以伴隨狀態法及小波分析增進延伸卡曼濾波器對地下水參數推估之效率

Applying Adjoint State Method and Wavelet Analysis to Extended Kalman Filter to Enhance the Efficiency on Groundwater Parameter Estimation

張丁心(Ting-Hsin Chang)

指導教授 ： 余化龍

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201703765

摘要

參數推估在地下水模型當中有很重要的地位。當我們在建立地下水模型時，需要水文地質參數才能夠執行，但是由於土壤的異質性使得地下水參數推估有很高的不確定性。因此，本研究利用延伸卡曼濾波器來解決這樣的問題。延伸卡曼濾波器為一遞迴型的最佳化運算模式，可以處理非線性動態系統的推估問題。除此之外，由於卡曼濾波器的計算過程中，狀態轉換函數會需要耗費比較多的時間，因此，使用伴隨狀態法來增進計算效率。另外，當地下水問題中有考慮抽水補注的時候，加入頻率分析的方法，如小波分析及經驗正交函數分析，先用小波分析過濾出所要分析的頻率，再用經驗正交函數找出抽水補助的特徵。
本研究共有四個模擬試驗，前面三個是在局限含水層。第一個和第二個模擬試驗是用來驗證伴隨狀態法對計算效率的提升。第三個則是考慮抽水補注，當作其中需要推估的參數。第四個則是與其他三個不同，考慮在非侷限含水層中狀況。本研究提供了參數推估當中，結合多種數學方法的新思維。

關鍵字

伴隨狀態法 ； 經驗正交函數 ； 延伸卡曼濾波器 ； 地下水 ； 參數推估 ； 小波分析

並列摘要

Parameter estimation is a significant region in groundwater modeling. When constructing groundwater model, hydrogeological parameters are necessary. However, the observation data of parameters is not sufficient. Moreover, because of the heterogeneity of soil, parameter estimation contains high uncertainty. Therefore, Kalman Filter is applied to handle this issue. In addition, to improve the computational ability, Adjoint State Method replaces the conventional method while calculating State Transition Matrix in Kalman Filter process. Moreover, signal analysis method, such as Empirical Orthogonal Function (EOF) and Wavelet Analysis, can enhance the capability of Kalman Filter when dealing with problem containing sink/source. This study contain four simulation cases. The first case and the second case is a set of comparison which aims to validate that the Adjoint State Method can improve the efficiency of Kalman Filter. The third case contains the situation with sink/source. Frequency analysis methods are joined in this part. Different from another three cases, the fourth case is under the situation of unconfined aquifer.This study provides a new viewpoint which combine several methods to handle groundwater parameter estimation.

並列關鍵字

Ajoint State Method ； Empirical Orthogonal Function ； Extended Kalman Filter ； groundwater ； parameter estimation ； Wavelet Analysis

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