Using Radial Basis Function for Water
Quality Events Detection
Eyal Brill
Contents
1 Introduction: The Problem of Water Quality Events Classification . . . . . . . . . . . . . . . . . . . . . . . . 142
2 RBF: Structure and Basic Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
3 RBF Parameters Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4 An Illustrative Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5 Real-World Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6 Using Other Kernel Functions for RBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Appendix: Result of Run 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Abstract The current chapter demonstrates utilization of radial basis function
(RBF) as a tool for detection and classification of abnormal events in water
quality. The methodology is based on calibration of a RBF based on historical
true events classified by human experts. The aim of the process is selection of
parameters that ensure zero false negative events. The chapter describes the main
method of using RBF and then compares four different kernel functions which
are used for implementing the RBF. The case study part of the chapter illustrates
actual analysis of real-world data as well as an illustrative example. The
chapter concludes with some practical advice on how kernel functions should be
selected for this task.
Keywords Abnormality, Radial basis function, Water quality events
E. Brill (*)
Faculty of Technology Management (MOT), Holon Institute of Technology (HIT), Holon,
Israel
e-mail: eyalb@hit.ac.il
Andrea Scozzari, Steve Mounce, Dawei Han, Francesco Soldovieri,
and Dimitri Solomatine (eds.), ICT for Smart Water Systems: Measurements and
Data Science, Hdb Env Chem (2021) 102: 141–166, https://doi.org/10.1007/698_2019_424,
© Springer Nature Switzerland AG 2019, Published online: 9 May 2020
141
Quality Events Detection
Eyal Brill
Contents
1 Introduction: The Problem of Water Quality Events Classification . . . . . . . . . . . . . . . . . . . . . . . . 142
2 RBF: Structure and Basic Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
3 RBF Parameters Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4 An Illustrative Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5 Real-World Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6 Using Other Kernel Functions for RBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Appendix: Result of Run 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Abstract The current chapter demonstrates utilization of radial basis function
(RBF) as a tool for detection and classification of abnormal events in water
quality. The methodology is based on calibration of a RBF based on historical
true events classified by human experts. The aim of the process is selection of
parameters that ensure zero false negative events. The chapter describes the main
method of using RBF and then compares four different kernel functions which
are used for implementing the RBF. The case study part of the chapter illustrates
actual analysis of real-world data as well as an illustrative example. The
chapter concludes with some practical advice on how kernel functions should be
selected for this task.
Keywords Abnormality, Radial basis function, Water quality events
E. Brill (*)
Faculty of Technology Management (MOT), Holon Institute of Technology (HIT), Holon,
Israel
e-mail: eyalb@hit.ac.il
Andrea Scozzari, Steve Mounce, Dawei Han, Francesco Soldovieri,
and Dimitri Solomatine (eds.), ICT for Smart Water Systems: Measurements and
Data Science, Hdb Env Chem (2021) 102: 141–166, https://doi.org/10.1007/698_2019_424,
© Springer Nature Switzerland AG 2019, Published online: 9 May 2020
141