使用加成性高斯歸屬函數之模糊類神經網路

Abstract

本論文是以模糊類神經網路（Fuzzy Neural Network）為基礎，提出一個調整歸屬函數的新方法。我們首先介紹模糊類神經網路，此網路具有模糊邏輯及神經網路的特性。第二部份證明高斯函數可以由數個標準差較小的其他高斯函數所組成。第三部份為修改模糊類神經網路的歸屬函數成為五層模糊類神經網路（FNN5）。第四部份利用五層模糊類神經網路去近似幾個函數並證明五層模糊類神經網路是一個廣泛近似器。最後，我們將這個方法應用到調整比例積分（PI）控制器。我們經過模擬後，發覺模糊類神經網路與五層模糊類神經網路在精確度的要求上，都有很良好的模擬結果，但是五層模糊類神經網路在微調時，比模糊類神經網路更具有精確的效果。

In this thesis, a new method to tune the membership functions of fuzzy neural network (FNN) is presented. First we study the FNN it inherits the property of both fuzzy inference system and neural network. Then we present that any gaussian function can be represented by the linear combination of gaussian functions with small standard deviation. Therefore, it can be substituted for the second layer of FNN (called FNN5). We use the FNN5 to approximate some functions and prove that it is a universal approximator. Furthermore, apply this proposed method to tune PI controller based on gain phase margin (GPM) specifications. Both FNN and FNN5 have high performance by the simulation verification, however FNN5 is more accurate than FNN on fine-tuning. Abstract (English) ii Acknowledgements iii Contents iv List of Figures vi List of Tables viii 1 Introduction 1 2 Fuzzy Neural Network 4 2.1 Fuzzy Inference System and Neural Network 4 2.2 Structure of the FNN 7 2.3 Basic Nodes Operation 9 2.4 Supervised Gradient Descent Learning 12 3 Approximations by Using Gaussian Functions 16 3.1 Universal Approximation Theorem 17 3.2 Examples 22 3.3 Composition of the Membership Functions of FNN 25 4 Additive Gaussian Membership Function in Fuzzy Neural Network 26 4.1 Structure of the FNN5 27 4.2 Layer Operation of the FNN5 29 4.3 Supervised Learning 32 4.4 Initialization 34 4.5 Convergence 36 5 Simulation Results 39 5.1 Example 1： 39 5.2 Example 2： 43 5.3 Example 3： 47 5.4 Example 4： 52 6 Conclusion 57 Bibliography 58