Abstract
This paper presents a recently introduced Kernel Machine, called Geometrical Kernel Machine, used to predict disruptive events in nuclear fusion reactors. The algorithm proposed to construct the Kernel Machine is able to automatically determine both the number of neurons and the synaptic weights of a Multilayer Perceptron neural network with a single hidden layer. It has been demonstrated that the resulting network is able to classify any finite set of patterns defined in a real domain. The prediction problem has been here modeled as a two classes classification problem. The geometrical interpretation of the network equations allows us both to develop the disruption predictor and to manage the so called ageing of the kernel machine. In fact, using the same kernel machine, a novelty detection system has been integrated in the predictor, increasing the overall system performance, and the reliability of the predictor.
Similar content being viewed by others
References
Delogu, R., Fanni, A., & Montisci, A. (2008). Geometrical Synthesis of MLP Neural Networks. Neurocomputing, 71, 919–930. doi:10.1016/j.neucom.2007.02.006.
Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford: Clarendon Press.
Cybenko, G. (1989). Approximation by Superpositions of a Sigmoidal Function. Mathematics of Control Signals and Systems, 2(4), 303–314.
Kim, J. H., Park, S. K. (1995). The Geometrical Learning of Binary Neural Networks. IEEE transactions on neural networks, 6(1), 237–247. doi:10.1109/72.363432.
Huang, S. C., Huang, Y. F. (1991). Bounds of the Number of Hidden Neurons in Multilayer Perceptrons. IEEE transactions on neural networks, 2(1), 47–55. doi:10.1109/72.80290.
Sartori, M. A., Antsaklis, P. J. (1991). A Simple Method to Derive Bounds on the Size and to Train Multilayer Neural Networks. IEEE transactions on neural networks, 2(4), 467–471. doi:10.1109/72.88168.
Bobrovsky, L., & Boldak, C. (2000). "Dipolar Designing of Neural Layers for Image Segmentation", Proc. Of the Int. Conf. On Engineering Applications of Neural Networks (EANN2000). England: Kingston University.
Vapnik, V. N. (1998). Statistical Learning Theory. New York: Wiley.
Bennett, K. P., & Bredensteiner, E. J. (2000). Duality and geometry in SVM classifiers. Proc. 17th International Conf. on Machine Learning pp. 57–64. San Francisco, CA: Morgan Kaufmann.
Crisp, D., & Burges, C. J. C. (1999). A geometric interpretation of ν-SVM classifiers. In S. A. Solla, M. S. Kearns, & D. A. Cohn (Eds.), Advances in Neural Information Processing Systems (vol. 11, (pp. 244–251)). Cambridge, MA: MIT Press.
Mavroforakis, M., & Theodoridis, S. (2006). A geometric approach to support vector machine (SVM) classification. IEEE transactions on neural networks, 17(3), 671–683. doi:10.1109/TNN.2006.873281.
Pautasso, G., et al. (2002). On-line prediction and mitigation of disruption in ASDEX Upgrade. Nuclear Fusion, 42, 100–108. doi:10.1088/0029-5515/42/1/314.
Cannas, B., Fanni, A., Marongiu, E., & Sonato, P. (2004). Disruptions forecasting at JET using Neural Networks. Nuclear Fusion, 44, 68–76. doi:10.1088/0029-5515/44/1/008.
Yoshino, R. (2005). Neural-net predictor for beta limit disruptions in JT-60U. Nuclear Fusion, 45, 1232–1246. doi:10.1088/0029-5515/45/11/003.
Cannas, B., Delogu, R. S., Fanni, A., Sonato, P., & Zedda, M. K. (2007). Support Vector Machines for disruption prediction and novelty detection at JET. Fusion engineering and design, 82, 1124–1130. doi:10.1016/j.fusengdes.2007.07.004.
Cannas, B., Fanni, A., Sonato, P., Zedda, M. K., & JET EFDA contributors (2007). “A prediction tool for real-time application in the disruption protection system at JET”. Nuclear Fusion, 47, 1559–1569. doi:10.1088/0029-5515/47/11/018.
Machine Learning Repository, U.C.I.: [Online]. Available http://www1.ics.uci.edu/~mlearn/MLRepository.html.
Prechelt, L. (1994). Proben1—a set of neural networks benchmark problems and benchmarking rules, Technical Report No. 21/94. Karlsruher, Germany: University Karlsruher.
Markou, M., & Singh, S. (2003). Novelty Detection: a review–part 1: statistical approaches. Signal Processing, 83, 2481–2497. doi:10.1016/j.sigpro.2003.07.018.
Markou, M., & Singh, S. (2003). Novelty Detection: a review–part 2: neural network based approaches. Signal Processing, 83, 2499–2521. doi:10.1016/j.sigpro.2003.07.019.
Acknowledgment
The authors would like to thank Mike Johnson and David Howell for providing the manual classification of the disruptions, and Tim Hender, Richard Buttery and Simon Pinches for supporting the work, and for the useful discussions.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work, supported in part by the Euratom Communities under the contract of Association between EURATOM/ENEA, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
Rights and permissions
About this article
Cite this article
Cannas, B., Delogu, R.S., Fanni, A. et al. Geometrical Kernel Machine for Prediction and Novelty Detection of Disruptive Events in TOKAMAK Machines. J Sign Process Syst 61, 85–93 (2010). https://doi.org/10.1007/s11265-009-0345-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11265-009-0345-4