Abstract
Time series novelty or anomaly detection refers to automatic identification of novel or abnormal events embedded in normal time series points. In the case of water demand, these anomalies may be originated by external influences (such as climate factors, for example) or by internal causes (bad telemetry lectures, pipe bursts, etc.). This paper will focus on the development of markers of different possible types of anomalies in water demand time series. The goal is to obtain early warning methods to identify, prevent, and mitigate likely damages in the water supply network, and to improve the current prediction model through adaptive processes. Besides, these methods may be used to explain the effects of different dysfunctions of the water network elements and to identify zones especially sensitive to leakage and other problematic areas, with the aim to include them in reliability plans. In this paper, we use a classical Support Vector Machine (SVM) algorithm to discriminate between nominal and anomalous data. SVM algorithms for classification project low-dimensional training data into a higher dimensional feature space, where data separation is easier. Next, we adapt a causal learning algorithm, based on the reproduction of kernel Hilbert spaces (RKHS), to look for possible causes of the detected anomalies. This last algorithm and the SVM’s projection are achieved by using kernel functions, which are necessarily symmetric and positive definite functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Augusteijn, M.F., Folkert, B.A.: Neural network classification and novelty detection. International Journal of Remote Sensing 23(14), 2891–2902 (2002)
Chimphlee, W., Abdullah, A.H., Sap, M.N., Srinoy, S., Chimphlee, S.: Anomaly-based intrusion detection using fuzzy rough clustering. In: 2006 International Conference on Hybrid Information Technology (ICHI 2006), vol. 1, pp. 329–334 (2006)
Fukumizu, K., Bach, F., Gretton, A.: Statistical consistency of kernel canonical correlation analysis. Journal of Machine Learning Research 8, 361–383 (2007)
Gretton, A., Bousquet, O., Smola, A.J., Schölkopf, B.: Measuring Statistical Dependence with Hilbert-Schmidt Norms. In: Jain, S., Simon, H.U., Tomita, E. (eds.) ALT 2005. LNCS, vol. 3734, pp. 63–77. Springer, Heidelberg (2005)
Herrera, M., García–Díaz, J.C., Pérez, R., Martínez, J.F., López, P.A.: Interpolación con redes neuronales artificiales en series temporales intervenidas para la predicción de la demanda urbana de agua. In: Proceedings NOLINEAL 2007. Ciudad Real, Spain (2007)
Herrera, M., Torgo, L., Izquierdo, J., Pérez, R.: Predictive models for forecasting hourly urban water demand (submitted, 2009)
Izquierdo, J., López, P.A., Martínez, F.J., Pérez, R.: Fault detection in water supply systems using hybrid (theory and data–driven) modelling. Mathematical and Computing Modelling 46, 341–350 (2007)
Karatzouglou, A.: Kernel methods software, algorithms and applications. PhD. dissertation, Technischen Universitat Wien, Austria (2006)
Karatzouglou, A., Meyer, D., Hornik, K.: Support Vector Machines. R. Journal of Statistical Software 15(9) (2006), http://www.jstatsoft.org/v15/i09 (accessed on January 2009)
Ma, J., Perkins, S.: Time-series novelty detection using one-class support vector machines. In: Proceedings of the International Joint Conference on Neural Networks, vol. 3, pp. 1741–1745 (2003)
Mercer, J.: Functions of positive and negative and their connection with the theory of integral equations. Philos. Trans Royal Soc. 209, 415–446 (1909)
Nong, Y., Qian, C.: Computer intrusion detection through EWMA for autocorrelated and uncorrelated data. IEEE Transactions on Realibility 52(1), 75–82 (2003)
Pearl, J.: Causality: Models, reasoning, and inference. Cambridge University Press, Cambridge (2000)
Rocco, M.C., Zio, E.: A support vector machine integrated system for the classification of operation anomalies in nuclear components and systems. Reliability Eng. & System Safety 92, 593–600 (2007)
Rossman, L.: EPANET-User’s Manual. United States Environmental Protection Agency (EPA), Cincinnati, OH (2000)
Schölkopf, B., Smola, A.: Learning with kernels. MIT Press, Cambridge (2002)
Shawe-Taylor, J., Cristianini, N.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Spirtes, P., Gylmour, C.: An algorithm for fast recovery of sparse causal graphs. Social Science Computer Review 9, 67–72 (1991)
Sun, H.: Mercer theorem for RKHS on noncompact sets. Journal of Complexity 21(3), 337–349 (2005)
Sun, X., Janzig, D., Schölkopf, B., Fukumizu, K.: A kernel-based causal learning algorithm. In: Proc. 24th Annual International Conference on Machine Learning (ICML 2007), pp. 855–862 (2007)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)
Vapnik, V.: Statistical Learning Theory. John Wiley and Sons, Chichester (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herrera, M., Pérez-García, R., Izquierdo, J., Montalvo, I. (2009). Scrutinizing Changes in the Water Demand Behavior. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-02894-6_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02893-9
Online ISBN: 978-3-642-02894-6
eBook Packages: EngineeringEngineering (R0)