无偏GM(1,1)幂模型初始条件的优化

针对无偏GM(1,1)幂模型初始条件的优化问题，分别考虑模型结构参数已知和未知的情形下的优化方法。在结构参数已知的情形下，构建优化模型使得原始序列的一阶累加生成序列与其模拟值的误差平方和在理论上达到最小，并给出了最优初始条件的解析解；在结构参数未知的情形下，将最优初始条件视为待定变量，建立基于预测误差最小化准则的非线性优化模型，并通过Matlab求解优化的初始条件和结构参数。结果表明，提出的优化方法能够显著地提高无偏GM(1,1)幂模型的预测精度。

Optimization of initial value in unbiased GM(1,1) power model

In view of the problem of optimizing the initial value in an unbiased GM (1,1) power model, two optimization methods are studied under the conditions that the structural parameters are known and unknown respectively. An optimization model minimizing the sum of error squares of first-order accumulated generating sequence and its simulated one in theory is constructed, and the analytical solution of this model is also deduced when the structural parameters are known. Under the condition that the structural parameters are unknown, optimal initial conditions are considered as pending variables, a nonlinear optimization model based on the prediction error minimization criterion is also established and solved to obtain the best initial value and structural parameters by Matlab. The results show that the prediction accuracy of traditional unbiased GM(1,1) power model is significantly improved by the proposed optimization method.