博碩士論文 102552008 詳細資訊




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姓名 温惠筑(Huei-Chu Wen)  查詢紙本館藏   畢業系所 資訊工程學系在職專班
論文名稱 分數冪次型灰色生成預測模型誤差分析暨電腦工具箱之研發
(The Error Analysis in GM(1,1) Model by using Fractional Power in Grey Generating and the Development of Toolbox)
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摘要(中) 在灰色系統理論的GM(1,1)模型,是屬於預測模型,主要是構建在一階微分的模型,而是採取兩個相鄰點的平均值(背景值)所產生的。根據過去的研究,發現背景值是影響預測誤差最重要的因素,因此許多論文都集中在背景值的調整,包括背景值中alpha值的數位跳躍變動,或者背景值中alpha值的連續變動以低預測的誤差,但是在此種形式下背景值,有時仍無法充分顯現離散點所隱含之規律,因此形成GM(1,1)模型的誤差無法大幅降低。因此本論文提出了一種新的方法,內容包含三大要項,首先將背景值以分數的型態表示,並且結合組合數學的方法獲得實際的數值,最為降低誤差的基礎。接著整合GM(1,1)模型,實際分析降低預測誤差的內容,做出分析結果之數學模式。最後本文還自行研發體工具箱,做為減少複雜的計算和驗證最終結果的準確性,不僅擺脫傳統的背景值方法,也打開了GM(1,1)模型降低預測誤差的新方向。
摘要(英) bstract

According to the basic of empirical mathematical operation of GM(1,1) model in grey system theory, the background value is used to establish in the first order differential model, and the traditional method is taken the average of the two neighbor points. According to the past research in GM(1,1) model, it can fine that the background value not only is the main influence factor, but also is the most important influence factor in prediction error. Therefore, the paper based on the past research, focused on the adjustment of the background values, present a new approach, which is called the fractional order accumulation method, and combine with the combination mathematics method to get the mathematics result. Besides, the paper also develops computer toolbox to reduce the complex calculation and to verify the accuracy of final results. From the mentioned above, the paper it not only get rid of the default of traditional background value method, but also to open a new approach for GM(1,1) model.
關鍵字(中) ★ 灰色系統理論
★ GM(1,1)
★ 背景值
★ 誤差
★ alpha值
★ 分數
關鍵字(英) ★ GM((1,1)
★ Background value
★ Error
★ Fractional order accumulation
★ Computer toolbox
論文目次
目錄

摘要
Abstract
目錄 i
圖目錄 iii
表目錄 v
第一章 緒論 1
1.1研究背景 1
1.2研究動機與目的 1
1.3相關文獻探討 2
1.4研究方法與步驟 3
1.5論文整體架構 4
第二章 灰色系統理論 5
2.1灰色系統理論介紹 5
2.2灰色GM(1,1)基本模型 7
2.3 GM(1,1)模型誤差分析 11
第三章 分數幂次型灰色生成模型 13
3.1 基本數學模型 13
3.2矩陣方法計算分數幂次型矩陣 14
3.3組合數學方法計算分數幂次型矩陣 15
3.4分數幂次型生成矩陣工具箱之研發 18
第四章 分數幂次整合型GM(1,1)模型 25
4.1 分數幂次整合型GM(1,1)模型計算分析步驟 25
4.2分數幂次整合型GM(1,1)模型工具箱之研發 26
4.3實例分析-電力負載之GM(1,1)分析 29
第五章 結論 37
參考文獻 39
參考文獻
參考文獻
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指導教授 施國琛、陳正一 審核日期 2017-7-17
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