基于BP神经网络的粮食产量与化肥用量相关性研究

针对太湖流域化肥用量和粮食产量数据，利用BP神经网络算法，建立了粮食产量与化肥用量之间的关系模型，以指导化肥减施增效。共收集了1980—2014年共35a太湖流域16个县市每个县市的单位面积化肥用量和单位面积粮食产量数据。通过自回归滑动平均模型（ARMA），对两类数据进行时间序列分析，对数据中存在的缺项进行了填补。实验表明，对于单位面积粮食产量数据，用ARMA(2,6)模型能够达到较佳的填补效果，均方误差小于0.2，R2＞0.85。对于单位面积化肥用量数据，用ARMA(3,7)模型较优，均方误差小于0.02，R2>0.80。说明ARMA模型数据填补效果较好。将填补后的不同县的数据通过BP神经网络建立模型，描述了各县市单位面积化肥用量和粮食产量的关联关系。实验表明，该方法拟合的均方误差小于0.12，R2＞0.80，说明BP神经网络是一种准确度较高的拟合方法。通过分析各县拟合结果，表明化肥用量有阈值，化肥用量低于该阈值，粮食产量将会较快速增长，高于该阈值，粮食产量将不再增长，过多的施用化肥并不能取得高产。

Correlation between Grain Yield and Fertilizer Use Based on Back Propagation Neural Network

A strong correlation exists between fertilizer application and grain yield. Due to many factors affecting grain yield, the existing fitting methods of correlation between the two variables lead to large errors. Aiming at the data of fertilizer application and grain yield in Taihu Lake Basin, the back propagation (BP) neural network was used in this paper to model the correlation between the two variables accurately, which could guide to reduce use of fertilizer. This paper collected average fertilizer use and grain yield data per acre in 35 years i.e. from 1980 to 2014, in 16 counties and cities in Taihu Lake Basin. Missing items were filled automatically through a time series analysis approach called auto-regressive and moving average model (ARMA). For average grain yield data, ARMA(2, 6) model had higher accuracy with mean square error (MSE) less than 0.2 and R2 more than 0.85. For average fertilizer use, ARMA(3, 7) model had higher accuracy with MSE less than 0.02 and R2 more than 0.80. Then BP neural network with a single hidden layer (1-10-1) was established to fit correlation fertilizer use and grain yield data in each country. Goodness of the fit with BP neural network was better than other methods, with MSE less than 0.12 and R2 more than 0.80. Results indicate that there is a threshold for fertilizer use. When fertilizer is used less than the threshold, grain yield per acre is more, whereas when it is more than the threshold, grain yield per acre fluctuates and the average keeps invariant. The correlation implies excessive application of fertilizers can not achieve high yields.