A hybrid fuzzy‐fractal approach for time series analysis and plant monitoring

We describe in this article a new hybrid fuzzy‐fractal approach for plant monitoring. We use the concept of the fractal dimension to measure the complexity of a time series of observed data from the plant. We also use fuzzy logic to represent expert knowledge on monitoring the process in the plant. In the hybrid fuzzy‐fractal approach, a set of fuzzy if‐then rules are used to classify different conditions of the plant. The fractal dimension is used as an input linguistic variable in the fuzzy system to improve the accuracy in the classification. An implementation of the proposed approach is shown to describe in more detail the method. © 2002 Wiley Periodicals, Inc.

[1]  Oscar Castillo,et al.  Soft Computing for Control of Non-Linear Dynamical Systems , 2001 .

[2]  J. Yen,et al.  Fuzzy Logic: Intelligence, Control, and Information , 1998 .

[3]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[4]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[5]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[6]  Douglas M. Patterson,et al.  Nonlinear Dynamics, Chaos, And Instability , 1994 .

[7]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[8]  L. Scharf,et al.  Statistical Signal Processing: Detection, Estimation, and Time Series Analysis , 1991 .

[9]  Charles Hsu.  Advanced signal processing technology by soft computing , 2000 .

[10]  Hartmut Jürgens,et al.  Chaos and Fractals: New Frontiers of Science , 1992 .

[11]  Oscar Castillo,et al.  A new fuzzy-genetic approach for the simulation and forecasting of international trade non-linear dynamics , 1998, Proceedings of the IEEE/IAFE/INFORMS 1998 Conference on Computational Intelligence for Financial Engineering (CIFEr) (Cat. No.98TH8367).

[12]  David L. Elliott,et al.  Neural Systems for Control , 1997 .

[13]  Edgar E. Peters.  Fractal Market Analysis: Applying Chaos Theory to Investment and Economics , 1994 .

[14]  Guanrong Chen,et al.  Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems , 2000 .

[15]  P. Melin,et al.  An adaptive model-based neuro-fuzzy-fractal controller for biochemical reactors in the food industry , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[16]  C. Tricot.  Curves and Fractal Dimension , 1994 .

[17]  Oscar Castillo,et al.  A new fuzzy-fractal-genetic method for automated mathematical modelling and simulation of robotic dynamic systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[18]  Michael F. Shlesinger,et al.  Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers , 1993 .

[20]  Christopher C. Yang,et al.  Modeling errors for dimensional inspection using active vision , 1999 .

[21]  Oscar Castillo,et al.  A new method for adaptive model-based control of non-linear dynamic plants using a neuro-fuzzy-fractal approach , 2001, Soft Comput..

[22]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[23]  Benoît B. Mandelbrot,et al.  Die fraktale Geometrie der Natur , 1987 .

[24]  Oscar Castillo,et al.  DEVELOPING A NEW METHOD FOR THE IDENTIFICATION OF MICROORGANISMS FOR THE FOOD INDUSTRY USING THE FRACTAL DIMENSION , 1994 .

[25]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[26]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[27]  Lakhmi C. Jain,et al.  Artificial Intelligence Techniques in Breast Cancer Diagnosis and Prognosis , 2000 .

[28]  Stephen Semmes,et al.  Some Novel Types of Fractal Geometry , 2001 .

[29]  Benoit B. Mandelbrot,et al.  Fractals and Scaling in Finance , 1997 .

[30]  Richard D. Braatz,et al.  Data-driven Methods for Fault Detection and Diagnosis in Chemical Processes , 2000 .

[31]  Lotfi A. Zadeh,et al.  Quantitative fuzzy semantics , 1971, Inf. Sci..

[32]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .