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
7期
1822~1827
,共null页
灰色系统 离散灰色模型 小样本 扰动分析
灰色繫統 離散灰色模型 小樣本 擾動分析
회색계통 리산회색모형 소양본 우동분석
grey system; discrete grey model; small sample; perturbation analysis
针对灰色预测模型为什么适用于“小样本”建模的问题进行了研究．以离散灰色模型为例，利用最小二乘问题解的扰动理论证明了灰色一阶累加方法在扰动相等的情况下，原始序列样本量较大，解的扰动界较大；样本量较小，解的扰动界较小．为了使离散灰色模型解的扰动界变小，本文提出了分数阶累加离散灰色模型．实例说明分数阶累加离散灰色模型的实用性．
針對灰色預測模型為什麽適用于“小樣本”建模的問題進行瞭研究．以離散灰色模型為例，利用最小二乘問題解的擾動理論證明瞭灰色一階纍加方法在擾動相等的情況下，原始序列樣本量較大，解的擾動界較大；樣本量較小，解的擾動界較小．為瞭使離散灰色模型解的擾動界變小，本文提齣瞭分數階纍加離散灰色模型．實例說明分數階纍加離散灰色模型的實用性．
침대회색예측모형위십요괄용우“소양본”건모적문제진행료연구．이리산회색모형위례，이용최소이승문제해적우동이론증명료회색일계루가방법재우동상등적정황하，원시서렬양본량교대，해적우동계교대；양본량교소，해적우동계교소．위료사리산회색모형해적우동계변소，본문제출료분수계루가리산회색모형．실례설명분수계루가리산회색모형적실용성．
Why grey model is suitable for small sample is explained. Take discrete grey model as anexample, based on matrix perturbation theory, we prove that the larger sample, the bigger perturbationbound and the smaller sample, the smaller perturbation bound under the equal perturbation when we usethe traditional grey first order accumulate. The fractional order accumulate grey model is defined in orderto reduce perturbation bound and its availability and practicality are verified by an example.
