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研究生:黃彥禎
論文名稱:擴展式卡門濾波應用於滲漏水層參數之檢定
論文名稱(外文):Application of extended kalman filter for identifying leaky aquifer parameters
指導教授:葉弘德葉弘德引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:環境工程所
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:2002
畢業學年度:90
語文別:英文
論文頁數:60
中文關鍵詞:卡門濾波滲漏水層參數檢定
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本研究使用擴展式卡門濾波,檢定忽略及考慮滲漏層蓄水效應的滲漏水層參數。在忽略滲漏水層蓄水效應的例子中,針對拉格朗吉多項式內插得到等時距洩降資料,結合Hantush and Jacob的解透過卡門濾波遞迴演算的方式,可求得滲漏含水層三個參數的最佳值。在考慮滲漏層蓄水效應方面,同樣可運用結合卡門濾波與Neuman and Witherspoon的解,求得水層最佳的四個參數值。
本文所提方法可以快速的檢定得參數,利用部分觀測洩降數據就能得到良好的參數值,所以不必有長時間的抽水試驗。本研究方法可以應用在任意洩降時間段,因此在使用上沒有任何限制。檢定過程中,滲漏因子在最初時間段幾乎維持定值,此階段反應滲漏效應尚未影響水層的洩降,與受滲漏層影響的含水層抽水洩降的物理行為吻合。最後,為了瞭解數據若含有噪音對本方法分析結果的影響,本研究進行數據噪音的敏感度分析。分析的結果顯示,不論是白噪音或是有時間相關的噪音,對於檢定參數值的影響很小。

A method using extended Kalman filter (EKF) is presented to identify the aquifer parameters in leaky aquifer systems with and without considering the storage effect in the aquitard. In the case without considering the aquitard storage effect, the Hantush and Jacob’s solution combined with EKF can optimally determine the parameters for the leaky aquifer when analyzing the drawdown data interpolated by Lagrangian polynomial method. Coupled the Neuman and Witherspoon’s model, the EKF is also employed to estimate the four aquifer parameters.
The proposed method can quickly identify the parameters, using only part of observed drawdown data and the obtained parameters are shown to have good accuracy. In field implementation, combined with on site water level measurement and data logger, the long time of pumping test can be shortened. In the process of parameter identification the leakage factor changes marginally for the first few observations, which may be attributed to the fact that there is a time lag between the start of pumping and the leakage effect on the drawdown. Finally, for the purpose of exploring the influence of white noises and temporal correlated noises in drawdown data, the results of sensitivity analysis show that the EKF approach is still applicable.

CHINESE ABSTRACT………………………………………………….I
ABSTRACT………………………………………………….…………II
TABLE OF CONTENTS………………………………………………IV
LIST OF TABLES…………………………………………………….V
LIST OF FIGURES…………………………………………………….VI
NOTATIONS…………………………………………………………VII
CHAPTER 1 INTRODUCTION……………………………………..….1
1.1 Background………………………….………………………………………..1
1.2 Development and Evolution of Kalman Filter…………………………….....2
1.3 Objective and Scope of Study………………………………………………..3
CHAPTER 2 LITERATURE REVIEW………………….………..….…5
2.1 Theoretical Development………………………………..…………...….…5
2.2 Application of Kalman Filter to Identify Aquifer Parameter…….……….....7
CHAPTER 3 METHODOLOGY……………………………………..10
3.1 Discrete Extended Kalman Filter…………………………………………10
3.2 Lagrangian Polynomial……………………………………………………..14
CHAPTER 4 APPLICATION OF DISCRETE EKF…………………...16
4.1 Leaky Aquifer without Storage Effect in Confining Layer…………….….16
4.2 Leaky Aquifer with Storage Effect in Confining Layer…………………….19
4.3 Evaluation of ………………………………………………………..…22
4.4 Difference between the Present Study and Chander et al’s Work…………24
4.5 Lagrangian Polynomial Applied to Drawdown Data…………………….....24
CHAPTER 5 DATA ANALYSES AND DISCUSSION……………….26
5.1 Assessment for Estimation Errors……….………………………………….26
5.2 Parameter Identification for Leaky Aquifer without Considering Storage Effect..……………………………………………………………………..27
5.3 Parameter Identification for Leaky Aquifer with Considering Storage Effe………………………………………………………………………...29
5.4 Parameters Identification by Chander et al’s method…………...………….30
5.5 Sensitivity Test for the Measurement Noise………………………………...30
CHAPTER 6 CONCLUSIONS………………………………………..33
REFERENCES……………………………………………………...….35

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