**5. Concluding remarks**

The current chapter demonstrates how the simple pattern recognition of a curve created by a noise capture process, similar to a random walk, can be used to classify different types of abnormal events. The presented algorithm uses the imaginary center of gravity of the water quality measurements in order to measure the noise of the process captured as traveling distance. It has been shown that the created curve has a maximum value, due to the nature of the process. This threshold is violated when abnormal events occur.

Four different types of abnormal events were examined: malfunctioning of sensors, operational change, water source change and contamination events. Numerical examples based on real data show that each of the events has a different "signature", which enables the identification of the event's nature.

The current chapter shows how water analytics can be used as part of the information system which helps operators protect the water system. The above framework can also assist control systems in regard to the automatic classification process of observed events, in order to reduce the level of false alarms in water monitoring systems. For example, this may be achieved by eliminating alarms like the first three types analyzed in this study and notifying operators only in the case of contamination event alarms.

[9] Jin W, Tung A, Han J. Mining top-n local outliers in large databases. In: Proc. ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining (SIGKDD), San Francisco,

Identifying Water Network Anomalies Using Multi Parameters Random Walk: Theory and Practice

http://dx.doi.org/10.5772/intechopen.71566

47

[10] Tang J, Li H, Cao Y, Tang Z. Email data cleaning. In: KDD'05, August 21-24, 2005,

[11] Stefano C, Sansone C, Vento M. To reject or not to reject: That is the question: An answer in the case of neural classifiers. IEEE Transactions on Systems, Man, and Cybernetics,

[12] Odin T, Addison D. Novelty detection using neural network technology. In: Proceedings

[13] Hawkins S, He H, Williams GJ, Baxter RA. Outlier detection using replicator neural networks. In: Proceedings of the 4th International Conference on Data Warehousing and Knowledge Discovery. Aix-en-Provence, France, September 4-6, 2002. pp. 170-180 [14] Williams G, Baxter R, He H, Hawkins S, Gu L. A comparative study of RNN for outlier detection in data mining. In: Proceedings of the IEEE International Conference on Data

Mining. IEEE Computer Society, Maebashi City, Japan, December 2002; p. 709

[15] Cheng H, Tan P-N, Potter C, Klooster S. Detection and characterization of anomalies in multivariate time series Haibin Cheng, Pang Ning Tan, Christopher Potter, Steven Klooster. In: Proceedings of the 2009 SIAM International Conference on Data Mining;

[16] Brill E. Dynamic Brownian motion with Density superposition for abnormality detec-

[17] Brown R. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. The Philosophical

[18] Einstein A. Investigations on the theory of Brownian movement. Annalen der Physik.

[19] Davis M, Etheridge A. Louis Bachelier's Theory of Speculation: The Origins of Modern

[20] Black F, Scholes M. The pricing of options and corporate liabilities. Journal of Political

Chicago, Illinois, USA. Copyright 2005 ACM 1-59593-135-X/05/0008; 2005

Part C (Applications and Reviews). 2000;**30**(1):84-94

tion. PCT. Application number: 14601862; 2015

Magazine. 2009;**4**:161-173. DOI: 10.1080/14786442808674769

Finance. Princeton; Oxford: Princeton University Press, JSTOR; 2006

of the COMADEN Conference; 2000

CA. 2001

2009

1905;**322**(8):549-560

Economy. 1973;**81**(3):637-654
