Parameters determination of the modified J-A model with an optimization algorithm

Abstract

J-A model is widely used in hysteresis modeling as well as performance simulation of the magnetic materials. To achieve preferable adequacy, a modified J-A model is given, however, accurate solution of the parameters is very important for the modified J-A model, especially for over-determined nonlinear equations. In response to solving the over-determined nonlinear equations, this paper first turned the problem of the over-determined nonlinear equations into solving the minimum value of a multivariate function by means of the least square method. While the multivariate function is of high nonlinearity (the function is not continuous and the matrix of the partial derivatives is singular), solution methods using derivative calculation were abandoned, and the direct seeking methods with no derivative calculations(simplex algorithm) were involved to solve the problem. In the end the solution was validated with the use of the genetic algorithm and the simulated annealing algorithm.