GM(1,1)幂模型的派生模型

为了进一步完善灰色幂模型体系, 分析了经典GM(1,1)模型和GM(1,1)幂模型之间的变换关系, 在GM(1,1)幂模型的定义型和白化型的基础上, 推导了GM(1,1,x⁽²⁾)幂模型、GM(1,1,x⁽¹⁾)幂模型、GM(1,1,b)幂模型、GM(1,1,exp)幂模型和GM(1,1,C)幂模型五种派生型GM(1,1)幂模型, 构建了GM(1,1)幂模型群. 结果表明, GM(1,1)幂模型与GM(1,1)模型的时间响应函数在本质上是一致的, 不同的GM(1,1)幂模型派生模型在结构、内涵、解析式、功能方面存在一定的区别, 体现了灰色系统解非唯一性原理. 在实际应用中, 可以依据一定的准则, 在默认解群中找出一个最合适的白化解.

Models derived from GM(1,1) power model

In order to further complement the system of grey power models, this paper analyzes the transformation relationships between the classic GM(1,1) model and GM(1,1) power model, and deduces five derived models including GM(1,1,x⁽²⁾) power model, GM(1,1,x⁽¹⁾) power model, GM(1,1,b) power model, GM(1,1,exp) power model and GM(1,1,C) power model based on the defined and whitened GM(1,1) power models. A group of grey power models including classic GM(1,1) power model and the derived five models is built finally. The results show that time response functions of GM(1,1) model and GM(1,1) power model are essentially the same. Different derived models have different structures, contents and solutions, reflecting the principal of non-unique solution in grey system theory. In practical applications, the most appropriate whitened solution can be identified from group of default solutions under the corresponding objectives.