整合最佳控制理論與類神經網路於地下水管理規劃

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(1)國立交通大學土木工程研究所博士論文. 整合最佳控制理論與類神經網路於地下水管理規劃 Applying Optimization Control Theory and Artificial Neural Network to Groundwater Management. 研究生：朱宏杰指導教授：張良正博士. 中華民國九十七年七月.

(2) 整合最佳控制理論與類神經網路於地下水管理規劃 Applying Optimization Control Theory and Artificial Neural Network to Groundwater Management. 研究生：朱宏杰. Student : Hone-Jay Chu. 指導教授：張良正. Advisor : Dr. Liang-Cheng Chang. A Thesis Submitted to Department of Civil Engineering National Chiao Tung University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Civil Engineering July 2008 Hsinchu, Taiwan, Republic of China. 中華民國九十七年七月.

(3) 謝誌在交大七年的研究生涯，感謝吾師張良正教授對於本論文之指導及研究生涯中對學生工作態度及學問研究之啟發，尤其對研究上的觀念與原則，經由與老師的討論，使學生受益匪淺。承蒙口試委員台灣大學徐年盛、童慶斌等教授，逢甲大學陳昶憲教授及交通大學洪士林、單信瑜等教授、中州技術學院蕭金財教授及水利署張國強博士，細心指正審閱拙文，並於口試時給予寶貴之意見，使本文更加完備，在此謹致衷心謝意。我的研究方向延續著張老師與財哥的研究，應用最佳化控制理論於地下水管理。回顧我的研究生涯，前幾年相當辛苦，雖然不斷的嘗試既新穎又有前瞻性研究的題目，卻一直沒有突破，越走越狹隘，後來，直到研究團隊中學弟浚瑋成功應用類神經網路做長期的連續預測地下水位，再經由張老師與金財、宇文學長的啟發後，想到可以將最佳化控制理論與類神經網路的研究相互結合，於是才有這篇論文的產生。這一路走來要感謝太多的人，這篇論文是屬於整個張老師的研究團隊，絕非一個人就能夠完成，包括財、仲、輝、生、文、超等學長及 Steve 的耐心指教，以及一大堆學弟與學妹的幫忙及合作，沒有你們我無法辦到，由衷地感謝大家。除此之外，我要感謝我的家人對我的支持，包括父母以及老婆，以及週遭支持、關心我的人們，謝謝你們對於我的提攜與照顧。. 朱宏杰謹致於交通大學土木研究所 97 年 7 月.

(4) 整合最佳化理論與類神經網路於地下水管理規劃學生：朱宏杰. 指導教授：張良正博士國立交通大學土木工程研究所. 摘要地下水資源的妥善管理實為當前水資源管理的重要課題，且就技術上而言，地下水管理規劃是個複雜的非線性動態的問題。一般而言，地下水位或污染團會隨時間而變動，因此合理的策略應配合系統的時變而變化，由於此種時變的特性，若應用傳統的非線性規劃或是較新的啟發式演算法等於地下水管理規劃時，將會產生因變數過多而造成計算量大增的困擾。微分動態規劃 (Differential Dynamic Programming)為求解動態系統優化策略的最佳方法之一，惟其計算量仍隨著狀態變數數目的增加而快速增加，因而限制其應用於大型實際案例。有鑑於此，本研究結合微分動態規劃及類神經網路(Artificial Neural Network)兩者，以微分動態規劃為優選模式之整體演算架構，嵌入類神經網路作為系統轉換函數，以類神經網路進行長期預測地下水位與汙染濃度變化，其訓練資料以地下水流與汙染傳輸數值模式產生。藉由類神經網路，地下水系統可以少數且關鍵的狀態變數來代表，有效降低狀態變數數目，使得計算量大幅降低。研究結果顯示，以 315 個節點為例，本研究發展之地下水水量管理模式之計算時間約為傳統演算法的 1/74; 以 364 個節點為例，本研究發展之地下水水質管理模式之計算時間約為傳統演算法的 1/26，計算效率皆有大幅提升，且可兼顧模擬的精確度，因而大為增加模式的應用價值。. I.

(5) Applying Optimal Control Theory and Artificial Neural Network to Groundwater Management Student：Hone-Jay Chu. Advisor：Dr. Liang-Cheng Chang. Department of Civil Engineering National Chiao Tung University Abstract Groundwater resources management is an important issue in water resources management and is a dynamic nonlinear problem from a system analysis point of view. Influenced by time-varying pumping and other hydrological conditions, groundwater flow or plume transport in a groundwater system varies in time and space. The optimization algorithms such as nonlinear optimization algorithms or heuristic methods have been applied to solve groundwater management problems. On the other hand, optimization algorithms based on the dynamic programming can solve dynamic optimization problems efficiently. However, the computational loading of a dynamic programming-like algorithm still increases proportionally to O(n3); where n is the total number of state variables. Following in previous researches, this study presents a novel approach for resolving groundwater management problems by applying a hybrid algorithm that combines a constrained differential dynamic programming (CDDP) with an artificial neural network (ANN). The ANN model is embedded in CDDP as a transfer function is to simulate the variation of groundwater level and distribution of pollutants plume caused by pumping. The training data in the ANN model was obtained by. II.

(6) repeating simulations of proposed hypothesis cases with varying pumping scenarios using the groundwater numerical model. By using the ANN model, the number of state variables was greatly decreased compared with embedding a numerical simulation model, thus greatly reducing computational requirements. Simulation results indicate that the proposed novel ANN-CDDP model requires only 1/74 the computing time of a conventional CDDP model for a groundwater supply problem with 315 total nodes, and requires only 1/26 the computing time of a conventional CDDP model for a groundwater remediation problem with 364 total nodes. The results show that the proposed model is capable of solving large field groundwater management problems.. III.

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