Solution of Jiles–Atherton vector hysteresis parameters estimation by modified Differential Evolution approaches

Differential Evolution (DE) is a simple and efficient stochastic global optimization algorithm of evolutionary computation field, which involves the evolution of a population of solutions using operators such as mutation, crossover, and selection. The basic idea of DE is to adapt the search during the evolutionary process. At the start of the evolution, the perturbations are large since parent populations are far away from each other. As the evolutionary process matures, the population converges to a small region and the perturbations adaptively become small. DE approaches have been successfully applied to solve a wide range of optimization problems. In this paper, the parameters set of the Jiles–Atherton vector hysteresis model is obtained with an approach based on modified Differential Evolution (MDE) approaches using generation-varying control parameters based on generation of random numbers with uniform distribution. Several evaluated MDE approaches perform better than the classical DE methods and a genetic algorithm approach in terms of the quality and stability of the final solutions in optimization of vector Jiles–Atherton vector hysteresis model from a workbench containing a rotational single sheet tester.

► To achieve good performance by using differential evolution algorithms, adaptive and self-adaptive improvements can be useful. ► The accuracy of the Jiles–Atherton vector hysteresis model is strongly dependent of the parameters set quality. ► The sensitivity of the differential evolution to its control parameters can lead to significant performance deterioration.