應用遺傳演算法與參數優選於地下水最佳觀測

Abstract

本研究目的為應用遺傳演算法(Genetic Algorithm)結合試驗設計原理，發展一以二維地下水流模式參數檢定為目的之最佳井網設計模式。在本研究中，試驗設計部份採用D-Optimal準則，而D-Optimal之內涵，為求取使得估計參數變異數矩陣行列式值為最小之設計組合，即使得估計參數之可靠度為最大，文中所探討之最佳井網設計目標，經合理簡化後，表示為取樣點數量及位置的函數。任一組井網設計結果，乃使用遺傳演算法(Genetic Algorithm)進行近似全域的搜尋，而得在一定成本限制下使估計參數可靠度達到最大之觀測井網佈置。 本文之水流數值模式及參數檢定模式，乃採用美國地質調查局(U.S.G.S.)所發展之MODFLOW及MODFLOWP程式。MODFLOWP程式乃是將非線性迴歸理論與MODFLOW程式結合，藉以優選由MODFLOW所建立之地下水流模式中的參數，並且得到估計參數的敏感度矩陣。最後，本文自行設計一虛擬之區域地下水流系統，運用數值算例，測試本研究所設計之井網佈置最佳化系統的成果。

This research is to develop a groundwater monitoring network design model by integrating the Genetic Algorithms (GA) and experiment design theory. The goal of experiment design is to minimize the estimated parameters' variance that can be expressed with the covariance matrix. Base on the D-Optimal criteria the algorithm seeks the number and locations of the sampling sites that minimize the determinant of the matrix, i.e., maximize the reliability of the estimated parameters. . This research apply the Genetic Algorithm, one of the global search algorithm, to search the optimal well locations, and the MODFLOWP developed by U.S.G.S. to implement the parameter optimization and compute the sensitivity matrix. The sensitivity matrix is then used to calculate the covariance matrix. Constrained by the available resources, the solution is the optimal network layout with the minimum parameter estimation covariance. At last, numerical examples are presented to demonstrate the results with the design system.