模糊類神經網路分析及其應用

Abstract

本論文針對所提出之模糊類神經網路(Fuzzy Neural Network, FNN)的特性做分析並提出此系統的應用。簡單來說，模糊類神經網路即是一個具有模糊推論能力之類神經網路，它結合了類神經網路與模糊邏輯兩者之優點。首先，我們探討FNN系統中，近似函數的精確度與其模糊歸屬函數之關係。並提出一調整歸屬函數的新方法，來增進FNN系統的近似精確度；此方法與一般常使用的對稱形態（三角、鐘型、高斯函數）之歸屬函數有所不同，經由逆傳遞法則的調整可產生特殊形狀的模糊歸屬函數，由模擬結果可知確實提高系統的近似精確度。 接著，我們使用FNN系統提出了幾種應用，其中包含設計PID控制器（基於增益與相位餘量，gain and phase margins）、Hammerstein系統的辨識與控制、模糊法則的簡化。在基於增益與相位餘量的PID控制器設計上，我們採用FNN來近似增益與相位餘量與PID係數間的關係，使用者只要給定適當的需求（規格）並輸入FNN，即可得到PID控制器。藉由此一方法可得到精確的結果並省去大量數值運算。接著，FNN被使用在Hammerstein系統的辨別與控制上，Hammerstein系統是一個由線性動態系統與非線性函數所組成的連結系統(cascade system)，其中靜態非線性函數與動態系統分別由FNN與ARMA (auto-regressive moving average)系統辨別，在此因為使用FNN而提高了辨別的精確度，並透過另一個FNN系統的訓練來解決此一系統的控制問題。最後我們利用FNN的特性(適應性的模糊歸屬函數與特殊的模糊分割)來簡化模糊控制法則。經由本論文中的模擬與應用結果可驗證FNN系統的高性能與可行性。 最後，基於此FNN系統，我們提出一遞迴式的機制，稱之為遞迴式模糊類神經網路(Recurrent Fuzzy Neural Network, RFNN）。RFNN的建構是由FNN推展而來，我們將FNN的第二層加入含有加權參數的迴授訊號，如此我們成功的將FNN的應用擴展至動態時間問題領域。因此RFNN擁有動態記憶之能力，以解決時間序列之動態問題；此外，RFNN系統以遞迴式多層網路實現了模糊推論引擎，亦保有原有FNN之特性(廣泛近似能力、學習機制、模糊推論能力與參數收斂特性等)，因此RFNN可說是FNN系統的一般化形式。在論文中，我們使用RFNN來解決非線性動態系統的辨別與控制問題，以驗證其可行性。

In this dissertation, we investigate a fuzzy neural network (FNN) system that combines the advantages of the fuzzy logic and neural network systems. The FNN system is a straight-forward implementation of fuzzy inference system with four layered network structure. This system combines the advantages of the fuzzy logic control and neural networks. Base on this FNN system, a recurrent structure of the FNN (RFNN) are proposed in this dissertation. The RFNN is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules. Temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network (FNN). Results for the FNN -fuzzy inference engine, universal approximation, and convergence analysis are extended to the RFNN. Moreover, the RFNN extends the basic ability of the FNN to cope with temporal problems. Subsequently, we discuss the relationship between membership and mapping accuracy of the FNN system. A new method to fine-tune the Gaussian membership functions of the FNN is proposed to improve the approximation accuracy which subverts the commonly used property of membership functions. For illustrating the effectiveness of our approach, several applications of the FNN are also presented, including the PID tuning method based on gain and phase margin specifications, identification and control of Hammerstein systems, and fuzzy rules Acknowledgement i Abstract in Chinese ii Abstract in English iv Contents v List of Figures vi List of Tables xi 1 Introduction 1 1.1 Introduction and Motivation．．．．．．．．．．．．．．．．．．．．．．．．．． 1 1.2 Research objectives．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．2 1.3 Overview．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．3 1.3.1 Organization of this dissertation ．．．．．．．．．．．．．．．．．．．．．． 3 1.3.2 Overview．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．3 2 Fuzzy Neural Network 6 2.1 Outlines．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 6 2.2 Structure of the fuzzy neural network．．．．．．．．．．．．．．．．．．．．．．．8 2.3 Reasoning method．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 8 2.4 Basic nodes operation．．．．．．．．．．．．．．．．．．．．．．．．．．．．．10 2.5 Supervised learning．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．13 2.6 Universal approximation．．．．．．．．．．．．．．．．．．．．．．．．．．．．15 3 Fine Tuning of Membership Functions 17 3.1 Introduction．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．17 3.2 Fine tuning of membership functions．．．．．．．．．．．．．．．．．．．．．．． 19 3.2.1 Gaussian function series．．．．．．．．．．．．．．．．．．．．．．．．．．19 3.2.2 Fine tuning method．．．．．．．．．．．．．．．．．．．．．．．．．．．．21 3.2.3 Tuning the FNN5．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 22 3.2.4 Convergence analysis．．．．．．．．．．．．．．．．．．．．．．．．．．． 23 3.2.5 Normalization of membership functions．．．．．．．．．．．．．．．．．．．． 24 3.3 Simulation results．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 26 4 Applications of the FNN systems 4.1 Tuning of PID controllers with specifications on gain and phase margins ......29 4.1.1 Introduction 4.1.2 Gain margin and phase margin 4.1.3 Tuning method using the FNN 4.1.4 Selection of training data and specification 4.1.5 Simulation results 4.2 Identification and Control of Hammerstein systems 4.2.1 Introduction 4.2.2 Hammerstein system 4.2.3 Identification model 4.2.4 Control design method 4.2.5 Convergence analysis 4.2.6 Simulation results 4.3 Fuzzy rules reduction 4.3.1 Introduction 4.3.2 Methods for reducing fuzzu rules 4.3.3 simulation result 2.6 Universal approximation．．．．．．．．．．．．．．．．．．．．．．．．．．．．15 5 Recurrent Fuzzy Neural Network 54 53.1 Introduction．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．54 5.2 Recurrent fuzzy neural networks: RFNN．．．．．．．．．．．．．．．．．．．．． 56 5.2.1 Structure of the RFNN．．．．．．．．．．．．．．．．．．．．．．．．．．．56 5.2.2 Layered operation ．．．．．．．．．．．．．．．．．．．．．．．．．．．．56 5.2.3 Fuzzy reasoning．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 59 5.3 Training architecture．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 61 5.3.1 Training architectures for identification and control．．．．．．．．．．．．．．． 61 5.3.2 Learning algorithm．．．．．．．．．．．．．．．．．．．．．．．．．．．．63 5.4 Stability analysis ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 65 5.4.1 Stability analysis for identification．．．．．．．．．．．．．．．．．．．．．．66 5.4.2 Stability analysis for indirect control．．．．．．．．．．．．．．．．．．．．． 68 5.5 Simulation results．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 71 6 Conclusion and Future research 6.1 Conclusion 6.2 Future researches