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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 余化龍(Hwa-Lung Yu) | |
| dc.contributor.author | Yu-Zhang Wu | en |
| dc.contributor.author | 吳郁璋 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:37:16Z | - |
| dc.date.available | 2020-07-16 | |
| dc.date.copyright | 2020-07-16 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2020-07-10 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58894 | - |
| dc.description.abstract | 由於水文現象之複雜性及觀測資料的有限性，且水文課題具有高度的不確定性；為減少水文模型推估上之不確定性；貝氏最大熵法可融合一般性知識及特定性知識，本研究以延伸卡曼濾波器架構下結合貝氏最大熵法，發展出貝氏最大熵濾波器，以減少水文模型與觀測資料間的差距，本研究可分成兩個部分進行探討：(1) 以動差近似法探討模型狀態及參數之不確定性，以一維移流反應方程模擬河川污染物傳輸為例，污染物傳輸過程中流速及生物化學反應的不確定性，造成污染物度模擬結果具有高度的不確定性；(2)透過知識融合方法整合一般性知識及特定性知識，以減少水文模型之不確定性，並減少模型與觀測資料上的差距，以地下水模型MODFLOW為例，於人造二維地下水侷限含水層中進行數值試驗，依觀測資料分佈型態分成兩種方法進行，第一，所觀測資料若假設為高斯分佈則可以透過延伸卡曼濾波器進行資料同化；第二，若存在非高斯觀測資料，透過貝氏最大熵濾波器進行資料同化。 研究成果顯示，(1)來自物理方程式之統計動差可以透過動差近似法獲得，這些統計動差可以當成貝氏最大熵法一般性知識，(2)貝式最大熵濾波器可融合一般性知識及特定性知識，其推估成果可以以機率密度函數呈現，不受觀測資料分布型態的限制，直接透過非高斯觀測資料進行資料同化。若一般性知識及特定性知識都只取前二階動差，貝式最大熵濾波器推估結果與延伸卡曼濾波器相同，因此，貝式最大熵濾波器比延伸卡曼濾波器更為實用。 | zh_TW |
| dc.description.abstract | Due to the complexity of hydrological phenomena and the limitation of observation data, hydrological issues have high uncertainty. Therefore, in order to reduce the uncertainty of the hydrological model, this study developed the Bayesian Maximum Entropy Filter(BMEF). It is a data assimilation approach which is capable for considering non-Gaussian observations by integrating Extended Kalman Filter(EKF) method under Bayesian Maximum Entropy(BME) framework. The general knowledge and the specific knowledge is synthesized through BME framework, by reducing the gap between hydrological models and observational data. This study can be divided into two parts: (1) The Moment Closure Method is used for explore the uncertainty of the model state and parameters. Take simulating the uncertainty of contamination transportation in the river flow by the one-dimensional advection-reaction equation for example. The uncertainty of the velocity and biochemical reaction during the contamination transportation caused the simulation results of the contamination transportation in a highly uncertain. (2) Furthermore, the general knowledge and the specific knowledge are integrated through BME framework, thus reducing the uncertainty of MODFLOW, and similarly reducing the gap between the model and the observation data. Taking the groundwater model MODFLOW as an example, as the numerical experiments are conducted in a synthetic two-dimensional confined aquifer, it is divided into two methods according to the distribution of observation data. First, if the observed data are gaussian assumption, data assimilation can be performed through EKF. Second, if the observation data exist some non-Gaussian distribution (no distributional assumption), data assimilation well be performed through the BMEF. this study shows two results, (1) The statistical momentum from the physical equations can be obtained through the Moment Closure Method. These statistical moments can be used in the constraint of BME for general knowledge bases. (2) BMEF can integrate general knowledge bases and specific knowledge bases. BME framework can consider the soft data with no distributional assumption. BMEF can be directly performed through non-Gaussian observation data. The estimated results can be presented as probability density function. If the general knowledge and specific knowledge are only taken from the first two moments, the results of the two filters are the same. Therefore, BMEF is more practical than Extended Kalman Filter. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:37:16Z (GMT). No. of bitstreams: 1 U0001-0907202008175600.pdf: 5307970 bytes, checksum: 8a7b5f3b14522d906acb5ede5b30a2ce (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 目錄 第一章、前言 1 1.1、研究動機 1 1.2、研究目的 3 1.3、研究方法 4 1.4、本文架構 6 第二章、文獻回顧 9 2.1、不確定性 9 2.2、濾波器發展過程 11 2.3、貝氏最大熵法 13 2.4、統計動差觀點 14 第三章、理論 17 3.1、地下水數值模型 17 3.2、延伸卡曼濾波器(EKF) 19 3.3、貝氏最大熵濾波器(BMEF) 23 3.4、動差近似法 25 第四章、案例探討 31 4.1、延伸卡曼濾波器(EKF)案例探討 31 4.1.1、EKF案例設計 31 4.1.2、EKF案例結果 39 4.1.2.1、EKF案例水位推估結果 41 4.1.2.2、EKF案例水力傳導係數推估結果 44 4.1.3、EKF案例討論 49 4.2、貝氏最大熵濾波器(BMEF)案例探討 50 4.2.1、BMEF案例設計 50 4.2.2、BMEF案例結果 60 4.2.2.1、BMEF更新模型誤差指標 60 4.2.2.2、案例4、案例5及案例6水位更新成果分析 62 4.2.2.3、案例4、案例5及案例6水力傳導係數更新成果分析 66 4.2.2.4、案例4、案例5及案例6比儲水係數更新成果分析 68 4.2.3、BMEF案例討論 72 4.3、動差近似法案例探討 74 4.3.1、動差近似法案例設計 74 4.3.2、動差近似法案例結果 82 4.3.2.1、動差近似法案驗證方式 82 4.3.2.2、動差近似法應用於河川污染傳輸案例結果(案例7) 84 4.3.2.3、動差近似法應用於反應率為常態分佈河川案例結果(案例8) 91 4.3.2.4、動差近似法應用於流速為常態分佈河川案例結果(案例9) 99 4.3.2.5、動差近似法計算效率 105 4.3.3、動差近似法案例討論 108 第五章、結論與建議 111 5.1、結論 111 5.2、建議 113 5.3、本論文部分已發表成果 114 附錄1 方程式對照表 115 參考文獻 123 圖目錄 圖1研究流程架構 7 圖2人工場址 32 圖3含水層高層：頂部高層(左)及底部高層(右) 33 圖4場址上方變動水位邊界 33 圖5 (a)第1到第3個觀測井 (b)第4到第6個觀測井 (c)第7到第9個觀測井之水位資料 35 圖6 邊界水位(a) hb_1 (b) hb_2 (c) hb_3 (d) hb_4 (e) hb_5 (f) hb_6 (g) hb_7 (h) hb_8 (i) hb_9 (j) hb_10邊界水位內差值與真實值的關係 36 圖7對數水力傳導係數觀測資料與真實值的關係 37 圖8案例1分析及預報水位誤差平方和 圖 41 圖9案例2分析及預報水位誤差平方和 圖 42 圖10案例3分析及預報水位誤差平方和 圖 43 圖11預報的水位誤差平方和 44 圖12 與時間的關係 45 圖13案例3水力傳導係數推估結果 49 圖14人工場地中觀測及推估相關位置，●表示地下水水位觀測井位置，▼表示上方定水頭邊界位置，▲表示土壤種類觀測位置，⋆表示展現推估PDF位置。 52 圖15由圖14中山脈稜線邊界(hb_14)向下至海岸邊界之地層斷面圖 52 圖16(a)模擬含水層的頂層和(b)底部的高程 54 圖17邊界條件 (a)hb_1~hb_7 (b)hb_8~hb_12 (c)hb_13~hb_18 (d)hb_19~hb_23 水位變化的時間序列 55 圖18觀測井(a)h_1~h_4(b)h_5~h_8(c)h_9~h_12(d)h_13~h_16地下水水位觀測資料 56 圖19猜測上邊界水位(a)hb_1(b)hb_5(c)hb_9(d)hb_13(e)hb_17(f)hb_21水位資料 57 圖20土壤種類資料(a)對數水力傳導係數(b)比儲水係數資料區間與實際值(⋆)之間的關係 58 圖21地下水水位MSE 61 圖22案例6第2時刻中(a)K_1(b)K_2(c)K_3(d)K_4水位PDF 64 圖23案例6第46時刻中(a)K_1(b)K_2(c)K_3(d)K_4水位PDF 65 圖24案例6第63時刻中(a)K_1(b)K_2(c)K_3(d)K_4水位PDF 66 圖25水力傳導係數MSE 67 圖26案例6第2時刻中(a)K_5(b)K_6的水力傳導係數PDF 68 圖27比儲水係數估算中MSE 70 圖28案例6第2時刻中(a)K_5(b)K_6比儲水係數PDF 72 圖29污染物濃度一階動差邊界條件 75 圖30污染物濃度第1、2、4、6天邊界與內部位置之共變異係數關系圖 78 圖31 平衡時(超過10天)邊界點與內部點之共變異係數 78 圖32污染物濃度二階動差邊界條件 79 圖33 污染物濃度三階動差邊界條件 80 圖34案例7以動差近似法所得求得之污染物濃度(a)一階(b)二階(c)三階動差 85 圖35案例7不同時空間下濃度的變異數 88 圖36案例7不同時間下內部第一點( =2km )與不同距離的共變異係數 89 圖37案例7中動差近似法與蒙地卡羅法(a)一階(b)二階(c)三階動差比較圖 90 圖38案例8中動差近似法所求得污染物濃度(a)一階(b)二階(c)三階動差 92 圖39案例8動差近似法與蒙地卡羅法之(a)一階(b)二階(c)三階動差比較圖 96 圖40案例8不同時空間位置下濃度的變異數 97 圖41 案例8不同時間下內部第一點( =2km )與不同距離的共變異係數 97 圖42案例8不同時空間下污染物濃度之偏度係數 98 圖43 案例9中以動差近似法所得之污染物濃度(a)一階(b)二階(c)三階動差 100 圖44案例9動差近似法與蒙地卡羅法之(a)一階(b)二階(c)三階動差比較圖 103 圖45案例9不同時空間位置下濃度的變異數 104 圖46案例9不同時空間下污染物濃度之偏度係數 104 表目錄 表 1案例1、案例2及案例3使用觀測性資料 38 表2案例1 峰值 45 表3每年第一個月的 46 表4 案例4、案例5及案例6使用觀測性資料 58 表5每年地下水水位MSE峰值 63 表6每年水力傳導係數MSE峰值 68 表7每年比儲水係數MSE峰值 69 表 8 案例7-案例9使用參數差異 81 表9蒙地卡羅法不同抽樣數之耗時與 距離 106 表10 不同來源比例之偏度係數 107 | |
| dc.language.iso | zh-TW | |
| dc.subject | 參數校準 | zh_TW |
| dc.subject | 延伸卡曼濾波器 | zh_TW |
| dc.subject | 貝式最大熵濾波器 | zh_TW |
| dc.subject | 動差近似法 | zh_TW |
| dc.subject | 地下水模型 | zh_TW |
| dc.subject | Bayesian Maximum Entropy Filter(BMEF) | en |
| dc.subject | Moment Closure Method | en |
| dc.subject | Calibrations of parameters | en |
| dc.subject | Groundwater model | en |
| dc.subject | Extended Kalman Filer(EKF) | en |
| dc.title | 貝式最大熵法與資料同化方法之整合 | zh_TW |
| dc.title | Investigating Bayesian Maximum Entropy for Data Assimilation Approach | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 張倉榮(Tsang-Jung Chang),譚義績(Yih-Chi Tan),陳主惠(Chu-hui Chen),,羅偉誠(wei-cheng Lo) | |
| dc.subject.keyword | 延伸卡曼濾波器,貝式最大熵濾波器,動差近似法,參數校準,地下水模型, | zh_TW |
| dc.subject.keyword | Extended Kalman Filer(EKF),Bayesian Maximum Entropy Filter(BMEF),Moment Closure Method,Calibrations of parameters,Groundwater model, | en |
| dc.relation.page | 134 | |
| dc.identifier.doi | 10.6342/NTU202001402 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2020-07-10 | |
| dc.contributor.author-college | 生物資源暨農學院 | zh_TW |
| dc.contributor.author-dept | 生物環境系統工程學研究所 | zh_TW |
| 顯示於系所單位： | 生物環境系統工程學系 | |
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