4. Parameter Estimation: Definition and Sampling Design

Process control and supervision are based mainly on the use of models. These models have to be as accurate as possible to generate reliable results. Complex systems, like water distribution networks, need such models in order to comprehend them. Models presented in Chap. 3 are used in simulation, optimization, supervision, leak detection, etc. When the model is generated, large errors are introduced. These errors discourage the technicians unless they are corrected in a first calibration effort: macrocalibration. This is an ad hoc process that is done manually. The methodology, carried out by the experts, can be partially addressed using artificial intelligence (AI) algorithms. Once the major errors are solved, the parameter tuning, microcalibration, is posed as an optimization problem. Before these procedures are applied, the problem and the information available have to be analysed in order to assure the reliability of the resulting model. Given a number of parameters to be estimated, the measurements required for guaranteeing the identifiability and the well-posedness of the problem may be too exigent. Thus, the sampling design is often associated with a redefinition of the parameters to be estimated. In this chapter, both the parameterization and the sampling design are presented proposing a methodology that has given promising results with real water distribution networks.