Hysteresis Simulator

A basic hysteresis simulation is implemented using the Flatley Model, originally implemented by Marco Buzio, and now translated to Python in the following package: https://gitlab.cern.ch/dsb/hysteresis/hysteresis-simulator.

Implementation of Jiles-Atherton model with open-source matlab code

A crude version of the Jiles-Atherton model was originally implemented by Verena, but then superseeded by using open-source Octave code on GitHub and running it through oct2py. Open Source Implementation of Different Variants of Jiles-Atherton Model of Magnetic Hysteresis Loops paper.

Eddy current decay implementation

Eddy current decay is implemented in as

$$\begin{array}{rl}{\dot{I}}_{\text{e},t}& =-{\tau }_{EM}{\dot{H}}_t-\frac{I_{\text{e},t}}{\tau }\\ I_{\text{e},t+1}& =I_{\text{e},t}+{\dot{I}}_{\text{e},t}\Delta t\\ B_{\text{e},t}& =c{I}_{\text{e},t}\end{array}$$

And since $H=I/{\ell }_m$, so $\dot{H}=\dot{I}/{\ell }_m$, and therefore

$$\begin{array}{rl}{\dot{I}}_{\text{e}}& =-{\tau }_{EM}^{\prime }\dot{I}-\frac{I_{\text{e}}}{\tau }\\ & =a\dot{I}+b{I}_{\text{e}}\end{array}$$

and $B_{\text{e}}=c{I}_{\text{e}}$ This solves the differential equation for $I_{\text{e}}$, however we are interested in $B_{\text{e}}$, and since ${\dot{B}}_{\text{e}}=c{\dot{I}}_{\text{e}}$, we end up with

$$\begin{array}{rl}{\dot{B}}_{\text{e}}& =ac\dot{I}+b{B}_{\text{e}}\\ & =d\dot{I}+b{B}_{\text{e}}\end{array}$$

where

$$\begin{array}{rl}d& =-c{\tau }_{EM}/{\ell }_m\\ b& =-1/\tau \end{array}$$

Note that the eddy current decay constant is in fact not a constant, as discussed with Marco, and is in fact described as $\tau \approx {\mu }_r^2/L$, or with a first order approximation $\tau \approx f(I)$, or $\tau \approx L/R$.

Supposing that $\tau$ is indeed $\tau (I)$, we need to compute it using a fully connected layer, as opposed to with an torch.nn.Parameter.