Applying a smart fuzzy adaptive regression to runoff estimation

A smart adaptive fuzzy based regression is proposed in order to describe a non-constant behavior of the runoff as a function of the precipitation. This methodology can be applied in similar hydrological processes. Hence, for high precipitation, beyond a fuzzy threshold, a conventional linear (crisp) relation between precipitation and runoff is established, while for low precipitation, a curve with different behavior must be derived. Between these curves and for a runoff range each curve holds to some degree. Hence, a simplified Sugeno architecture scheme is established based on no many logical rules. The training process is achieved based on a combination between the Particle Swarm Optimization (PSO) method and the conventional least square method.