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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

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2017

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Vol. 27, no. 2

309--322

EN

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.

2

Bounding approach to parameter estimation without prior knowledge on modeling error and application to quality modeling in drinking water distribution systems

Duzinkiewicz K.

Archives of Control Sciences

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2006

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Vol. 16, no. 1

51-70

EN

Parameter estimation of an autoregressive with moving average and exogenous variable ARMAX model is discussed in this paper by using bounding approach. Bounds on the model structure error are assumed unknown, or known but too conservative. To reduce this conservatism, a point-parametric model concept is proposed, where there exist a set model parameters and modeling error corresponding to each input. Feasible parameter sets are defined for point-parametric model. bounded values on the model parameters and modeling error can then be computed jointly by tightening the feasible set using observations under deliberately designed input excitations. Finally, a constantly bounded parameter model is established, which can be used for robust output prediction and control.

3

Building optimal bounding volumes for real-time 3D visualization

Iones A., Zhukov S., Krupkin A.

Machine Graphics and Vision

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1998

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Vol. 7, No. 1/2

245-258

EN

Bounding volume hierarchies are widely employed in many areas of Computer Graphics. Usually they are used as crude approximations of scene geometry to speed up time-consuming computations such as visibility tests for frustum culling,ray shooting, etc. A number of bounding volume types have been disscrused by various researchers. They include bounding spheres,(14), axis-aligned and oriented bounding boxes (OBBs), (12,13) ,and others. Although it is practically possible to use any of these bounding volumes, some types prove to be particulary useful ib certain applications. E. g., Gottschalk et al. ([13]) used OBBs to implement a very effective exact collision detection scheme. In this paper we address the problem of efficient bounding volume selection, the solution of which allows us to significantly accelerate such operations as visibility tests for frustum culling and ray shooting. We prove that minimal surface area (minimal perimter in 2D) oriented bounding box is optimal among all the oriented bounding boxes whit respect to the tree operations stated agove. Then,we develop a numbers of algorithms to create optimal oriented bounding boxes and thier approximations and finaly discuss the results of our practical implementation.