改良動態維度搜尋法於地下水模式參數檢定 之應用

Abstract

動態維度搜尋法(Dynamically Dimensioned Search Algorithm)係由Bryan Tolson於2007年所發表的新型態搜尋演算法，屬於一種啟發式演算法(Heuristic Algorithm)，適用於高維度之優選問題，亦曾應用於地下水模式參數檢定問題中，惟若應用原始之動態維度搜尋法，各個參數之更新機率皆是相同，而此將使得演算法後期之參數更新效率相對不佳，因此為提高此演算法應用於地下水參數優選之適用性，有必要針對此進行改進。 本研究將以地下水參數優選為目標，改良原始動態維度搜尋法之參數選定及更新方式，以提高整體參數優選模式之效率。其中選定參選進行更新之機率，從原來之均勻分布修正為以水位誤差大小決定選取機率，參數修正量之正負號亦以水位誤差為參考。本研究為進一步提高收斂效率，亦探討修正鄰近擾動參數，分階段進行參數檢定之效率，並分別以設計案例及濁水溪沖積扇現地模式進行探討，由於動態維度搜尋法具隨機性，因此每項探討皆重複20次計算，再觀察其目標 函數收斂值的平均值與標準偏差，研究結果顯示，修正後的動態維度搜尋法及分階段優選，皆能夠大幅地改善檢定效率。其中濁水溪沖積扇之檢定結果中，各分區之觀測水位與模擬水位的相關係數高達0.999以上，且檢定出來的淨補注量分布，符合現地土地利用之狀況，可間接驗證其檢定結果之可信度，本研究提出之修正型動態維度搜尋法及分階段優選方式，具效率性及容易使用，可為地下水參數檢定之良好工具。

This study modifies Dynamically Dimensioned Search Algorithm (DDS), which is a heuristic algorithm developed by Bryan Tolson in 2007, for high dimension optimization problems. The proposed algorithm is applied to a parameter identification problem of groundwater problems. The original DDSA assumes equal probability of parameter selection for update and decreasing number of selected parameters while the number of iteration is increasing. These assumptions reduce the efficiency of the search process due to predefined maximum number of iteration and the difficulty of selecting proper parameters especially when the number of iteration is large. This study modified these limitations using a new parameter selection mechanism based on error information obtained from state variables, higher selection probability for higher error, to improve the selection and update of the parameters. The proposed algorithm is applied to highly dimensional parameter identification problems: (1) a hypothetical groundwater simulation model and (2) the groundwater basin of Chou-Shui River Alluvial Fan. In this application, the state variable is groundwater level. To evaluate the convergence efficiency, several scenarios are used and 20 simulation runs are repeated for each scenario. The mean and standard deviation of the optimal objective values show that the proposed algorithm and two-phase search, which mimics global-local search using different step sizes, obtain best results. The relation coefficient between the simulated and observed water levels in the case of Chou-Shui River Alluvial Fan is 0.999. The identified groundwater recharge agrees with the land use which can be seen as indirect verification of the proposed algorithm.