含非线性时间项的无偏灰色模型构建与应用

针对含二次多项式时间项灰色模型存在着从差分到微分的跳跃性误差,提出了其无偏模型,此模型无需已知白化方程解析解。借助新变量将原白化方程转化为矩阵微分方程,根据方程的解直接建立离散时间响应函数的递推公式,利用直接建模法给出无偏模型的参数估计,采用精细积分法直接对数据进行高精度的模拟(预测),并以误差平方和最小为目标对初始点进行优化。从理论上证明了该模型具有含线性时间项非齐次指数规律重合性和伸缩变换一致性,从非齐次指数序列和能源消费实例上也验证了所构建模型的无偏性和有效性,具有更好的拟合(预测)精度。

Unbiased Grey Model With Nonlinear Time Terms and Its Applications

An unbiased grey model with quadratic polynomial time terms is proposed for the jumping error from difference to differential, which does not require the analytic solution of its whitenization equation. The recurrence relation of the discrete time response function is directly deduced by the solution of the matrix differential equation, which is transformed from the whitenization equation by introducing new variables. Using the relation, the parameter estimations of the proposed unbiased grey model is constructed by direct modeling. The fitted value is directly calculated by high precise direct integration method with high precision. Besides, the initial point is optimized according to the minimum of the square sum of the error. The characteristics of the proposed unbiased model, linear nonhomogeneous exponential law coincidence and linear transformation consistency, are theoretically proved. The results of nonhomogeneous exponential series and energy consumption data also verify unbiasedness and effectiveness of the proposed model, and demonstrate better fitting an predicting accuracy.