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Global‐local optimization for parameter structure identification in three‐dimensional groundwater modeling
Author(s) -
Tsai Frank T.C.,
Sun NeZheng,
Yeh William W.G.
Publication year - 2003
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr001135
Subject(s) - mathematical optimization , global optimization , residual , mathematics , optimization problem , sensitivity (control systems) , parameter space , inverse problem , parameter identification problem , estimation theory , identification (biology) , algorithm , model parameter , statistics , mathematical analysis , botany , electronic engineering , engineering , biology
This paper develops two global‐local optimization methods for three‐dimensional parameter structure identification in groundwater modeling. Parameter structure identification is formulated in terms of solving a generalized inverse problem, which allows for a determination of an appropriate level of parameter structure complexity, and the identification of its pattern and the associated parameter values. The structure complexity is determined by calculating the parameter structure error measured in the prediction space or management space, while the structure pattern and the associated parameter values are identified simultaneously by minimizing the fitting residual measured in the observation space. The former requires solving a continuous maximum‐minimum (max‐min) optimization problem, and the latter requires solving a combinatorial optimization problem. In this paper, Voronoi zonation is used to parameterize the unknown distributed parameter. For each given level of structure complexity a sequential global‐local optimization method, which consists of a genetic algorithm, a quasi‐Newton method, and local search, is developed to solve the combinatorial problem. In addition, the continuous max‐min problem is transformed to a hierarchical optimization problem and solved by a hybrid global‐local method. Sensitivities of state variables to the unknown parameters are calculated by the sensitivity equations. The validity and applicability of the proposed methodology are demonstrated by numerical experiments. We have shown that the choice of an objective function in model application impacts the determination of the parameter structure complexity.