2020年北京市水资源脆弱性进行评价,研究结果表明:当不考虑外调水和再生水时,2020年北京市在1956—2012年来水条件下的水资源脆弱性值均约为0.88,水资源均处于极度脆弱状态;利用再生水和南水北调水后,2020年在不同来水条件下的水资源脆弱性均有所降低,平均下降幅度仅为17.2%。本文建立的水资源脆弱性非线性评估函数模型可以避免人为的干扰,具备单调性、有界性和变化的连续平稳性等性质,能定量模拟和刻画水资源脆弱性与指标之间的变化关系。
[Abstract]:A general nonlinear assessment model of water resources vulnerability is constructed by using differential equation modeling technology. Based on the dimensionality reduction of indicators, the nonlinear relationship between water resources vulnerability and indicators is studied. Firstly, the dimensionality reduction model is established based on projection pursuit technique, and the dimensionality reduction of multidimensional index is processed. Then the Lagrange function method is used to solve the optimal projection direction. Secondly, the differential equation model of water resource vulnerability is established according to the properties and characteristics of the evaluation function, and the nonlinear function model between water resource vulnerability and index is simulated by solving the equation to estimate unknown parameters. By using the established model, the changes of water resources vulnerability in Beijing from 1979 to 2012 were quantitatively studied, and the sensitive factors affecting Beijing water resources vulnerability were screened. The results were in accordance with the actual situation in Beijing and showed the applicability of the model. Based on the analysis of water resources supply and demand balance, the vulnerability of water resources in Beijing in 2020 is evaluated. The results show that the vulnerability of water resources in Beijing in 1956-2012 is about 0.88, and the water resources are in extremely fragile state when the external transfer and reclaimed water are not taken into account. After utilizing reclaimed water and transferring water from south to north, the vulnerability of water resources under different water conditions decreased in 2020, with an average decrease of 17.2g. The nonlinear assessment function model of water resources vulnerability established in this paper can avoid human disturbance, have the properties of monotonicity, boundedness and continuous stability of change, and can quantitatively simulate and depict the relationship between water resources vulnerability and indexes.
【作者单位】：解放军理工大学气象海洋学院;北京师范大学水科学研究院水沙科学教育部重点实验室;
【基金】：国家自然科学基金资助项目(51609254;51479003;51279006)
【分类号】：TV213.4

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