Genetic algorithm based identification of nonlinear systems by sparse Volterra filters

A parsimonious parameterization scheme is proposed to model the sparse Volterra filter so that the number of Volterra kernels to be estimated is greatly reduced. Representing the Volterra filter using a linear vector equation, the genetic algorithm is applied to search the significant terms among all possible candidate vectors. As the significant terms are detected, the associated Volterra kernels are estimated using the least square error method. The problem to be solved is, in essence, the application of the genetic algorithm to combinatorial optimization. An operator called forced mutation is proposed along with the genetic algorithm to overcome the difficulties usually encountered when applying the genetic algorithm to combinatorial optimization.