Identification, verification and validation of process models in wastewater engineering: a critical review

This article presents a critical review of the existing methodologies for process mathematical modelling in the area of wastewater engineering. It is argued that model identifiability is not a major issue in mathematical modelling. Model verifiability is a very demanding criterion that can be replaced by a less stringent one: model observability. The issue of ‘complex models versus reduced-order models’ is to be resolved by introducing a new concept: optimal model complexity. The traditional procedures of model validation are not adequate and a mathematical framework for model quality evaluation is needed.