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研究生: 謝鴻琳
Horng-Lin Shieh
論文名稱: 以模糊群聚為基礎的強健式函數趨近法
A Fuzzy-Clustering-Based Robust Approach of Function Approximation
指導教授: 楊英魁
Ying-Kuei Yang
口試委員: 黃漢邦
none
連耀南
none
鄧洪聲
none
蘇仲鵬
none
孫宗瀛
none
吳傳嘉
Chwan-Chia Wu
黎碧煌
Bih-Hwang Lee
學位類別: 博士
Doctor
系所名稱: 電資學院 - 電機工程系
Department of Electrical Engineering
論文出版年: 2006
畢業學年度: 94
語文別: 中文
論文頁數: 177
中文關鍵詞: 模糊模式函數趨近強健式
外文關鍵詞: Fuzzy modeling, Function Approximation, Robust
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  • 近年來,在科學應用上,對一個未知的系統行為函數建模(modeling)一直是非常重要的研究課題。但是當取得的系統知識不完整、口語化的知識表達或是以專家知識描述系統的操作行為等等,便無法以一個完整的數學模式對系統行為函數來建模。這個問題一直到模糊理論(fuzzy theory)被提出來,才有突破性發展,並逐漸發展成為系統建模的有效工具。
    但是,在實際應用系統的取樣資料中,由於各種因素影響,常常使得取樣資料中存有一般雜訊(noise)或大誤差(outlier)的資料。若將這些雜訊或大誤差資料直接使用在系統行為函數的建模上,往往使得所建立的系統模式與實際的系統行為產生很大的誤差,這種現象稱為「過度適應」(overfitting)。
    為了解決這個問題,本文提出一個非監督模糊建模方式,可直接由具有雜訊及大誤差的輸入-輸出取樣資料中擷取模糊規則,以建立系統行為的近似函數。所提方法主要有兩個特色:(1) 提出一個強健式 fuzzy c-means(RFCM)演算法,以降低雜訊及大誤差的影響。(2)提出一個模糊資料篩選器(FDS),可尋找資料轉折特徵點,藉以將一個非線性系統分割成片段的子系統組合。因此,可以建立起一個較少規則及較少誤差的Takagi and Sugeno模糊模式。本文中利用多個實驗證明所提方法可以用在不同的資料領域上,且在效能上,比其他方法好。


    In recent scientific applications, modeling an unknown system is a very important research subject. However, it is difficult to well model a system by mathematics model when the acquired system knowledge is incomplete, linguistic interpretations or expertise descriptions by experts. It had been no breakthrough on solving the problem until the proposal of fuzzy theory that has become one of efficient methodologies on system modeling.
    Due to influence of various factors, the sampling data used for system modeling often include noises and outliers. If such sampling data is directly being used to model a system, there will be a big difference, named overfitting, on the system behavior between the resultant modeled system and the actual system.
    To overcome this problem, this thesis presents an unsupervised fuzzy model construction approach to extracting fuzzy rules directly from numerical input–output sampling data for nonlinear systems bound with noises and outliers. There are two core ideas in the proposed method: (1) The robust fuzzy c-means (RFCM) algorithm is proposed to greatly mitigate the influence of data noises and outliers; and (2) A fuzzy-based data sifter (FDS) is proposed to locate good turning-points to partition a given nonlinear data domain into piecewise clusters so that a Takagi and Sugeno fuzzy model can be constructed with fewer rules and less errors. Several experiments are illustrated and their results have shown the proposed approach has good performance in various kinds of data domains with data noises and outliers

    第一章 緒 論 1 1.1 研究動機與目的 2 1.2 研究方法 4 1.2.1 系統建模(System Modeling) 4 1.2.2模糊建模(fuzzy modeling) 10 1.2.3 研究方法 15 1.3 論文架構 16 第二章 規則式模糊系統建模與函數近似的方法 17 2.1 規則式模糊系統 20 2.2 規則式模糊系統模式 22 2.2.1 語言式模糊模式(Linguistic Fuzzy Models) 22 2.2.2 模糊關係模式(Fuzzy Relational Models) 31 2.2.3 TSK規則式模糊模式(TSK rule-based fuzzy model) 35 2.3 函數近似的方法 39 2.3.1主要曲線的簡介 40 2.3.2 支持向量機器(SVM) 46 2.3.3 以模糊群聚為主的函數近似 49 2.4 強健式模糊群聚法(Robust Fuzzy Clustering ) 55 第三章 強健式模糊群聚演算法 63 3.1 以距離分析的模糊群聚資料分類 66 3.2 強健式模糊c-means 演算法 74 3.3 實驗結果與比較 84 3.4 本章結論 96 第四章 強健式函數趨近演算法 98 4.1 簡介 99 4.2 以資料分佈為基礎的群聚分割演算法 102 4.2.1 模糊資料篩選器組織架構 108 4.2.2 滑動窗與資料流 109 4.2.3 模糊轉折點特徵型樣與模糊轉折點吻合值 111 4.3 線性迴歸(Linear Regression) 121 4.4細調(fine-tuning) 124 4.5 實驗結果 128 第五章 結論與未來研究方向 153 5.1 結論及貢獻 154 5.2 未來研究方向 157 參考文獻 159 附錄 167

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