On numerical implementation of hysteresis models

The paper gives a brief description of the Preisach-Krasnoselskii model [1,2] for scalar hysteresis and a geometric interpretation of the model. Previously, it was assumed that numerical implementation of the Preisach model required the evaluation of double integrals. The intent of this paper is to develop a new method of numerical implementation of the model, which avoids the need for numerical evaluation of double integrals and to report some computational results obtained by the new method. The new procedure is based on explicit formulas for the integrals and it directly involves the experimental data which is used for the identification of the Preisach-Krasnoselskii model.