Volterra-system identification using adaptive real-coded genetic algorithm

In this paper, a floating-point genetic algorithm (GA) for Volterra-system identification is presented. The adaptive GA method suggested here addresses the problem of determining the proper Volterra candidates, which leads to the smallest error between the identified nonlinear system and the Volterra model. This is achieved by using variable-length GA chromosomes, which encode the coefficients of the selected candidates. The algorithm relies on sorting all candidates according to their correlation with the output. A certain number of candidates with the highest correlation with the output are selected to undergo the first evolution "era." During the process of evolution the candidates with the least significant contribution in the error-reduction process is removed. Then, the next set of candidates are applied into the next era. The process continues until a solution is found. The proposed GA method handles the issues of detecting the proper Volterra candidates and calculating the associated coefficients as a nonseparable process. The fitness function employed by the algorithm prevents irrelevant candidates from taking part in the final solution. Genetic operators are chosen to suit the floating-point representation of the genetic data. As the evolution process improves and the method reaches a near-global solution, a local search is implicitly applied by zooming in on the search interval of each gene by adaptively changing the boundaries of those intervals. The proposed algorithms have produced excellent results in modeling different nonlinear systems with white and colored Gaussian inputs with/without white Gaussian measurement noise.