
系統識別號 
U00261901201117505400 
論文名稱(中文) 
非均勻有理化基底雲形類神經網路之研究與應用 
論文名稱(英文) 
Study on NonUniform Rational BSplines Neural Networks and their Applications 
校院名稱 
成功大學 
系所名稱(中) 
電機工程學系碩博士班 
系所名稱(英) 
Department of Electrical Engineering 
學年度 
99 
學期 
1 
出版年 
99 
研究生(中文) 
吳宏文 
研究生(英文) 
HungWen Wu 
學號 
n2891108 
學位類別 
博士 
語文別 
英文 
論文頁數 
123頁 
口試委員 
指導教授鄭銘揚 召集委員張帆人 口試委員陳添智 口試委員蘇德仁 口試委員蔡聖鴻 口試委員莊智清 口試委員李祖聖 口試委員蘇文鈺

中文關鍵字 
非均勻有理化基底雲形
類神經網路
數位影像處理
行波超音波馬達
速度控制

英文關鍵字 
Nonuniform Bsplines (NURBS)
neural network
digital image process
traveling wave ultrasonic motor (TWUSM)
speed control

學科別分類 

中文摘要 
本論文之主旨在於針對非均勻有理化基底雲形類神經網路及其應用作深入探究。首先，基於非均勻有理化基底雲形曲線之概念，提出一嶄新的非均勻有理化基底雲形曲線類神經網路。由於行波超音波馬達特性複雜且其電壓對速度特性可用曲線表示，故將所提出之非均勻有理化基底雲形曲線類神經網路應用在行波超音波馬達之前饋補償器與回授控制器的設計問題上。其次，依據非均勻有理化基底雲形曲面之觀念，我們更進一步推演出一全新的非均勻有理化基底雲形曲面類神經網路。由於數位影像可用曲面方式描述之，故將所提出之非均勻有理化基底雲形曲面類神經網路應用於處理影像修補與影像壓縮問題上。在本論文所探討的非均勻有理化基底雲形曲線與曲面類神經網路中，其主要之架構乃以前饋式網路為其主體。與其他常見之類神經網路相較，其最大差異處在於第一層隱藏層中的活化函數是以基底函數取代常用的雙彎曲函數。同時，本論文採用倒傳遞演算法來完成非均勻有理化基底雲形曲線與非均勻有理化基底雲形曲面類神經網路中合宜控制點與權重值之學習。此外，本論文亦針對非均勻有理化基底雲形曲線與非均勻有理化基底雲形曲面類神經網路的相關參數值與節點值之選取方式以及應用流程作詳盡之描述與探討。最後，本論文提出數個範例並佐以模擬數據與實驗結果驗證所提方法之可行性與有效性。

英文摘要 
An indepth study on the NonUniform Bsplines (NURBS) neural networks and their applications is conducted in this dissertation. Firstly, based on the concept of the NURBS curve, the NURBS Curve Neural Network (NURBSCNN) is proposed. Since the characteristic curve that describes the relationship between the input voltage and the output speed for the traveling wave ultrasonic motor (TWUSM) is highly complex and nonlinear, the proposed NURBSCNN is applied to implement the feedforward compensator and speed controller for the TWUSM. Secondly, exploiting the idea of NURBS surface, the NURBS Surface Neural Network (NURBSSNN) is proposed. Since a digital image can be represented by a NURBS surface, the proposed NURBSSNN is employed to cope with the image compression and image restoration problems in this dissertation. Both the proposed NURBSCNN and NURBSSNN belong to the category of feedforward neural networks. Compared with other commonly used neural networks, the most significant difference is that the activation functions of the first hidden layers in the proposed neural networks are blending functions rather than the commonly used sigmoid functions. The backpropagation algorithm is exploited to learn appropriate values of the control points and weights in the proposed NURBSCNN and NURBSSNN. Moreover, the selection methods for the values of the corresponding parameter and knot vector in the NURBSCNN and NURBSSNN, as well as their application flowcharts, are elaborated upon and discussed in detail. The feasibility and effectiveness of the proposed approaches are demonstrated by several illustrative examples in this dissertation.

論文目次 
Abstract (Chinese) i
Abstract (English) ii
Acknowledgment iv
Contents v
List of Tables viii
List of Figures ix
Symbols and Abbreviations xiv
Chapter 1 Introduction 1
1.1 Motivation 2
1.2 Literature review 4
1.2.1 The application of NURBS on the control of TWUSM 4
1.2.2 The application of NURBS on image compression and restoration 6
1.3 Dissertation contributions 9
1.4 Dissertation organization 10
Chapter 2 Background of BSplines Curves and Surfaces 11
2.1 Introduction 11
2.2 Bspline curves 12
2.3 Degree of a Bspline curve 14
2.4 Control points 15
2.5 Parameterization and knot vectors 16
2.5.1 Parameterization 16
2.5.2 Knot vectors 21
2.6 Bspline basis functions 25
2.7 Bspline surfaces 31
2.8 Rational Bspline curves and surfaces 32
2.9 Summary 35
Chapter 3 NURBS Curve Neural Networks and NURBS Surface Neural Networks 36
3.1 Introduction 36
3.2 The proposed NURBSCNN 38
3.2.1 Derivation of NURBSCNN 38
3.2.2 Learning rules for updating the control points and weights of NURBSCNN 40
3.3 The proposed NURBSSNN 42
3.3.1 Derivation of NURBSSNN 42
3.3.2 Learning rules for control points and weights of NURBSSNN 44
3.4 Summary 46
Chapter 4 Design of Feedforward Compensator and Speed Controller for TWUSM Using NURBSCNN 47
4.1 Introduction 47
4.2 Feedforward compensator design for TWUSM using NURBSCNN 49
4.2.1 Parameterization for feedforward compensator 52
4.2.2 Determination of knot vectors for feedforward compensator 53
4.3 Speed feedback controller design for TWUSM using NURBSCNN 56
4.3.1 Parameterization for speed feedback controller 57
4.3.2 Determination of knot vectors for speed feedback controller 58
4.4 Speed control architecture for TWUSM 61
4.5 Simulation and experimental results 63
4.5.1 Simulation results of feedforward compensator 63
4.5.2 Experimental results of speed control 65
4.6 Summary 97
Chapter 5 Application of NURBS Surface Neural Networks to Digital Image Processing 98
5.1 Introduction 98
5.2 NURBS surface representation of a digital image 100
5.3 Image compression using NURBSSNN 102
5.3.1 Parameterization and knot vectors determination for image compression 103
5.3.2 Selection of compression ratio 104
5.4 Corrupted image restoration using NURBSSNNs 106
5.4.1 Parameterization for image restoration 107
5.4.2 Determination of knot vectors for image restoration 108
5.5 Experimental results 109
5.5.1 Experimental results of image compression 109
5.5.2 Experimental results of corrupted image restoration 111
5.6 Summary 112
Chapter 6 Conclusions 114
6.1 Conclusions 114
6.2 Further work 115
References 117
Publication List 122
Vita 123

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