本篇論文主要在於探討使用灰色線性微分方程與灰色線性差分方程所建立的預測模型之差異。由於灰色預測大都使用於離散數據，而灰色線性微分方程所建立之預測模型卻以連續系統作為建模基礎，故從系統建構之合理性而言，灰色線性差分方程所建立之預測模型應優於灰色微分方程所建立之預測模型。此外，傳統灰色建模皆是以最小平方法求解模型參數，考慮此法在系統受到干擾時常會造成模型參數估計偏差，以致影響預測結果，故在文中使用遺傳演算法來求解系統之模型參數。本篇論文最後以兩個實際工程數據為例，比較各類模型之建模精度與預測精度。

In this thesis, the comparison between using linear differential and linear difference equation for grey modeling has been presented. It is shown that the use of linear difference equation is more straightforward than that of linear differential equation for grey modeling. In order to reduce the modeling error, genetic algorithms are also used to search the coefficients of the grey model instead of using the tranditional least square approach. Experimental results have shown that the modeling error can be further reduced by using the genetic search of the coefficients of the grey model.

摘要I
目錄III
圖索引V
表索引VIII
第一章 緒論1
1.1 研究動機與目的1
1.2 文獻回顧2
1.3 內容大綱3
第二章 灰色理論5
2.1灰色系統概論5
2.2 灰色系統模型7
2.3灰色預測11
第三章 灰色建模14
3.1 灰色線性微分方程之建模14
3.2 灰色線性差分方程之建模19
3.3 灰色建模之誤差檢驗及後驗差檢驗23
第四章 遺傳演算法理論基礎25
4.1遺傳演算法的基本概念25
4.1.1編碼26
4.1.2解碼27
4.1.3適應性函數27
4.1.4複製27
4.1.5交換29
4.1.6突變30
4.2 遺傳演算法的數學基礎31
4.2.1名詞定義31
4.2.2 Schema定理的推導32
第五章 實例分析35
5.1 52100軸承鋼磨耗試驗35
5.1.1 實驗方法與步驟35
5.2 52100軸承鋼磨耗量之灰預測38
5.2.1 灰色線性微分方程建模39
5.2.2 灰色線性差分方程建模43
5.3 8750熱處理鋼之勃氏硬度值之灰預測52
5.3.1 灰色線性微分方程建模52
5.3.2 灰色線性差分方程建模60
5.4 灰色滾動建模69
第六章 結論73
參考文獻74

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