Analysis of Fuzzy Neural Networks and Its Applications

• Main Authors: Ching-Hung Lee, 李慶鴻
• Other Authors: Ching-Cheng Teng
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/53710177302734251220

博士 === 國立交通大學 === 電機與控制工程系 === 88 === 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