基于分数阶灰色模型的农业用水量预测  

Prediction of agricultural water consumption based on fractional grey model

作　　者：李俊[1] 宋松柏[1] 郭田丽 王小军[2,3] Li Jun;Song Songbai;Guo Tianli;Wang Xiaojun(College of Water Resources and Architectural Engineering,Northwest A&F University,Yangling 712100,China;Hydrology and Water Resources Department,Nanjing Hydraulic Research Institute,Nanjing 210029,China;Research Center for Climate Change of Ministry of Water Resources,Nanjing 210029,China)

机构地区：[1]西北农林科技大学水利与建筑工程学院,杨凌712100 [2]南京水利科学研究院水文水资源研究所,南京210029 [3]水利部应对气候变化研究中心,南京210029

出　　处：《农业工程学报》2020年第4期82-89,共8页Transactions of the Chinese Society of Agricultural Engineering

基　　金：中央财政水资源节约、管理与保护项目(126302001000150005);国家自然科学基金项目(51479171、51179160、50879070)。

摘　　要：针对农业用水量序列的振荡特性以及传统灰色预测模型的过拟合问题,该文提出分数阶灰色预测模型。将农业用水量振荡序列转化为单调递减非负序列,并以转化序列为基础,根据"阶数最大(或最小)"、"历史数据拟合最好"2个目标函数构造优化模型,采用改进NSGA-Ⅱ(non-dominated sorting genetic algorithm Ⅱ,NSGA-Ⅱ)进行模型求解。根据验证集拟合结果优选出模型阶数,结合分数阶反向累加灰色模型(fractional order reverse accumulation grey model),以通辽市和宝鸡市为例,进行农业用水量的预测。为了检验模型性能,将该文模型分别与传统GM(1,1)模型、自回归模型、基于小波分析理论组合模型进行对比。结果表明,该文模型对于通辽市、宝鸡市与鄂尔多斯市的农业用水量预测的相对误差分别为2.33%、0.31%和1.77%。同时,该文模型预测误差最小(比自回归模型分别低1.11%(通辽)、6.18%(宝鸡);比传统GM(1,1)模型分别低3.32%(通辽)、0.97%(宝鸡)),具有一定实用性,研究结果可为区域农业用水量预测提供依据。Due to the shortage of water resources, serious water pollution, improper use of water and the occupation of agricultural water rights by other industries, China’s agriculture will face the risk of water shortage in the future. Due to the amount of water resources in North China is relatively small compared with that in South China, coupled with extensive operating methods and the low level of agricultural irrigation technology, water resources are wasted seriously, the problem of agricultural water shortage in North China is more serious. Optimal allocation of water resources is one of the main measures to alleviate the shortage of agricultural water resources, and is an important means to achieve sustainable use of water resources. Accurate prediction of regional agricultural water consumption is the key to optimal allocation of water resources. Grey model is a method to study "poor information", "small sample" and uncertainty problems, which is widely used in economics, finance and other fields. The amount of historical data of annual agricultural water consumption is not enough, which is affected by many factors, and has concussion. Therefore, it is suitable to use grey model to predict agricultural water consumption. The oscillation characteristics of agricultural water consumption data series have a certain impact on the prediction accuracy of the model. To resolve these problems, an improved fractional grey prediction model is proposed in this paper. Based on the monotonically decreasing non-negative series which transformed from the oscillation series of the agricultural water consumption, a multi-objective optimization model was constructed according to the two objective functions of "maximum(or minimum) order" and "the best fit of historical data", which was solved by the improved non-dominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) method. Agricultural water consumption in the test set for the research areas of Tongliao city(42°15′N-45°59′N, 119°14′E-123°43′E), Ordos city(37°35′24″N

关 键 词：农业 水 模型 分数阶 灰色预测 振荡序列 过拟合 多目标优化 

分 类 号：TV213.4[水利工程—水文学及水资源]