Hysteresis Modeling Based On Least Squares Support Vector Machines

Hysteresis is widely present in the electrical control and power systems, and it is important to the stable operation of the equipment and the safety of operation. Hysteresis loop features unconventional, non-smooth, non-linear, non-resolution, one-to-many mapping. The accurate modeling of hysteresis phenomena existing in a variety of applications is one of the prerequisites to ensure the robustness of the system operation.In this paper, two key issues about the nonlinearity and the one-to-many mapping are discussed and researched in depth. At the same time, the simulation and experimental results are given and the comparative analysis of the algorithm speed and the mean square error is carried out.The least squares support vector machines are proposed to build the hysteresis model in this paper based on the full comparative analysis of three kinds of hysteresis modeling program:JA model, Preisach model, Neural networks model so far. The least squares support vector machines are essentially an estimation strategy of a function based on structural risk minimization principle for the problem of small sample, and the nonlinear problem of hysteresis is solved by using its strong nonlinear approximation ability and good generalization performance. During the training of the network, the history information of hysteresis is sent into the network by the form of matrix as one of the input vector components, which solving the problem about one-to-many mapping of the hysteresis.The simulation and experiment are done at the same time in order to explore the rule of the least squares support vector machines when dealing with the hysteresis nonlinear. For the purpose of the full recognition of hysteresis characteristics, the dynamic hysteresis identification is worked out about multi-ring in the case of different amplitudes with same frequency, and the law of hysteresis is obtained systematically when the loop at different positions in the concentric hysteresis loop cluster is used for testing. The least squares support vector machines and Neural networks are used at the same time on the dynamic modeling of hysteresis in order to contrast. The JA model for dynamic simulation of hysteresis is built in this paper by using the Simulink blocks of Matlab in order to avoid solving the complicated differential equations and solving Langevin function that will appear singular solution, and it gives the simulation data and the smooth hysteresis loop. At the same time, the experimental data of hysteresis is obtained by the experimental platform based on soft magnetic materials.Neural networks are regarded as the function estimation strategy based on the empirical risk minimization principle and also be used to solve the hysteresis non-linear, but there are several defects whit it, for example, easy to fall into local minima in optimization, over-fitting and the number of hidden layer neurons is not easy identified. By the modeling results of simulation and experimental we can find that the running time of the program of least squares support vector machines is only about one-third to that of Neural networks, the mean square error is lower than Neural networks about an order of magnitude, the errors change over time is litter, and all of these show that the program proposed of hysteresis modeling based on the least squares support vector machines is feasible and the performance is relatively good.