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Engineering Evolutionary Intelligent Systems pp 211–250Cite as

Cluster-wise Design of Takagi and Sugeno Approach of Fuzzy Logic Controller

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 82))

Summary

We have a natural quest to know input-output relationships of a process. A fuzzy logic controller (FLC) will be an appropriate choice to tackle the said problem, if there are some imprecisions and uncertainties associated with the data. The present chapter deals with Takagi and Sugeno approach of FLC, in which a better accuracy is generally obtained compared to Mamdani approach but at the cost of interpretability. For most of the real-world processes, the input-output relationships might be nonlinear in nature. Moreover, the degree of non-linearity could not be the same over the entire range of the variables. Thus, the same set of response equations (obtained through statistical regression analysis for the entire range of the variables) might not hold equally good at different regions of the variable-space. Realizing the above fact, an attempt has been made to cluster the data based on their similarity among themselves and then cluster-wise linear regression analysis has been carried out, to determine the response equations. Moreover, attempts have been made to develop Takagi and Sugeno approach of FLC clusterwise, by utilizing the above linear response equations as the consequent part of the rules, which have been further optimized to improve the performances of the controllers. Moreover, two types of membership function distributions, namely linear (i.e., triangular) and non-linear (i.e., 3rd order polynomial) have been considered for the input variables, which have been optimized during the training. The performances of the developed three approaches (i.e., Approach 1: Cluster-wise linear regression; Approach 2: Cluster-wise Takagi and Sugeno model of FLC with linear membership function distributions for the input variables; Approach 3: Cluster-wise Takagi and Sugeno model of FLC with nonlinear (polynomial) membership function distributions for the input variables) have been tested on two physical problems. Approach 3 is found to outperform the other two approaches.

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Abbreviations

a :

Abrasive mesh size (micro-m)

a 0, a 1,…, a p :

Coefficients

A 1, A 2, …, A p :

Membership function distributions corresponding to the linguistic terms

c :

% concentration of the abrasive

C 1 :

Welding speed (cm/min)

C 2 :

Wire feed rate (cm/min)

C 3 :

% cleaning

C 4 :

Arc gap (mm)

C 5 :

Welding current (Amp)

CO ij :

Calculated value ofj-th output for i-th case

D ij :

Euclidean distance between i and j

¯D :

Mean distance

E i :

Entropy of i-th data point

gk :

Half base-width of membership function distribution of x k variable

G :

Generation number

h ijk :

Variation of the value of a co-efficient

n :

No. of clusters

n′:

No. of cycles

N :

No. of data points

O 1 :

Front height of weld bead (mm)

O 2 :

Front width of weld bead (mm)

O 3 :

Back height of weld bead (mm)

O 4 :

Back width of weld bead (mm)

p :

No. of input variables

p c :

Crossover probability

p m :

Mutation probability

P :

Population size

q :

No. of output variables

Q :

No. of fired rules

R :

Dimension of data points

R a :

Surface roughness (micro-m)

S ij :

Similarity between the data points i and j

T :

No. of training cases

[T]:

Hyperspace

TO ij :

Target value of j-th output for i-th case

v :

Flow speed of abrasive media (cm/min)

w i :

Control action of i-th rule

x 1, x 2, …, x p :

Set of input dimensions of a variable

x 1′, x 2′, …, x N ′:

Data points

y :

Output

α :

Constant

β :

Threshold for similarity

γ :

Threshold for determining a valid cluster

μ :

Membership function value

FLC :

Fuzzy logic controller

GA :

Genetic Algorithm

H :

High

KB :

Knowledge base

L :

Low

M :

Medium

MRR :

Material removal rate (mg/min)

References

  1. Cherkassky V, Gehring D, Mulier F (1996) Comparison of adaptive methods for function estimation from samples. IEEE Trans Neural Netw 7:969–984

    Article  Google Scholar 

  2. Dickerson JA, Kosko B (1996) Fuzzy function approximation with ellipsoidal rules. IEEE Trans Syst Man Cybern Part B 26:542–560

    Article  Google Scholar 

  3. Sommer V, Tobias P, Kohl D, Sundgren H, Lundstrom L (1995) Neural networks and abductive networks for chemical sensor signals: a case comparison. Sens Actuators B 28:217–222

    Article  Google Scholar 

  4. Kleinsteuber S, Sepehri N (1996) A polynomial network modeling approach to a class of large-scale hydraulic systems. Comput Elect Eng 22:151–168

    Article  Google Scholar 

  5. Cordon O, et al. (2004) Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Set Syst 141(1):5–31

    Article  MATH  MathSciNet  Google Scholar 

  6. Ivakhnenko AG (1971) Polynomial theory of complex systems. IEEE Trans Syst Man Cybern SMC-1:364–378

    Article  MathSciNet  Google Scholar 

  7. Ivakhnenko AG, Madala HR (1994) Inductive learning algorithms for complex systems modeling. CRC, Boca Raton, FL

    MATH  Google Scholar 

  8. Ivakhnenko AG, Ivakhnenko GA (1995) The review of problems solvable by algorithms of the group method of data handling (GMDH). Pattern Recogn Image Anal 5(4):527–535

    Google Scholar 

  9. Ivakhnenko AG, Ivakhnenko GA, Muller JA (1994) Self-organization of neural networks with active neurons. Pattern Recogn Image Anal 4(2):185–196

    Google Scholar 

  10. Oh SK, Pedrycz W (2002) The design of self-organizing polynomial neural networks. Inf Sci 141:237–258

    Article  MATH  Google Scholar 

  11. Oh SK, Pedrycz W, Park BJ (2003) Polynomial neural networks architecture: analysis and design. Comput Electr Eng 29(6):703–725

    Article  Google Scholar 

  12. Park HS, Park BJ, Oh SK (2002) Optimal design of self-organizing polynomial neural networks by means of genetic algorithms. J Res Inst Eng Technol Dev 22:111–121 (in Korean)

    Google Scholar 

  13. Oh SK, Pedrycz W (2003) Fuzzy polynomial neuron-based self-organizing neural networks. Int J Gen Syst 32(3):237–250

    Article  MATH  Google Scholar 

  14. Pedrycz W, Reformat M (1996) Evolutionary optimization of fuzzy models in fuzzy logic: a framework for the new millennium. In: Dimitrov V, Korotkich V (eds.) Studies in fuzziness and soft computing, pp 51–67

    Google Scholar 

  15. Pedrycz W (1984) An identification algorithm in fuzzy relational system. Fuzzy Set Syst 13:153–167

    Article  MATH  MathSciNet  Google Scholar 

  16. Oh SK, Pedrycz W (2000) Identification of fuzzy systems by means of an auto-tuning algorithm and its application to nonlinear systems. Fuzzy Set Syst 115(2):205–230

    Article  MATH  MathSciNet  Google Scholar 

  17. Michalewicz Z (1996) Genetic algorithms + Data structures = Evolution programs. Springer, Berlin Heidelberg Newyork

    MATH  Google Scholar 

  18. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbour

    Google Scholar 

  19. Jong DKA (1996) Are genetic algorithms function Optimizers?. In Manner R, Manderick B (eds.) Parallel problem solving from nature 2, North-Holland, Amsterdam

    Google Scholar 

  20. Box DE, Jenkins GM (1976) Time series analysis forcasting and control. Holden Day, California

    Google Scholar 

  21. Tong RM (1980) The evaluation of fuzzy models derived from experimental data. Fuzzy Set Syst 13:1–12

    Article  Google Scholar 

  22. Sugeno M, Yasukawa T (1991) Linguistic modeling based on numerical data. IFSA 91, Brussels, Comput Manage & Syst Sci:264–267

    Google Scholar 

  23. Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1(1):7–31

    Article  Google Scholar 

  24. Xu CW, Zailu Y (1987) Fuzzy model identification self-learning for dynamic system. IEEE Trans Syst Man Cybern SMC 17(4):683–689

    Article  MATH  Google Scholar 

  25. Chen JQ, Xi YG, Zhang ZJ (1998) A clustering algorithm for fuzzy model identification. Fuzzy Set Syst 98:319–329

    Article  MathSciNet  Google Scholar 

  26. Gomez-Skarmeta AF, Delgado M, Vila MA (1999) About the use of fuzzy clustering techniques for fuzzy model identification. Fuzzy Set Syst 106:179–188

    Article  Google Scholar 

  27. Kim ET, et al. (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 5(3):328–337

    Article  Google Scholar 

  28. Kim ET, et al. (1998) A simple identified Sugeno-type fuzzy model via double clustering. Inf Sci 110:25–39

    Article  Google Scholar 

  29. Leski J, Czogala E (1999) A new artificial neural networks based fuzzy inference system with moving consequents in if-then rules and selected applications. Fuzzy Set Syst 108:289–297

    Article  MATH  MathSciNet  Google Scholar 

  30. Lin Y, Cunningham III GA (1995) A new approach to fuzzy-neural modeling. IEEE Trans Fuzzy Syst 3(2):190–197

    Article  Google Scholar 

  31. Wang Y, Rong G (1999) A self-organizing neural-network-based fuzzy system. Fuzzy Set Syst 103:1–11

    Article  Google Scholar 

  32. Park HS, Oh SK, Yoon YW (2001) A new modeling approach to fuzzy-neural networks architecture. J Control Autom Syst Eng 7(8):664–674 (in Korean)

    Google Scholar 

  33. Oh SK, Kim DW, Park BJ (2000) A study on the optimal design of polynomial neural networks structure. Trans Korean Inst Electr Eng 49D(3):145–156 (in Korean)

    Google Scholar 

  34. Oh SK, Pedrycz W, Kim DW (2002) Hybrid fuzzy polynomial neural networks. Int J Uncertain, Fuzziness Knowl-Based Syst 10(3):257–280

    Article  MATH  Google Scholar 

  35. Wang LX, Mendel JM (1992) Generating fuzzy rules from numerical data with applications. IEEE Trans Syst Man Cybern 22(6):1414–1427

    Article  MathSciNet  Google Scholar 

  36. Crowder III RS (1990) Predicting the mackey-glass time series with cascade-correlation learning. In: Touretzky D, Hinton G, Sejnowski T (eds.) Proceedings of the 1990 connectionist models summer school, Carnegic Mellon University

    Google Scholar 

  37. Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  MathSciNet  Google Scholar 

  38. Maguire LP, Roche B, McGinnity TM, McDaid LJ (1998) Predicting a chaotic time series using a fuzzy neural network. Inf Sci 112:125–136

    Article  MATH  Google Scholar 

  39. James LC, Huang TY (1999) Automatic structure and parameter training methods for modeling of mechanical systems by recurrent neural networks. Appl Math Model 23:933–944

    Article  MATH  Google Scholar 

  40. Oh SK, Pedrycz W, Ahn TC (2002) Self-organizing neural networks with fuzzy polynomial neurons. Appl Soft Comput 2(IF):1–10

    Google Scholar 

  41. Lapedes AS, Farber R (1987) Non-linear signal processing using neural networks: prediction and system modeling. Technical Report LA-UR-87-2662, Los Alamos National Laboratory, Los Alamos, New Mexico

    Google Scholar 

  42. Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197:287–289

    Article  Google Scholar 

  43. Cho MW, Kim GH, Seo TI, H YC, Cheng HH (2006) Integrated machining error compensation method using OMM data and modified PNN algorithm, International Journal of Machine Tool and Manufacture 46(2006):1417–1427

    Article  Google Scholar 

  44. Menezes LM, Nikolaev NY (2006) Forecasting with genetically programmed polynomial neural networks. International Journal of Forecasting 22(2):249–265

    Article  Google Scholar 

  45. Pei JS, Wright JP, Smyth AW (2005) Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond. Compt Methods Appl Mech Eng 194(42–44): 4481–4505

    Article  MATH  MathSciNet  Google Scholar 

  46. Nariman-Zadeh N, Darvizeh A, Jamali A, Moeini A (2005) Evolutionary design of generalized polynomial neural networks for modelling and prediction of explosive forming process. J Mater Process Technol 164–165:1561–1571

    Article  Google Scholar 

  47. Delivopoulos E, Theocharis JB (2004) A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method. Inf Sci 168(1–4):133–170

    MATH  MathSciNet  Google Scholar 

  48. Huang LL, Shimizu A, Hagihara Y, Kobatake H (2003) Face detection from cluttered images using a polynomial neural network. Neurocomputing 51:197–211

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721 302 West Bengal, India

    Tushar Kumar Pratihar & Dilip Kumar Pratihar

Authors
  1. Tushar Kumar Pratihar
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  2. Dilip Kumar Pratihar
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Editor information

Editors and Affiliations

  1. Centre for Quantifiable Quality of Service in Communication Systems (Q2S), Centre of Excellence Norwegian University of Science and Technology, O.S. Bragstads plass 2E, N-7491, Trondheim, Norway

    Ajith Abraham

  2. Department of Computer Science Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Kogalniceanu 1, 400084, Cluj - Napoca, Romania

    Crina Grosan

  3. Department of Electrical & Computer Engineering, University of Alberta, ECERF Bldg., 2nd floor, Edmonton, AB, T6G 2V4, Canada

    Witold Pedrycz

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Kumar Pratihar, T., Kumar Pratihar, D. (2008). Cluster-wise Design of Takagi and Sugeno Approach of Fuzzy Logic Controller. In: Abraham, A., Grosan, C., Pedrycz, W. (eds) Engineering Evolutionary Intelligent Systems. Studies in Computational Intelligence, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75396-4_8

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  • DOI: https://doi.org/10.1007/978-3-540-75396-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75395-7

  • Online ISBN: 978-3-540-75396-4

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