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研究生:葉一隆
研究生(外文):Yi-Lung Yeh
論文名稱:斜率灰色模式與一維灰色地下水流分析
論文名稱(外文):Slope Grey Model and Analysis of One-Dimensional Grey Groundwater Flow
指導教授:林俊男林俊男引用關係
指導教授(外文):Chun-Nan Lin
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:農業工程學研究所
學門:工程學門
學類:其他工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
中文關鍵詞:斜率灰色模式灰色地下水流系統灰色達西定律灰色水力傳導係數屏東平原
外文關鍵詞:Slope grey modelGrey groundwater flow systemGrey Darcy''s lawGrey hydraulic conductivityPingtung plain
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地下水流系統受許多無法完全控制之因素所影響,諸如含水層特性,抽水位置,抽水時段,補注位置等。因此,地下水流系統可視為一灰色系統。本論文之目的包括:(1)分析地下水位灰色模式建立所需資料點數對模式精度與預測結果之影響。(2)由資料變化特性,提出斜率灰色模式,以改善灰色模式之精度。(3)建立灰色地下水流之數學描述方程式,以反應地下水流系統為灰色系統。
首先,本論文應用灰色理論來建立地下水位觀測井所得之地下水位之灰色模式,探討灰色模式中生成係數對灰色模式精度之影響,並以灰關聯度來分析最佳之生成係數值。利用所建立之灰色模式來分析屏東平原之林園站、昭明站及大潭站等三觀測井之地下水位變化。由分析結果得知均值生成係數所建立之灰色模式並非最佳之預測模式,而以動態之生成係數( ),並配合灰關聯分析,可得最佳之灰色預測模式。此外,由屏東平原之林園站、昭明站及大潭站等三站地下水位觀測值分析得知建立模式所用之點數並非愈多愈好,完全依據數列累加生成後滿足指數律函數之點數來決定,否則將降低模式之精度。
本論文依資料之特性,將系統之資料分成遞增、遞減及跳躍三種型態,並分析各種資料型態之斜率與級比。配合線性規劃之概念,分別求得各灰微分方程式間之係數值,以資料之特性來決定採用之係數值,來建立斜率灰色模式。由斜率灰色模式分析結果可知傳統利用最小二乘法所得之灰色模式之誤差並非為最小。
其次,本論文將地下水流系統之灰色特性以灰色水力傳導係數表示,擴展達西定律成為灰色達西定律,利用灰色達西定律與質量守恆定理推導得灰色地下水流方程式。當地下水流系統之灰色特性以灰色水力傳導係數表示時,水力傳導係數為一灰色變數,因此水力傳導係數之值為區間界限值。由灰色地下水流方程式所得之地下水位或流通量將亦為一區間界限值,由區間界限值可知該區域之最高與最低地下水位或流通量之極值狀況,對地下水資源之利用規劃與決策可提供更有彈性之選擇。
The groundwater flow system is influenced by many uncontrollable factors, such as aquifer properties, pumping period, and pumping and recharge locations. Therefore, the analyzing system of groundwater flowing pattern can be treated as a grey system. The objectives of this dissertation are: (1) to analyze the influence of necessary data on the accuracy and predicting capability of the grey model, (2) to propose a slope grey model based on the properties of data variation in order to improve the accuracy of the grey model, (3) to construct equations for grey groundwater flow system to support the groundwater flow system as a grey system.
Firstly, a grey model was built to predict groundwater level. The influence of generating coefficients on model accuracy was examined. Then, the optimal generating coefficient was analyzed based on grey relational method. The procedure in the grey model was applied to three observation wells; Linyuan, Jauming, and Tatan in Pingtung plain to predict the annual change of groundwater level. The results showed that the model based on mean generating coefficients was not an optimal prediction model. On the other hand, the dynamic generating coefficients ( ), combined with grey relational method, could obtain an optimal grey model for groundwater level prediction. The accuracy of grey model was not necessarily improved by increasing the size of data set; rather, it depended on the satisfaction of accumulated generating data approaching exponential function, otherwise, the model accuracy would decrease.
The data were grouped into three types in this dissertation, increase, decrease and jump types. The slopes and class ratio of these three types were analyzed. Applying the concept of linear programming, the parameters in grey differential equations were calculated. The coefficient was used, according to data characteristics, to construct a slope grey model. The results showed that a slope grey model using the traditional least-square method did not produce the minimum error.
Incorporating the grey hydraulic conductivity in the grey model, Darcy’s law was expanded to become grey Darcy’s law. Further, grey groundwater flow equation was derived from combining grey Darcy’s law and mass conservation theory. Because of the grey characteristic of hydraulic conductivity when presented in a groundwater flow system, the grey hydraulic conductivity was expressed as a grey variable. Because the variable was within an interval, the water level and flux calculated by grey groundwater flow equation was likewise within an interval. In an area, the extreme conditions of the highest and lowest numbers within the interval offered flexible options for the planning and decision making of groundwater resource utilization.
封面
目錄
中文摘要
英文摘要
圖目錄
表目錄
第一章緒論
§1-1研究動機
§1-2文獻探討
§1-3研究目的與方法
第二章地下水位灰色預測分析
§2-1灰色系統概述
§2-2灰色預測理論之建立
§2-3屏東平原地下水位灰色預測分析
§2-4屏東平原灰色預測模式誤差分析
§2-5結果與討論
第三章斜率灰色模式
§3-1觀測資料之特性
§3-2斜率灰色模式
§3-3模式計算與誤差分析
§3-4地下水位斜率灰色模式分析
第四章一維灰色地下水流分析
§4-1灰色達西定律
§4-2灰色地下水流方程式
§4-3一維灰色地下水流分析
§4-4結果與討論
第五章結論與建議
§5-1結論
§5-2建議
參考文獻
簡歷
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