  The present study proposes a new structure selection approach for non-linear
system identification based on Two-Dimensional particle swarms (2D-UPSO). The
2D learning framework essentially extends the learning dimension of the
conventional particle swarms and explicitly incorporates the information about
the cardinality, i.e., number of terms, into the search process. This property
of the 2D-UPSO has been exploited to determine the correct structure of the
non-linear systems. The efficacy of the proposed approach is demonstrated by
considering several simulated benchmark nonlinear systems in discrete and in
continuous domain. In addition, the proposed approach is applied to identify a
parsimonious structure from practical non-linear wave-force data. The results
of the comparative investigation with Genetic Algorithm (GA), Binary Particle
Swarm Optimization (BPSO) and the classical Orthogonal Forward Regression (OFR)
methods illustrate that the proposed 2D-UPSO could successfully detect the
correct structure of the non-linear systems.
