Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system’s framework is followed by evaluation of its performance. Simulations prove that the presented approach is both flexible and efficient.
Aizerman, M., Braverman, E. and Rozonoer, L. (1964). Theoretical foundations of the potential function method in pattern recognition, Automation and Remote Control 25: 821-837.
Alpaydin, E. (2010). Introduction to Machine Learning, The MIT Press, Cambridge, MA.
Barshan, E., Ghodsi, A., Azimifar, Z. and Jahromi, M.Z. (2011). Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds, Pattern Recognition 44(7): 1357-1371.
Brdyś, M., Grochowski, M., Gminski, T., Konarczak, K. and Drewa, M. (2008). Hierarchical predictive control of integrated wastewater treatment systems, Control Engineering Practice 16(6): 751-767.
Campbell, W.M., Campbell, J.P., Reynolds, D.A., Singer, E. and Torres-Carrasquillo, P.A. (2006). Support vector machines for speaker and language recognition, Computer Speech and Language 20(2-3): 210-229.
Duzinkiewicz, K., Borowa, A., Mazur, K., Grochowski, M., Brdys, M.A. and Jezior, K. (2008). Detection and localisation in drinking water distribution networks by multiregional PCA, Studies in Informatics and Control 17(2): 135-152.
Hoffman, H. (2007). Kernel PCA for novelty detection, Pattern Recognition 40(3): 863-874.
Hott, K. (2008). Robust face recognition under partial occlusion based on support vector machine with local Gaussian summation kernel, Image and Vision Computing 26(11): 1490-1498.
Isermann, R. (1984). Process fault detection based on modeling and estimation methods-A survey, Automatica 20(4): 387-404.
Jackson, J.E. (1991). A User’s Guide to Principal Components, Wiley, Newark, NJ.
Jezior, K., Mazur, K., Borowa, A., Grochowski, M. and Brdys, M. A. (2007). Multiregional PCA for leakage detection and localisation in DWDS-Chojnice case study, in J. Korbicz, K. Patan and M. Kowal (Eds.), Fault Diagnosis and
Fault Tolerant Control, Academic Publishing House EXIT, Warsaw, pp. 303-310.
Kulczycki, P. and Charytanowicz, M. (2010). A complete gradient clustering algorithm formed with kernel estimators, International Journal of Applied Mathematics and Computer Science 20(1): 123-134, DOI: 10.2478/v10006-010-0009-3.
Li, J., Li, X. and Tao, D. (2008). KPCA for semantic object extraction in images, Pattern Recognition 41(10): 3244-3250.
Lima, C.A. and Coelho, A.L. (2011). Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study, Artificial Intelligence in Medicine 53(2): 83-95.
Mashford, J., Silva, D.D., Marney, D. and Burn, S. (2009). An approach to leak detection in pipe networks using analysis of monitored pressure values by support vector machine, Proceedings of the 3rd International Conference on Network and System Security, Gold Coast, Australia, pp. 534-539.
Mercer, J. (1909). Functions of positive and negative type, and their connection with the theory of integral equations, Philosophical Transactions of the Royal Society of London, Series A 209(441-458): 415-446.
Nogayama, T., Takahashi, H. and Muramatsu, M. (2003). Generalization of kernel PCA and automatic parameter tuning, IEIC Technical Report 103(389): 43-48.
Nowicki, A. and Grochowski, M. (2011). Kernel PCA in application to leakage detection in drinking water distribution system, in P. Jedrzejowicz, N.T. Nguyen and K. Hoang (Eds.), ICCCI (1), Lecture Notes in Computer Science, Vol. 6922, Springer, Berlin, pp. 497-506.
Patan, K. and Korbicz, J. (2012). Nonlinear model predictive control of a boiler unit: A fault tolerant control study, International Journal of Applied Mathematics and Computer Science 22(1): 225-237, DOI: 10.2478/v10006-012-0017-6.
Schölkopf, B., Mika, S., Burges, C.J.C., Knirsch, P., Mu¨ller, K.-R., Ra¨tsch, G. and Smola, A.J. (1999). Input space versus feature space in kernel-based methods, IEEE Transactions on Neural Networks 10(5): 1000-1017.
Schölkopf, B., Smola, A. and Mu¨ller, K.R. (1998). Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation 10(5): 1299-1319.
Shawe-Taylor, J. and Cristianini, N. (2004). Kernel Methods for Pattern Analysis, Cambridge University Press, Cambridge.
Slišković, D., Grbic´, R. and Hocenski, Ž. (2011). Methods for plant data-based process modeling in soft-sensor development, Automatika 52(4): 306-318.
Thornton, J., Sturm, R. and Kunkel, G. (2008). Water Loss Control, McGraw-Hill Companies, New York, NY.
Venkatasubramanian, V., Rengaswamy, R. and Kavuri, S. (2003a). A review of process fault detection and diagnosis, Part II: Qualitative models and search strategies, Computers and Chemical Engineering 27(3): 313-326.
Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. and Yin, K. (2003b). A review of process fault detection and diagnosis, Part III: Process history based methods, Computers and Chemical Engineering 27(3): 327-346.
Venkatasubramanian, V., Rengaswamy, R., Yin, K. and Kavuri, S. (2003c). A review of process fault detection and diagnosis, Part I: Quantitative model-based methods, Computers and Chemical Engineering 27(3): 293-311.
Xiao-Li, C. and Jiang Chao-Yuan, G.S.-Y. (2008). Leakage monitoring and locating method of water supply pipe network, Proceedings of the 7th International Conference on Machine Learning and Cybernetics, Kunming, China, pp. 497-506.
Xiong, H., Swamy, M. and Ahmad, M.O. (2005). Optimizing the kernel in the empirical feature space, IEEE Transactions on Neural Networks 16(2): 460-474.