Title

應用貝氏最大熵濾波器於地下水模型參數推估之研究-以濁水溪沖積扇為例

Translated Titles

Application of Bayesian Maximum Entropy Filter in parameter calibration of groundwater flow model in Choshui River Alluvial Fan

DOI

10.6342/NTU201603040

Authors

莊紹榕

Key Words

延伸卡曼濾波器 ; 貝氏最大熵濾波器 ; Extended Kalman Filer ; Bayesian Maximum Entropy Filtering

PublicationName

臺灣大學生物環境系統工程學研究所學位論文

Volume or Term/Year and Month of Publication

2016年

Academic Degree Category

碩士

Advisor

余化龍

Content Language

繁體中文

Chinese Abstract

由於水文地質觀測資料有限性以及高度不確定性,地下水模型參數推估一直是地下水文研究中一個重要的議題。在許多的參數推估方法中,卡曼濾波器能提供透過地下水量測以即時校準參數的方法,相關方法如延伸卡曼濾波器(Extended Kalman Filter)和集合卡曼濾波器(Ensemble Kalman Filter)在近年來都被廣泛應用於地下水參數推估的研究上。然而在具有高度不確定性的水文地質觀測下,卡曼濾波的方法無法考慮非高斯的不確性資料,。貝氏最大熵濾波器為一可考慮不確定性的參數推估方法。 本研究利用貝氏最大熵濾波器以同時考慮不確定性資料和確定性資料下進行參數推估。 本研究主要以Python及QGIS對地下水模型(MODFLOW)建模、結合延伸卡曼濾波器和貝氏最大熵濾波器演算法於濁水溪沖積扇的地下水參數推估上。推估的參數為水力傳導係數(Hydraulic Conductivity)和比儲水係數(Specific Storage)。嘗試在有限的觀測井資料和具有高度不確定性的資料下,進行參數推估。 本研究中有虛擬例子I,虛擬例子II和真實例子。在虛擬例子I共有6個案例。在案例1中加入了確定性資料為水位、水力傳導係數及比儲水係數;案例2至案例4則陸續加入邊界水位、水力傳導係數及比儲水係數的不確定性資料,而在案例5則是將邊界水位的不確定性資料取出,案例6和案例5加入的資料一樣,但是則將邊界水位設定成·不隨時間變化。虛擬例子II中共有3個案例,此虛擬例子則是考慮極少資料的情況,在案例7加入水位確定性資料;案例8和9則陸續加入邊界水位和水力傳導係數的不確定性資料。 在真實例子中,加入的水位觀測資料為1992年至2011年的地下水觀測井資料;水力傳導係數及比儲水係數則使用經濟部中央地質調查所的地質資料。利用以上資料,建立地下水模型並加入至延伸卡曼濾波器及貝氏最大熵濾波器進行參數更新。 結果顯示在虛擬例子I及虛擬例子II中,加入了不確定性資料下更新參數對推估的結果是有幫助。另外,加入的資料種類越多,對推估的結果越好。但在現實中,往往無法擁有那麼多資料。在例子7為僅使用觀測井水位資料進行多個參數更新。結果顯示,雖然在前期的更新效果沒那麼好,但隨著更新的時間增加,其更新的效率也逐漸變好。這也讓在資料缺乏的情況,此方法一樣能對參數進行更新。

English Abstract

Due to the limited hydrogeological observation and its high levels of uncertainty, therefore use of groundwater model to estimate hydrogeological study has been an important issue. There are many methods of parameter estimation, Kalman filter provides a real-time calibration of parameters through measurement of groundwater, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applying in groundwater research. However, due to the properties of the high uncertainty of hydrogeological data, Kalman Filter method does not consider the uncertainty of data. Bayesian Maximum Entropy Filtering provides a method can consider the uncertainty of data to parameter estimation. With this two methods, we can estimate parameter by given hard data and soft data in the same time steps. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation. There are total three cases in our research, which is the virtual case I, virtual case 2 and a real case. There are six cases in virtual case I. In case 1, input data are all hard data which is hydraulic water level, hydraulic conductivity, and specific storage; in case2 to case 4, we add soft data of boundary water level , hydraulic conductivity, and specific storage succesively. In case 5and 6, we remove the soft data of boundary water level; but in case 6, we assume that model boundary water level does not change over time. There is three cases in virtual case II, In this case, we only consider minimum data. In case 7,we only input hard data of hydraulic water level ; in case 8 and 9,we inout soft data of boundary water level and hydraulic conductivity. In real case, we use the data of obersvation data of water level from year 1992 to 2011; hard data of hydraulic conductivity and specific storage from Central Geological Servey.With the use of above data in modeling, create groundwater model with MODFLOW and integrate with Extended Kalman Filter and Bayesian Maximum Entropy Filtering in parameter estimation. Results show that in virtual case I and II, with the use of soft data in parameter estimation, will increase the precision of parameter estimation. But in reality, we do not have so much information. Therefore, in case 7,we only use the hard data of observation data of water level in parameter estimation. Eventhough, the effect of paramter estimation during prophase is not good, but with the time over in updating, the effect of parameter estimation has well performance. Therefore, in the case of lack of information, this method also can use is parameter estimation.

Topic Category 生物資源暨農學院 > 生物環境系統工程學研究所
生物農學 > 生物科學
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