Detecting Ambiguities in Regression Problems using TSK Models

Regression refers to the problem of approximating measured data that are assumed to be produced by an underlying, possibly noisy function. However, in real applications the assumption that the data represent samples from one function is sometimes wrong. For instance, in process control different strategies might be used to achieve the same goal. Any regression model, trying to fit such data as good as possible, must fail, since it can only find an intermediate compromise between the different strategies by which the data were produced. To tackle this problem, an approach is proposed here to detect ambiguities in regression problems by selecting a subset of data from the total data set using TSK models, which work in parallel by sharing the data with each other in every step. The proposed approach is verified with artificial data, and finally utilised to real data of grinding, a manufacturing process used to generate smooth surfaces on work pieces.

[1]  Gaurav S. Sukhatme,et al.  Fault detection and identification in a mobile robot using multiple model estimation and neural network , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[2]  Shitong Wang,et al.  Outlier Detecting in Fuzzy Switching Regression Models , 2004, AIMSA.

[3]  Mehmet Kaya,et al.  Determination of fuzzy logic membership functions using genetic algorithms , 2001, Fuzzy Sets Syst..

[4]  Francisco Herrera,et al.  Tuning fuzzy logic controllers by genetic algorithms , 1995, Int. J. Approx. Reason..

[5]  Michel Ménard,et al.  Fuzzy clustering and switching regression models using ambiguity and distance rejects , 2001, Fuzzy Sets Syst..

[6]  Fernando A. C. Gomide,et al.  Design of fuzzy systems using neurofuzzy networks , 1999, IEEE Trans. Neural Networks.

[7]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[8]  M. K. Banerjee,et al.  FBF-NN-based modelling of cylindrical plunge grinding process using a GA , 2005 .

[10]  Yung C. Shin,et al.  Construction of fuzzy systems using least-squares method and genetic algorithm , 2003, Fuzzy Sets Syst..

[11]  H. D. Cheng,et al.  Automatically Determine the Membership Function Based on the Maximum Entropy Principle , 1997, Inf. Sci..

[12]  D. S. Yeung,et al.  Optimizing fuzzy knowledge base by genetic algorithms and neural networks , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[13]  R. Quandt A New Approach to Estimating Switching Regressions , 1972 .

[14]  Hidetomo Ichihashi,et al.  Neuro-Fuzzy GMDH and Its Application to Modelling Grinding Characteristics , 1995 .

[15]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Hans Kurt Tönshoff,et al.  Self-tuning fuzzy-controller for process control in internal grinding , 1994 .

[17]  Cornelius T. Leondes,et al.  Fuzzy Theory Systems: Techniques and Applications , 1999 .

[18]  Gaurav S. Sukhatme,et al.  Fault detection and identification in a mobile robot using multiple-model estimation , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[19]  Peter S. Maybeck,et al.  Multiple model adaptive controller for the STOL F-15 with sensor/actuator failures , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[20]  T. Warren Liao,et al.  A neural network approach for grinding processes: Modelling and optimization , 1994 .

[21]  Kenneth Rose,et al.  Mixture of experts regression modeling by deterministic annealing , 1997, IEEE Trans. Signal Process..

[22]  Dan Simon,et al.  Training fuzzy systems with the extended Kalman filter , 2002, Fuzzy Sets Syst..

[23]  F. Klawonn,et al.  Techniques and Applications of Control Systems Based on Knowledge-Based Interpolation , 1999 .

[24]  J. B. Ramsey,et al.  Estimating Mixtures of Normal Distributions and Switching Regressions , 1978 .

[25]  Aytekin Bagis,et al.  Determining fuzzy membership functions with tabu search - an application to control , 2003, Fuzzy Sets Syst..

[26]  R.J. Hathaway,et al.  Switching regression models and fuzzy clustering , 1993, IEEE Trans. Fuzzy Syst..

[27]  Ming-Kuen Chen,et al.  Neural network modelling and multiobjective optimization of creep feed grinding of superalloys , 1992 .

[28]  Ingo Renners,et al.  Optimizing fuzzy classifiers by evolutionary algorithms , 2000, KES'2000. Fourth International Conference on Knowledge-Based Intelligent Engineering Systems and Allied Technologies. Proceedings (Cat. No.00TH8516).

[29]  Dilip Kumar Pratihar,et al.  Design of a genetic-fuzzy system to predict surface finish and power requirement in grinding , 2004, Fuzzy Sets Syst..

[30]  Yongsheng Gao,et al.  A Self-Tuning Based Fuzzy-PID Approach for Grinding Process Control , 2002 .