系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
12期
3199~3203
,共null页
非等间距 非齐次 灰色模型
非等間距 非齊次 灰色模型
비등간거 비제차 회색모형
non-equidistant; non-homogenous; grey model
传统的GM（1,1）模型在拟合非齐次指数序列时往往存在较大偏差,针对现实中大量存在的非等间距近似非齐次指数序列,本文首先根据非等间距灰色模型建模机理,提出一个非等间距非齐次灰色模型,推导出模型参数的最小二乘估计及时间响应函数表达式;其次,关于模型初始条件,建立无约束优化模型;最后,实证分析表明,该改进模型在拟合精度和实用性上均有明显改善,从而拓宽了灰色模型适用范围.
傳統的GM（1,1）模型在擬閤非齊次指數序列時往往存在較大偏差,針對現實中大量存在的非等間距近似非齊次指數序列,本文首先根據非等間距灰色模型建模機理,提齣一箇非等間距非齊次灰色模型,推導齣模型參數的最小二乘估計及時間響應函數錶達式;其次,關于模型初始條件,建立無約束優化模型;最後,實證分析錶明,該改進模型在擬閤精度和實用性上均有明顯改善,從而拓寬瞭灰色模型適用範圍.
전통적GM（1,1）모형재의합비제차지수서렬시왕왕존재교대편차,침대현실중대량존재적비등간거근사비제차지수서렬,본문수선근거비등간거회색모형건모궤리,제출일개비등간거비제차회색모형,추도출모형삼수적최소이승고계급시간향응함수표체식;기차,관우모형초시조건,건립무약속우화모형;최후,실증분석표명,해개진모형재의합정도화실용성상균유명현개선,종이탁관료회색모형괄용범위.
There is higher bias on fitting non-homogenous series. For those non-homogenous and non- equidistant series, a non-homogenous and non-equidistant grey model is put forward which is based on the theory of traditional grey model in this paper. In the first, estimates of the parameters and the time respond function are given by least squares. In the second, an unconstrained optimum model is built about initial condition. In the end, empirical analysis shows that the improved model has better performance in fitting and practicality. And so, the application of grey model can be extended.
