A new approach for plant monitoring using type-2 fuzzy logic and fractal theory

Abstract

We describe in this paper a new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy-fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 fuzzy logic approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.

Keywords:

• Type-2 fuzzy logic
• fractal theory
• plant monitoring
• diagnostics

Notes

Oscar Castillo is a full-time professor in the Computer Science Department of Tijuana Institute of Technology since 1985. He holds a Ph.D. in Computer Science from Kensington University, USA, a Master Degree in Applied Mathematics from National Polytechnic Institute of Mexico, and a Bachelor of Science Degree in Electrical Engineering from Tijuana Institute of Technology. He is a member of IEEE Neural Networks Society, IEEE Fuzzy Systems Technical Committee, NAFIPS and New York Academy of Sciences. His main research areas are fuzzy logic, neural networks, genetic algorithms, robotics and control of dynamical systems. He has received several awards for his achievements in research and teaching during his work in Tijuana Institute of Technology. He has received many research grants from government and industry to direct his many research projects. He has also collaborated with researchers from other countries in several projects of great importance. He has over 130 technical papers in proceedings, journals and edited books. Because of his many contributions he has been elected to the Editorial Board of several journals in computational intelligence. He is author of the book entitled “Soft Computing for Control of Non-Linear Dynamical Systems” published by Springer-Verlag, Germany, in January 2001, co-author of the book “Modelling, Simulation and Control of Non-Linear Dynamical Systems” published by Taylor and Francis, Great Britain, in January 2002, and author of the book “Soft Computing and Fractal Theory for Intelligent Manufacturing” published by Springer-Verlag, Germany, in January 2003.

Patricia Melin holds a Ph.D. in Computer Science from Kensington University, USA, a Professional Certificate in Microcomputer Engineering from the University of California in San Diego (UCSD), and a Bachelor Degree in Biochemical Engineering from Tijuana Institute of Technology. Her current research interests are in neural networks, fuzzy logic, control of non-linear dynamical systems and mathematical modeling and simulation of complex engineering systems. She has published more than 120 technical papers in journals, edited books and conference proceedings. She has received several awards in recognition of her many academic achievements. She has been a member of IEEE Control Systems Society since 1998, a member of IEEE Neural Networks Society since 2002, and a member of New York Academy of Sciences since 1999, and has been a technical reviewer for several conferences. She is a full-time professor at Tijuana Institute of Technology since 1998, and has work in applied research projects with the industry. Also, she has directed and participated in several research projects in collaboration with well-known universities and research institutes. She is author of the book “Modelling, Simulation and Control of Non-Linear Dynamical Systems” published by Taylor and Francis, Great Britain in January 2002, co-author of the book “Soft Computing for Control of Non-linear Dynamical Systems” published by Springer-Verlag, Germany in January 2001, and co-author of the book “Soft Computing and Fractal Theory for Intelligent Manufacturing” published by Springer-Verlag, Germany, in January 2003.