An intelligent piecewise linear modeling approach from noisy data and its applications to water supply system

The modeling of complex systems poses a great challenge due to the multitude of unknowns and complexity involved. Meanwhile, the piecewise linear (PWL) model has been proven to have the ability to approximate complex nonlinear systems. The construction of a PWL model entail to partitioning the state space into finite regions, and estimating the parameters of each subsystem. In this paper, we propose a novel approach to accomplish these two tasks via an intelligent Voronoi partition approach and solving a series of optimization problems. Firstly, we estimate the certain range of the subsystem parameters of one region directly from noisy data. This estimation is fulfilled by set operation between noise zonotope and the input-state data set, the optimal subsystem parameters are obtained by minimizing the noise zonotope. Secondly, this procedure is applied to all regions, a cost function is designed based on these noise zonotopes, by changing the partition, the cost function varies. Finally, an annealing simulation (SA) algorithm is utilized to search for the most adequate partition to ensure the fitting accuracy. The effectiveness of the proposed method is demonstrated through a numerical example and on experimental data from an actual water supply system.