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研究生: 陳憲宗
Chen, Shien-Tsung
論文名稱: 支撐向量機及模糊推理模式應用於洪水水位之即時機率預報
Real-time Probabilistic Flood Stage Forecasting Using Support Vector Machines and Fuzzy Inference Model
指導教授: 游保杉
Yu, Pao-Shan
學位類別: 博士
Doctor
系所名稱: 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年: 2006
畢業學年度: 94
語文別: 英文
論文頁數: 196
中文關鍵詞: 模糊推理模式支撐向量機模式更新機率預報蘭陽溪洪水水位
外文關鍵詞: Lan-Yang River, flood stage, updating, probabilistic forecasting, support vector machines, fuzzy inference
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  • 即時洪水預報模式為重要且實用的非工程性洪災消減措施,本研究以洪水水位為預報變量,應用支撐向量機及模糊推理模式來發展洪水預報模式,即時預報蘭陽大橋未來一至六小時的洪水水位及其機率分布。
    首先採用發展自統計學習理論的支撐向量機來建構定值水位預報模式,以水文反應時間的觀點來考慮輸入變量的階數,並依此建立三種不同架構的水位預報模式進行比較與探討;為克服傳統上以試誤法推估支撐向量機參數的缺點,本研究採用兩階段格網搜尋法配合交互驗證來進行系統化且較徹底的參數優選。經由六場洪水事件的驗證,結果顯示支撐向量機模式均具有良好的水位預報效能,且證實變量階數決定方法的合理性。
    接著針對支撐向量機水位預報模式的預報誤差序列,分別建立支撐向量迴歸與線性迴歸二種誤差修正模式來即時更新水位預報值,並藉由誤差序列的統計分析與檢定來探討模式更新修正的效能。
    最後本研究採用模糊推理模式來進行水位的機率預報,方法為改進模糊推理過程中的解模糊化步驟,使得模糊推理的輸出結果為機率函數;利用此方法估算水位預報誤差的機率分布,再結合支撐向量機水位預報模式的定值預報水位,則可得到洪水水位的即時機率預報值。經由水位歷線的區間預報及超過警戒水位的洪水案例探討,可實際展示機率水位預報的實用性。

    A flood warning system is a crucial non-structural approach for flood mitigation, and the essential part of the system is a real-time flood forecasting model. The flood stage, a more relevant variable than the discharge in practice, is used as the output variable to establish a real-time probabilistic flood forecasting model in this study. The Lan-Yang River was chosen as the study basin, and 18 flood events for model calibration and validation were extracted from collected hourly river stage and rainfall data.
    The support vector machine, a novel artificial intelligence-based method developed from statistical learning theory, was adopted to construct a deterministic flood stage forecasting model. The lags of the input variables are determined by applying the hydrological concept of the time of response, and a two-step grid search method is applied to find the optimal parameters, and thus to overcome the difficulties in constructing the learning machine. Two structures of models and a pruned model were developed to perform one- to six-hour-ahead stage forecasts.
    Two error correction models were then proposed to update the deterministic stage forecasts. The forecasting and updating performance was assessed by statistical tests pertaining to the forecast error series. The results demonstrate that although the deterministic stage forecasts are satisfactory, the updating method still can enhance the model performance to a small extent.
    Finally, the probabilistic flood stage forecasting was performed by applying a fuzzy inference model. This study modified the defuzzification process in order to produce probability distributions pertaining to the forecast errors that quantify the total uncertainty of the forecasting. The probabilistic stage forecasts can then be constructed by adding the error distributions to the deterministic stage forecasts. Consequently, the real-time probabilistic flood stage forecasting can be performed, and its applicability is demonstrated.

    Abstract i Acknowledgments iv Table of Contents v List of Tables ix List of Figures xi Chapter 1 Introduction 1 1.1 Motive and Subject Matter 1 1.2 Literature Review 4 1.2.1 River Stage Forecasting 4 1.2.2 Updating Method 4 1.2.3 Probabilistic Forecasting 5 1.2.4 Support Vector Machines 7 1.2.5 Fuzzy Inference Model 8 1.3 Overview of the Dissertation 9 Chapter 2 Support Vector Machines 13 2.1 Statistical Learning Theory 13 2.1.1 Machine Learning 13 2.1.2 Empirical Risk Minimization 14 2.1.3 Structural Risk Minimization 15 2.2 Support Vector Classification 18 2.2.1 Linear Support Vector Classification 18 2.2.2 Linear Support Vector Classification with a Soft Margin 22 2.2.3 Nonlinear Support Vector Classification 24 2.2.4 Kernel Function 26 2.3 Support Vector Regression 27 2.3.1 Linear Support Vector Regression 27 2.3.2 Nonlinear Support Vector Regression 30 2.4 Parameters of Nonlinear Support Vector Regression 33 2.4.1 Choice of Kernel 33 2.4.2 Properties of Parameters 34 2.5 Parameter Optimization 35 Chapter 3 Fuzzy Inference Model 37 3.1 Fuzzy Set Theory 37 3.2 Fuzzy Inference Model 39 3.2.1 Fuzzifying Inputs 39 3.2.2 Formulating Fuzzy Rules 40 3.2.3 Fuzzy Inference 41 3.2.4 Defuzzification 43 3.3 Other Types of Inference Mechanisms 44 3.3.1 Tsukamoto’s Fuzzy Inference Model 45 3.3.2 Takagi-Sugeno Fuzzy Inference Model 45 3.4 Defuzzification into a Probability Distribution 46 3.4.1 Basic Defuzzification Distributions Transformation 47 3.4.2 Importance Sampling Technique 48 Chapter 4 Study Area and Hydrologic Data Analysis 51 4.1 Study Area and Data Sets 51 4.2 Data Analysis and Processing 58 4.2.1 Determining Input Variables 58 4.2.2 Determining Lags 58 4.2.3 Normalizing Data 60 Chapter 5 Flood Stage Forecasting Model 65 5.1 Parameter Calibration 65 5.2 Real-time Forecasting Models 68 5.2.1 Model Structure Type I 68 5.2.2 Model Structure Type II 68 5.3 Criteria for Model Performance 72 5.4 Forecasting Results 76 5.5 Pruned Model 78 5.5.1 Model Construction 78 5.5.2 Forecasting Results 98 Chapter 6 Real-time Updating 109 6.1 Updating Methodology 109 6.1.1 Classification of Updating Methods 109 6.1.2 Error Correction 111 6.2 Statistical Analysis of Error Series 111 6.3 Updating by Error Correction 122 6.3.1 Error Correction Models 122 6.3.2 Results and Discussions 124 Chapter 7 Probabilistic Flood Stage Forecasting 145 7.1 Probabilistic Forecasting 145 7.2 Predictive Probability by Fuzzy Inference 148 7.3 Probabilistic Stage Forecasts 152 Chapter 8 Conclusions 181 8.1 Concluding Remarks 181 8.2 Suggestions and Future Directions 182 References 185

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