整合型優選演算法應用於分散式地下水模式之參數結構辨識

Abstract

本論文提出一整合型優選演算法應用於地下水模擬模式之參數辨識，其主要貢獻在於針對參數辨識之反向問題求解中最重要的兩項元素―參數化以及調整參數，進行最佳化處理；就參數化來說，本論文應用了三種分區方法―Voronoi diagram (VD)、multiplicatively weighted Voronoi diagram (MWVD)、以及 pattern zonation (PZ)，其中並將各分區方法加入內插技巧，進行水力傳導係數空間分佈之描繪應用，而每一種分區方法皆可視為此整合型優選演算法之部份元件。另外，本論文採用模擬退火法(simulated annealing algorithm, SA)以及禁忌演算法(Tabu search, TS)進行模式中參數的最佳化調整與辨識，其中更進一步利用伴隨狀態方法(adjoint state method, ASM)以及不同模擬網格大小之技巧，配合禁忌演算法改善模式參數辨識之效能與效率。 本論文並提出三個不同的應用，以証明此整合型優選演算法之可行性。首先利用模擬退火法以及Voronoi diagram進行台北盆地地下水侷限含水層參數結構之辨識；接著利用禁忌演算法配合三種不同的分區方法應用於假設案例，驗証其可行性；最後，採用禁忌演算法，配合伴隨狀態方法及不同模擬網格大小技巧，有效率地應用於片段均質以及連續型之水力傳導係數空間分佈之辨識。此外，模式的殘差、參數不確定性、模式結構誤差以及修正型的Akaike Information Criterion等多項指標，皆為本論文應用於模式複雜度之判斷依據，以避免過度參數化之情形發生。結果顯示，不論是模擬退火法、禁忌演算法或是禁忌演算法配合伴隨狀態方法，皆能有效地進行地下水模式之參數辨識。

The main contribution of this dissertation is proposing an integrated optimization algorithm for parameter structure identification in groundwater model simulation. The integrated optimization algorithm is applied to parameterization and parameter adjustment which are two essential components of solving inverse problems. As for parameterization, three zonation methods, Voronoi diagram (VD), multiplicatively weighted Voronoi diagram (MWVD), and pattern zonation (PZ), combined with the interpolation approach are presented in this dissertation to depict the spatial distribution of hydraulic conductivity. Each of these methods is able to be selected as a part of the integrated optimization algorithm. The simulated annealing algorithm (SA) and Tabu search (TS) are adopted in this dissertation to adjust the parameters. Moreover, the adjoint state method (ASM) and the coarse-fine grid search technique are allied with TS to enhance the efficiency in parameter adjustment. Three applications are represented in this dissertation to demonstrate the integrated optimization algorithm. First, SA and VD are used to identify the parameter structure of a confined aquifer. TS and three zonation methods are then applied to the parameter identification of hypothetical cases. TS allied with ASM are adopted with the coarse-fine grid search technique to identify both synthetically discrete and continuous hydraulic conductivity distribution efficiently and effectively. Meanwhile, the residual error, parameter uncertainty, structure error, and a modified Akaike Information Criterion values are used to help the determination of the model complexity over these applications. The results indicate that all SA, TS alone, and TS allied with ASM are able to optimize the parameter structure well.