Application of Interval Arithmetic Simulation Techniques to Wastewater Treatment Processes

A. Rauh, M. Kletting, H. Aschemann, and E.P. Hofer (Germany)


interval arithmetics, nonlinear systems, simulation, uncer tain system parameters, wastewater treatment


In this paper, interval arithmetic simulation techniques are applied to determine guaranteed enclosures of the state variables of both continuous and discrete-time systems with uncertain but bounded parameters. In the case of continuous-time systems, the proposed approach allows to calculate guaranteed interval bounds for the discretiza tion error arising from numerical simulation of differential equations. The derivation of interval bounds for the dis cretization error is presented for explicit one-step integra tion algorithms such as the explicit Euler method. After detailed descriptions of the simulation algorithms, this ap proach is applied to the simulation of an activated sludge model in biological wastewater treatment.

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