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標題: | 貝式最大熵法與資料同化方法之整合 Investigating Bayesian Maximum Entropy for Data Assimilation Approach |
作者: | Yu-Zhang Wu 吳郁璋 |
指導教授: | 余化龍(Hwa-Lung Yu) |
關鍵字: | 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, Extended Kalman Filer(EKF),Bayesian Maximum Entropy Filter(BMEF),Moment Closure Method,Calibrations of parameters,Groundwater model, |
出版年 : | 2019 |
學位: | 博士 |
摘要: | 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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58894 |
DOI: | 10.6342/NTU202001402 |
全文授權: | 有償授權 |
顯示於系所單位: | 生物環境系統工程學系 |
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