基于分数阶灰色模型的农业用水量预测

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。

Prediction of agricultural water consumption based on fractional grey model

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-40°51′40″N, 106°42′40″E-111°27′20″E) of Inner Mongolia autonomous region and Baoji city(33°35′N-35°06′N,106°18′E-108°03′E) of Shaanxi province was predicted by the grey model(GM(1,1)) model of fractional order reverse accumulation, the order of which was optimized according to the results of the test set fitting. The average error of the prediction was 2.23%,1.77% and 0.31%, respectively. In order to test the performance of the model, the model proposed in this paper was compared with the traditional GM(1,1) model, traditional autoregressive model and the combined model based on the wavelet analysis theory respectively. Among them, the average prediction error of GM(1,1) model for the Tongliao and Baoji city is 5.55% and 1.28%, but the detection is failed for the Ordos city. The average prediction error of autoregressive model for the three research areas is 3.34%, 4.17% and 6.49%. The average prediction error of agricultural water consumption in Ordos City of Inner Mongolia Autonomous Region based on the combination model of wavelet analysis theory is 2.87%. The results show that compared with GM(1,1) model, the prediction effect of the model in this paper is better, which depends on the objective function of "the best fitting of historical data" and the objective function of "the largest(or the smallest) order" to reduce the learning degree of the model for noise, because the model in this paper transforms the oscillating data and reduces the uncertainty of the data, so compared with the autoregressive model without data processing, the model in this paper is less affected by data volatility. In this paper, the idea of fractional order "in between" is used to improve the traditional gray model with positive integer as order, which can effectively improve the accuracy of the model. At the same time, the method of reverse accumulation is used to increase the use of new data. On the whole, for the prediction of agricultural water consumption in all research areas, the model in this paper has the minimum error, strong generalization ability and certain practicability, which can provide a basis for the prediction of regional agricultural water consumption and the allocation of agricultural water resources in northern China.