Also, the ANFISs were easily implemented as there were only two items that could be changed: the number input membership functions per an input variable, and the type of membership function used. Despite the fact that, only 2 input membership functions were used per input, the ANFIS was able to accurately model the outputs, and out perform the other AI methods tested. It would be of benefit to try more membership functions per input to see if the accuracy would improve significantly, however, the training time would increase if this was attempted. From the figure of the predicted vs. the actual for Output 4, it can be seen that this method models the relationship necessary for Output 4 extremely well. 

An observation that was made was that certain outputs or relationships were better modelled than others. This may be due to the relationship present in the given steam generator data, therefore, the outputs modelled more accurately may have stronger dependencies on the given inputs. It was seen that Output 3 had a high accuracy but the actual vs. predicted plots showed that certain output points were not being modelled well. There may be several reasons for this result, some of which have been mentioned in the sections above. A further investigation should be done if Output 3 were to be better represented. Also, this may be due to the fact that little is known about the dataset and more pre-processing may be required to eliminate data points that bias the training in some way. Another normalisation method could be tried for the pre-processing calculation.

The optimum parameters selected probably are not the best parameters that could be obtained if an exhaustive search was performed. However, an exhaustive search is computationally expensive and impractical to perform in reality. Therefore, a more empirical approach was used to select the free parameters for each of the AI methods implemented; making it a difficult task to obtain the optimum combination of the parameters which produces the best prediction performance. 

## Viii. C**Onclusion**

All Artificial Intelligence methods investigated were capable of modelling the steam generator data. The ANFIS
out performed the other methods giving the best accuracy overall. It was obvious from the plots of the predicted vs. actual outputs that the methods were able follow the general shape of the actual output data points. The Bayesian neural networks and the SVM gave comparable accuracy. The standard neural network gave a reasonable accuracy, however, was more difficult to tune than the other methods. 

The committees implemented, only slightly increased the accuracy obtained from that of the individual neural networks trained. Each method had their advantages and disadvantages in terms of the accuracy obtained, the time required to train, the time required to execute the AI system, the number of parameters to be tuned, and the complexity of the model produced. However, for the prediction of the steam generator data the Adaptive Neuro- Fuzzy System obtained R**EFERENCES**
[1] Jang JSR, Sun CT, Mizutani E. **Neuro-Fuzzy and Soft Computing:** 
A Computational Approach to Learning and Machine Intelligence**, Prentice Hall, Toronto, 1997.** 
[2] Statsoft. *Neural Networks***, Statsoft Electronic Textbook, 2003** 
 http://www.statsoft.com/textbook/stneunet.html Last accessed: April 2007 
[3] C.M. Bishop, *Neural Networks for Pattern Recognition*, 
 Oxford University Press Inc., New York, 1995 
[4] Mika S, Schäfer C, Laskov P, Tax D, Müller KR. *Support Vector* Machines, http://www.quantlet.com/mdstat/scripts/csa/html/node217.html, Last Accessed: 27 April 2007 
[5] Haykin S. *Neural Networks: A Comprehensive Foundation*, 
Prentice Hall, Second Edition, USA, 1999. 

[6] Bih J. *Paradigm Shift - An Introduction to Fuzzy Logic***, IEEE** 
 Potentials, 2006, pp 6 -21. 

[7] Stergiou C, Siganos D. *Neural Network* http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.h tml Last accessed: March 2007 
[8] Jinenez D. *Dynamically Weighted Ensemble Neural Networks for* Classification**, The University of Texas Health Science Centre at,** 
Department of Rehabilitation Medicine, San Antonio.

 http://camino.rutgers.edu/enspaper.pdf, Last accessed: 12 May 2007 
[9] Marwala T. **Fault Classification Using Pseudomodal Energies** 
and Probabilistic Neural Networks**. Journal of Engineering** 
Mechanics, November 2004, pp 1346- 1355. 

[10] Neal RM*. Bayesian Learning for Neural Networks***, Ph.D.** 
Dissertation, Graduate Department of Computer Science, University of Toronto, Toronto, 1995. 

[11] Neal RM. *Probabilistic Inference Using Markov Chain Monte* Carlo Methods**, Technical Report CRG-TR-93-1, Department of** 
Computer Science, University of Toronto, 1993. 

 [12] Smola AJ, Sch Olkopf B**. A Tutorial on Support Vector** 
Regression, C Kluwer Academic Publishers, **Statistics and** Computing 14, The Netherlands, **2004, pp 199–222.** 
 [13] Tay FEH, Cao L. **Application of Support Vector Machines in** 
Financial Time Series Forecasting**, The International Journal of** 
Management Science, Omega 29, 2001, pp 309-317. 

 [14] Sukyens JAK, Lukas L, Vandewalle J. *Sparse Approximation* using least Squares Support Vector Machines**, Circuits and** 
Systems, Proceedings ISCAS, The 2000 IEEE International Symposium, Volume 2, Geneva, 2000, pp 757-760. 

 [15] De Kruif BJ, Vries TJA. **Support-Vector-based Least Squares for** 
learning non-linear dynamics**, Decision and Control, Proceedings** 
of the 41st **IEEE Conference, Volume 2, 2002, pp 1343 -1348** 
 [16] Jang JSR. *ANFIS: Adaptive Network-based Fuzzy Inference* System**, Department of Electrical Engineering, and Computer** 
Science, University of California, Berkeley http://citeseer.ist.psu.edu/cache/papers/cs/13861/ftp:zSzzSzftp.cis.o hiostate.eduzSzpubzSzneuroprosezSzjang.adaptive_fuzzy.pdf/jang93a nfis.pdf Last access: April 2006 
 [17] Hellmann M. *Fuzzy Logic Introduction***, University of Rennes,** 
 France, March 2001. 

 http://www.fpk.tu-berlin.de/~anderl/epsilson/fuzzyintro4.pdf Last accessed: March 2007 
 [18] Jantzen J. *Tutorial on Fuzzy Logic***, Technical University of** 
Denmark, March 2006 http://fuzzy.iau.dtu.dk/download/logic.pdf Last accessed: April 2007 [19] Kaehler SD. *Fuzzy Logic Tutorial* http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html Last accessed: April 2007 
 [20] Majozi T. *Introduction to Fuzzy Set Theory***, Department of** 
Chemical Engineering, University of Pretoria, South Africa, 2004 http://dept.ee.wits.ac.za/~marwala/fuzzy.pdf