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Wikipedia / Preisach model of hysteresis

In electromagnetism, the Preisach model of hysteresis is a model of magnetic hysteresis. Originally, it generalized hysteresis as the relationship between the magnetic field and magnetization of a magnetic material as the parallel connection of independent relay hysterons. It was first suggested in 1935 by Ferenc (Franz) Preisach in the German academic journal . In the field of ferromagnetism, the Preisach model is sometimes thought to describe a ferromagnetic material as a network of small independently acting domains. A sample of iron, for example, may have evenly distributed magnetic domains, resulting in a net magnetic moment of zero.

Mathematically similar models seem to have been independently developed in other fields of science and engineering. One notable example is the model of capillary hysteresis in porous materials developed by Everett and co-workers. Since then, following the work of people like M. Krasnoselkii, A. Pokrovskii, A. Visintin, and I.D. Mayergoyz, the model has become widely accepted as a general mathematical tool for the description of hysteresis phenomena of different kinds.

Nonideal relay

The relay hysteron is the fundamental building block of the Preisach model. It is described as a two-valued operator. Its I/O map takes the form of a loop, as shown:

defines the "switch-on" threshold.

takes the path of a loop, and its next state depends on its past state.

is expressed as:

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Discrete Preisach model

The Preisach model consists of many relay hysterons connected in parallel, given weights, and summed. This can be visualized by a block diagram:

, the true hysteresis curve is approximated better.

approaches infinity, we obtain the continuous Preisach model.

Preisach plane

values. Depending on their distribution on the Preisach plane, the relay hysterons can represent hysteresis with good accuracy.

as any other case does not have a physical equivalent in nature.

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A modified formulation of the classical Preisach model has been presented, allowing analytical expression of the Everett function. This makes the model considerably faster and especially adequate for inclusion in electromagnetic field computation or electric circuit analysis codes.

Vector Preisach model

The vector Preisach model is constructed as the linear superposition of scalar models. For considering the uniaxial anisotropy of the material, Everett functions are expanded by Fourier coefficients. In this case, the measured and simulated curves are in a very good agreement. Another approach uses different relay hysteron, closed surfaces defined on the 3D input space. In general spherical hysteron is used for vector hysteresis in 3D, and circular hysteron is used for vector hysteresis in 2D.

Applications

The Preisach model has been applied to model hysteresis in a wide variety of fields, including to study irreversible changes in soil hydraulic conductivity as a result of saline and sodic conditions, the modeling of soil water retention and the effect of stress and strains on soil and rock structures.

See also

References