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研究生:黃志偉
研究生(外文):Chih-Wei Huang
論文名稱:結合灰色系統理論與馬爾可夫鏈進行地下水位預測
論文名稱(外文):Combine grey system theory and Markov chain to forecast groundwater level
指導教授:溫志超溫志超引用關係
指導教授(外文):Jet-Chau Wen
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:防災與環境工程研究所
學門:工程學門
學類:環境工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:146
中文關鍵詞:地下水位灰色理論馬爾可夫鏈
外文關鍵詞:Markov chainKey Word: Grey system theoryGroundwater level
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本研究主要是利用灰關聯分析推估降雨入滲至地下水位面的入滲時間。再以推估的入滲時間改良GM(1,2),進而預測地下水位的變化。最後則以隨機過程(馬爾可夫鏈)修正GM(1,2)的模式系統誤差。因此其研究目的有二。(1).以灰關聯分析推估的入滲時間來改良GM(1,2),以探討其預測地下水位的可能性。(2).以隨機過程(馬爾可夫鏈)修正GM(1,2)的模式系統誤差,以探討隨機過程(馬爾可夫鏈)修正GM(1,2)模式系統誤差的可行性。
研究中以BH05、BH06、BH08、BH10等4口地下水位觀測井,進行入滲時間分析、GM(1,2)模型建置、馬爾可夫鏈模型建置、灰色系統理論結合馬爾可夫鏈等四個方向的研究。
入滲時間分析方面。其所獲得入滲時間 分別為:
BH05:入滲時間為40小時。BH06:入滲時間為40小時。
BH08:入滲時間為39小時。BH10:入滲時間為44小時。
從上述結果可得知,4口地下水位觀測井其最佳入滲時間不盡相同。這是因為雲科大校園監測場址為一非均質等向的實驗場址,故有此一狀況產生;然而灰關聯度變化仍有相同的趨勢可循。
GM(1,2)模型建置方面。首先從灰建模結果中可發現。灰參數C1平均值介於0.9996。灰參數C2平均值介於0.0561。為次以驗證結果來分析。4口地下水位觀測井其 平均值介於5mm; 平均值介於8mm。其驗證精度可說是十分良好。終以灰預測的結果來分析。研究中將灰預測的預測時數從1小時增加至24小時。其4口地下水位觀測井的 平均從3mm上升至21mm。 平均由9mm上升至43mm。其代表GM(1,2)地下水位預測模型連續進行24小時的灰預測,仍可將 維持於21mm; 維持於43mm。其預測精度是可以接受的。
馬爾可夫鏈模型建置方面。首先以4口地下水位觀測井1小時至24小時的灰預測結果所求得的擾動值來分析。其中發現平均超過12小時,其擾動值的上下限就有可能會產生不穩定的變化。次以擾動值分布特性來分析。可以發現4口地下水位觀測井均為標準常態分佈。因此以馬爾可夫鏈來預測擾動值時,必須將隨機變數修改成標準常態分布隨機變數。終以擾動值預測來分析。4口地下水位觀測井的預測精度是可接受的。其預測範圍部分,由於馬爾可夫鏈建模中已將擾動值超出30mm與-30mm的離散值予以刪除;所以會造成其預測擾動值範圍遠低於擾動值範圍。
灰色系統理論結合馬爾可夫鏈的研究方面。研究中發現,灰色系統理論結合馬爾可夫鏈。其所預測的精度與未結合前相比較,屬於持平或略為降低。其原因乃是因馬爾可夫鏈的隨機預測,其為一標準常態隨機分布。所以其預測的擾動值,為一標準常態隨機變數,進而使得每次預測均為不同的數值。其所預測的擾動值僅能預測出其擾動值範圍、發生機率與平均值,而無法完全的預測出其變化。
In this study I used the grey relational analysis to infer that infiltration time during rainfall infiltrated into water-table. Then employ the Infiltration time improved the GM(1,2) to predict the changes in groundwater level. Finally a random process (Markov Chain) to amend the systematic errors of GM(1,2). For this reason the study had two purposes. (1) Used grey relational analysis to estimate the infiltration time to improve GM (1,2),then explored the possibility of predicted groundwater level. (2) Explored the feasibility of a random process (Markov Chain) to amend the systematic errors of GM(1,2).
In this study I set four groundwater observation wells BH05,BH06,BH08 and BH10. Used the observation data to analysis the infiltration time, built the GM(1,2),built the Markov Chain model final combined the grey system with Markov Chain.
After calculation could obtain the infiltration time Tbi.
BH05: infiltration time Tb5 =40hours. BH06: infiltration time Tb6 =40hours.
BH08: infiltration time Tb8 =39hours. BH10: infiltration time Tb10 =44hours.
According to the result, the best infiltration time in different well wasn’t the same. This because the field was a non-homogeneous and non-isotropic site, however the grey relational grade still had the similar trend.
In the built model process could find the average value of grey parameter c1 was 0.9996 and the average value of grey parameter c2 was 0.0561. After tested and verified Could obtain the average value of MAE was 5mm and the average value of RMSE was 8 mm. The verification accuracy was fairly good. Even I rise the forecast time from 1 hour to 24 hour the verification accuracy was still could accept.
In the Markov chin, after grey prediction I analyzed the disturbance value from 1 to 24 hours. I detected that if the time exceed 12 hours, the maximum and minimum disturbance value would produce unstable change. After analysis could find that the groundwater observation wells distribution were close to standard normal distribution. Therefore when used the Markov chin to prediction, the random variable must become normal distribution random variable. The prediction accuracy could be accept.
Finally I found that combined the grey system with Markov Chain, the prediction accuracy compared with the unbound before, is flat or slightly lower. This because the random predictions of Markov chin was a standard normal random distribution. Therefore the disturbance was a normal distribution random variable. The prediction value of disturbance only could project the disturbance range, the probability of its occurrence and average value but could not fully project the change.
摘要
ABSTRACT
誌謝
目錄
表目錄
圖目錄
Chapter 1 前言
1.1 相關文獻回顧
1.2 研究動機
1.3 研究目的
1.4 論文概要
Chapter 2 研究方法
2.1 灰色系統理論
2.2 資料處理
2.3 灰關聯分析
2.4 入滲時間分析
2.5 灰建模
2.6 擾動量計算
2.7 馬爾可夫鏈建模
2.8 結合灰色系統理論與馬爾可夫鏈進行地下水位預測
2.9 精度評估
Chapter 3 實驗方法
3.1 雲科大校園觀測場址
3.2 土壤物性分析及地下水位流向分析
3.3 地下水位觀測
3.4 降雨量觀測
3.5 觀測資料篩選
Chapter 4 結果與討論
4.1 入滲時間分析結果
4.2 灰色系統理論建模結果
4.3 馬爾可夫鏈建模結果
4.4 結合灰色系統理論與馬爾可夫鏈預測地下水位結果
4.5 討論
Chapter 5 結論
5.1 結論
參考文獻
Appendix 1
Appendix 2
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