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An interval estimator for chlorine monitoring in drinking water distribution systems under uncertain system dynamics, inputs and chlorine concentration measurement errors

Łangowski R., Brdys M. A.

International Journal of Applied Mathematics and Computer Science

2017

Vol. 27, no. 2

309--322

The design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability and robustness of the interval observer are investigated under uncertainty in system dynamics, inputs, initial conditions and measurement errors. The bounds on the estimated variables are generated by solving two systems of first-order ordinary differential equations. For that reason, despite a large scale of the systems, the numerical efficiency is sufficient for the on-line monitoring of the water quality. Finally, in order to validate the performance of the observer, it is applied to the model of a real water distribution network.

Forty-Five Years of the Rigid Finite Element Method

Wittbrodt E., Wojciech S.

Archive of Mechanical Engineering

2013

Vol. LX, nr 3

313--317

The Rigid Finite Element Method (RFEM) is an original Polish method for modelling dynamics of complex mechanical systems with flexible elements. Its origin dates back to the sixties of the last century. The idea of the Rigid Finite Element Method, inseparably connected with Professor Jan Kruszewski-Majewski from Gdansk University of Technology.

Monitoring of chlorine concentration in drinking water distribution systems using an interval estimator

Łangowski R., Brdyś M. A.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 2

199-216

This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water network and its performance is validated by simulations.