茶树树冠结构的多元差分方程组模型

Model of Difference Equations with Multi-variable for Tea Plant Canopy

茶树的生长、产量和品质受树冠结构的影响,因此利用数学模型来模拟茶树树冠指标的变化可以指导茶树的栽培和管理。考虑到茶树树冠各指标不但相互影响,而且与前几年生长数据相关,针对茶树树冠15个生长指标的18年数据,建立了多元差分方程组模型,并提出了一种结合利用聚类分析和神经网络进行模型参数估计的方法。计算表明,笔者研究中模型的平均相对误差绝对值(MAPE)为0.045828,低于一元差分方程模型的MAPE的平均值0.0618和一元回归方程模型的MAPE的平均值0.0842,精度有明显提高。该方法可以用于其他多维时间序列的差分方程组建模。

Tea tree growth,yield and quality are influenced by its canopy structure,therefore simulating tea tree canopy indexes by using mathematical models can instruct the tea cultivation and management.Considering the tea tree canopy each index not only affected each other,but also related to previous years growth data,the difference equations models with multi-variable were established for 18 years data of 15 growth indexes of tea plant canopy.A combination of clustering and neural network was employed to estimate the model parameters.Calculating results showed that the mean absolute percentage error（MAPE） of our model was 0.045828,which was less than the MAPE 0.0618 of one variable difference equation model,also less than the MAPE 0.0842 of a regression equation model.The results indicated that the predictive accuracy of our models was improved comparing with one variable models.This method can be used for modeling of multidimensional time sequence of difference equations.