Physica B 306 (2001) 84–90 A Preisach model identification procedure and simulation of hysteresis in ferromagnets and shape-memory alloys A. Ktena a , D.I. Fotiadis a , P.D. Spanos b , C.V. Massalas c, * a Department of Computer Science, University of Ioannina, GR 45110 Ioannina, Greece b Department of Mechanical Engineering and Materials Science, Rice University, Houston, USA c Department of Materials Science, University of Ioannina, GR 45110 Ioannina, Greece Abstract A Preisach model able to adjust to different systems with hysteresis is presented. The related identification scheme involved uses data from a major hysteresis curve and a least-squares error minimization procedure for the parameters of the characteristic density. The output sequence, f ðtÞ; is obtained by integrating the characteristic probability density function, rða; bÞ; of the elementary hysteresis operators, g ab ; operating on the input sequence uðtÞ over the Preisach plane. Once the appropriate operator is chosen and the Preisach plane adjusted accordingly, the parameters of the characteristic density are determined via a least-squares procedure minimizing the error between the experimental major curve and the calculated one. Results using two different scalar operators are discussed. Further, the reliability of the procedure is assessed by considering experimental data regarding two different magnetic samples and a shape-memory alloy sample. r 2001 Published by Elsevier Science B.V. Keywords: Preisach modeling; Hysteresis; Identification procedure 1. Introduction Hysteresis is a phenomenon encountered in several natural, mechanical, engineering, and socioeconomical systems. The causes vary from system to system: they depend on the components and structure of the system and the laws governing their behavior and interaction. The effect however is common in all of them. The output is delayed with respect to the input. Not any delay can be referred to as hysteresis. Visintin [1] defines hysteresis as the rate independent memory effect. In a system with hysteresis, for every input there may be more than one equilibrium states. Then, the output state is a function of the current input as well as previous inputs and/or the initial state. When such a system is bistable it may be characterized by a hysteresis loop like those shown in Figs. 3–5. This common phenomenology has motivated this work which aims at developing a general model of hysteresis capable of capturing the behavior of various systems. The vehicle for this is the Preisach formalism [2], a macroscopic scalar model of ferromagnetic hysteresis (magnetization vs. field) that, lately, has been extended to applications in other systems *Corresponding author. Tel.: +30-651-97446; fax: +30-651- 97200. E-mail address: cmasalas@cc.uoi.gr (C.V. Massalas). 0921-4526/01/$ - see front matter r 2001 Published by Elsevier Science B.V. PII:S0921-4526(01)00983-8