Modeling of quasistatic magnetic hysteresis with feed-forward neural networks

Abstract

A modeling technique for rate-independent (quasistatic) scalar magnetic hysteresis is presented, using neural networks. Based on the theory of dynamic systems and the wiping-out and congruency properties of the classical scalar Preisach hysteresis model, the choice of a feed-forward neural network model is motivated. The neural network input parameters at each time step are the corresponding magnetic field strength and memory state, thereby assuring accurate prediction of the change of magnetic induction. For rate-independent hysteresis, the current memory state can be determined by the last extreme magnetic field strength and induction values, kept in memory. The choice of a network training set is motivated and the performance of the network is illustrated for a test set not used during training. Very accurate prediction of both major and minor hysteresis loops is observed, proving that the neural network technique is suitable for hysteresis modeling.

Quasistatic hysteresis modeling with feed-forward neural networks: Influence of the last but one extreme values

“…This model [5] respects the properties of the PHM, particularly, the congruency. It is composed of two hidden layers with sigmoidal transfer functions in each neuron.…”

“…In Ref. [5], the authors use a feed-forward neural network (FFNN) to modelize the quasistatic magnetic hysteresis. We detail this model in the next section and use it as a departure point of analysis.…”

Neural-network-based approach to dynamic hysteresis for circular and elliptical magnetization in electrical steel sheet

“…The FFNN is static in nature and can model the static relation between a set of parameters determining the magnetic state of the system and the system output [3]. The network is trained with the Levenberg-Marquardt algorithm [7], using a training set of measured input-output pairs spanning the entire range of possible input and output values.…”

“…Feedforward neural networks (FFNNs) are universal function approximators and have as such been successfully applied to model quasi-static (when the frequency approaches zero) and dynamic (for ) unidirectional magnetization [3], [4], as well as quasi-static vector magnetization in the special case of circular and elliptical magnetization patterns in nonoriented SiFe steels [5]. Preisach-type models include the reduced amount of measurement data required for model identification and the ability to resolve limitations of the Preisach technique, e.g., in the case of vector magnetization [5].…”

Qualitative Ferromagnetic Hysteresis Modeling

“…However, there exist many approaches to develop a mathematical model to describe the hysteretic relationship between the magnetization M and the magnetic field H. the first approach was the hysteresis model of Preisach invented in the 1935 [1] and the second is the Jiles-Atherton (JA) model [2] . Artificial intelligence has also been applied to the modeling of magnetic hysteresis and parameters identification of these models such as neural network and genetic algorithm [3,4,5,6,7,8,9,10,11,12,13] . Like neural networks, fuzzy logic can be conveniently used to approximate any arbitrary functions [14,15,16] .…”