Robust On-Line Monitoring of Mixing Quality in Water Supply Networks

Abstract

The paper applies an algorithm for recursive estimation of variables and parameters in general dynamic networks that has been developed by [Brdys 99] to robust on-line monitoring of the mixing water quality in dynamic water networks. A complete hydraulic information is assumed to be available on-line. First a parsimonious parametrisation of a mathematical model of mixing quality is derived. Next a recursive estimation algorithm is designed that uses the model and available measurements to generate on-line robust estimates of unknown quantities. The parameters and variables are estimated simultaneously. Robustness of the estimates is achieved through non-probabilistic set-bounded modelling of uncertainty in the measurement and modelling errors. The stable and tight bounds on the estimated quantities are obtained by employing a concept of moving information window. The estimation scheme is very flexible in integrating the information available. In particular, if only concentrations of the quality parameters in a network inputs are measured, the estimator operates as the quality simulator under uncertain models and not accurately known inputs. This can be viewed as a sort of generic soft sensor. Performance of the monitoring scheme is illustrated by applications to two case-study networks. 1. Introduction Estimation of variables and parameters based on the available measurements and mathematical model became a routine activity which is carried out on-line during operation of water networks. Estimation of unmeasured flows and heads, concentrations of water quality parameters, parameters of pipes and other network elements can serve as the examples. The estimates are required for planning, decision making, operational control and network monitoring purposes. A proper integration of both the measurements and the model information into one estimation scheme is crucial in obtaining robust and quality estimates. These so called soft sensors can save on hard sensor investment. Moreover, using the dynamic models unable us to carry out a prediction. There exists an uncertainty in the estimation problem due to the measurement and modelling errors. Also, values of certain external inputs to the system are not exactly known. A traditional approach to modelling the uncertain factors utilises a probability theory. The estimates are produced by minimising a selected criterion which is typically mean of square of an estimation error . Often the probabilistic model is questionable regarding both the structure and the distribution parameters. Hence, it may not be possible to robustly assess a quality of the statistical estimates. An alternative approach to modelling an uncertainty for general estimation purposes was proposed by [Schweppe 1973] and applied to electrical power networks. An excellent survey paper by [Walter 1990] covers the parameter estimation area. In this approach, bounded sets are used to describe the limits of unknown instantaneous values of the uncertain quantities. The corresponding envelopes (tubes) constitute bounds on the unknown trajectories. This a priori information is more natural and can