動態維度搜尋法應用於河川不恆定流模式自動率定之研究

Abstract

動態維度搜尋法（Dynamically Dimensioned Search Algorithm）係由Bryan A. 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）。 本研究應用動態維度搜尋法於全流域河川不恆定流模式（Wu et al., 2007）之阻力參數率定最佳化研究，並以淡水河流域作為研究區域，選取2007年流域中重大的柯羅莎颱洪事件之洪水位觀測資料，進行河川阻力參數率定。率定完成後，再利用不同颱洪事件（韋帕颱洪與米塔颱洪，2007）之洪水位觀測資料來驗證動態維度搜尋法之適用性。其中，以新海橋、河口、中正橋、大華橋作為河川上游邊界點，在研究區域中依河道特性分為20個河段（reach），每個河段同時率定中低水位阻力參數與高洪水位阻力參數，共計有40個待定參數。 本研究問題在前人的研究中（詹明修，2004）與（黃怡君，2006），均是以遺傳演算法（Genetic Algorithm）做為主要的搜尋法則。雖然遺傳演算法在高維度求解空間中具有良好的搜尋能力，但由於可行求解空間（Feasible Region）過於龐大（41^16×61^24~10^68），加上遺傳演算法較為複雜的演算流程，使得求解效率偏低，亦即在率定出合理的參數之前，所需花費的計算時間過長，故本文嘗試利用動態維度搜尋法，建立一個可以在合理時間內自動率定出一組可靠最佳解的方法。 研究結果顯示：本文所使用的方法於率定全流域河川不恆定流模式之阻力參數上，除了可使模式較過往研究成果更加精確地描述淡水河流域的流況外，在率定成果的效率及穩定度上亦有所提升，故此動態維度搜尋法確實為一兼具有多樣性與強健性的自動化參數率定方法。

Dynamically dimensioned search algorithm is a new type of heuristic algorithm which was originally developed by Bryan A. Tolson in 2007. In this study, the dynamically dimensioned search algorithm is applied to automate the calibration process of a unsteady river flow model（Wu et al., 2007）in the Tamshui river basin. The observed data of Krosa（2007）typhoon flood levels are used for calibrating the resistance coefficients. Different flood events, Wipha（2007）and Mitag（2007）typhoons , are used to verify the applicability of calibrated resistance coefficients. In the studied area, the whole river systems are divided into 20 reaches, and each reach has two resistance coefficients（n_d and n_u）to be determined. Automatic calibration proposed in the past (Chan, 2004；Huang, 2006) are based on genetic algorithms which has potentials of solving high-dimension space with good search capabilities. Since the feasible solution region in the unsteady river flow model (CCCMMOC) is too large（41^16×61^24~10^68），the complex calculus process of the genetic algorithm becomes inefficient. As a result, the dynamically dimensioned search algorithm is proposed to calibrate automatically an optimal solution set in a reasonable period of time. The results showed that the dynamically dimensioned search algorithm is not only improving on the efficiency but also increasing the stability of calibrated results. Therefore, the dynamically dimensioned search algorithm is indeed a diverse and robust method for automatic calibration of the unsteady river flow model, CCCMMOC.