非齐次GM(1,1)模型的背景值优化及其应用

Optimization of Background Value in Grey Model of Non-homogeneous Exponential Sequence and Its Application

针对非齐次GM（1，1）模型中传统方法构造的背景值与真实背景值之间存在误差的情况，提出了一种背景值优化方法．首先，分析了背景值误差的来源及其对模型预测精度的影响；然后，通过积分变换重构了背景值，并利用非齐次指数序列及其一次累加、一次累减生成序列的相互关系，得到了重构背景值中参数的表达形式；最后，根据拟合误差最小原理解得了模型参数的估计值，进而得到了预测公式．经过实例应用，优化模型预测结果的平均相对误差为0．54％，表明优化背景值能够明显提高模型的预测精度．

Focused on the error of background value constructed by the traditional way and the true one in the non-homogeneous GM（1, 1） model, an optimized method of background value applicable to non-homogeneous exponential sequence was proposed. Firstly, the re- source of the error and its influence on the prediction precision of the model was analyzed. Secondly, background value was reconstructed through integral transformation. Then, based on the relationship among non-homogeneous exponential sequence, its 1-accumulated gener- ating operation sequence and its inverse accumulated generating operation one, parameter expressions of reconstructed background value were available. Finally, the model parameters were solved on the basis of the minimum fitting error and hence the prediction formula was shown. Through engineering application, the average relative error of prediction results of the modified model is 0.54%, which indicates a fact that optimizing background value is obviously able to improve prediction precision of the model.