反向累加生成的特性及GOM(1,1)模型的优化

针对反向累加序列的生成与建模问题, 分析了反向累加生成的准光滑性和准指数规律, 进而给出反向累加生成序列的灰建模条件. 证明了基于反向累加生成的齐次与非齐次离散指数函数之间的关系, 并经过理论推导得到了GOM(1,1)模型的最优背景值. 结果表明, 优化的背景值与GOM(1,1)模型的时间响应函数具有较好的一致性, 从而可以在理论上有效提高传统模型的精度. 最后通过实例验证了优化模型的实用性与有效性.

Properties of accumulated generating operation in opposite-direction and optimization of GOM(1,1) model

For the generating and modeling problem of accumulated sequences in opposite-direction, this paper has analyzed the quasi-smoothness and quasi-exponentially law of accumulated generating sequences in opposite-direction, and given the grey modeling conditions for such sequences. Besides, this paper has proved the relationship of homogenous and non-homogenous discrete exponential functions based on accumulated generating operation in opposite-direction, and after a series of theoretical analysis, the optimized background value of GOM(1,1) model has been given. The result shows that the optimized background value and the time response function of GOM(1,1) model have a better consistency, thus it can effectively improve the accuracy of the traditional model in theory. Finally, two applications are given to demonstrate the practicability and effectiveness of the optimized model.