Identification of nonlinear systems by the genetic programming-based Volterra filter

The genetic programming (GP) algorithm is utilised to search for the optimal Volterra filter structure. A Volterra filter with high order and large memories contains a large number of cross-product terms. Instead of applying the GP algorithm to search for all cross-products of input signals, it is utilised to search for a smaller set of primary signals that evolve into the whole set of cross-products. With GP's optimisation, the important primary signals and the associated cross-products of input signals contributing most to the outputs are chosen whereas the primary signals and the associated cross-products of input signals that are trivial to the outputs are excluded from the possible candidate primary signals. To improve GP's learning capability, an effective directed initialisation scheme, a tree pruning and reorganisation approach, and a new operator called tree extinction and regeneration are proposed. Several experiments are made to justify the effectiveness and efficiency of the proposed modified by the GP algorithm.