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。

An in-depth study on the Non-Uniform B-splines (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 back-propagation 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.

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