NARMAX model identification using a set-theoretic evolutionary approach

•The paper proposes an inventive method for nonlinear system identification.•The approach integrates three novel modeling and identification strategies.•It uses NARMAX models, set-based parameter identification, and evolutionary algorithms.•This method addresses both model structure selection and parameter estimation.•The method operates in different noise scenarios, especially correlated noise.

A method is presented for identification of system models that are linear in parametric structure, but arbitrarily nonlinear in signal operations. The fundamental parameter estimation task uses a set-theoretic analysis of the data to deduce feasible sets of solutions in light of certain model assumptions. In turn, measurable set solution properties are used to assess the viability of nonlinear regressor functions that “compete for survival” as components of the model best fit to represent the system. The strategy blends traditional system identification methods with three modeling strategies that are not commonly employed in signal processing: linear-time-invariant-in-parameters models, set-based parameter identification, and evolutionary selection of the model structure. The algorithm can identify nonlinear model structure and estimate parameters in the presence of different unknown noise scenarios, especially correlated noise. This paper reports the theoretical foundation of the methods and the simulation studies to illustrate the performance benefits.