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Summary

HysteronModel Base class for vector hysteron models

this = HysteronModel(Bs, M)

Piecewise linear shape functions are used. Hysteron evaluation methods must be subclassed.

The model is stateful (p, B); re-initialization is triggered whenever k_step_input < this.step in this.evaluate_H.

PROPERTIES

  • B_cand - current B-values

  • B_previous - previous B-values

  • B_saturation - saturation flux density

  • M - number of hysterons

  • dp - spacing between shape-function nodes

  • ksis - hysteron limits

  • p_cand - current hysteron values, possibly temporary

  • p_previous - previous hysteron values

  • shape_function_nodes - shape function interpolant x-data

  • shape_function_values - shape function interpolant y-data

  • step - current step

Methods

Class methods are listed below. Inherited methods are not included.

* HysteronModel Base class for vector hysteron models

this = HysteronModel(Bs, M)

Piecewise linear shape functions are used. Hysteron evaluation methods must be subclassed.

The model is stateful (p, B); re-initialization is triggered whenever k_step_input < this.step in this.evaluate_H.

* HysteronModel/PlayModel is a function.

this = PlayModel(Bs, M)

* HysteronModel/clear_copy is a function.

model = clear_copy(this)

* eval_nodefun Evaluate one “shape function of shape function”

f = eval_nodefun(this, b, k, m)

Evaluates a piecewise-linear function with the input argument b. This function has the value of 1 at b = this.nodes(m)(k), and 0 at all other nodes.

* evaluate_H Evaluate H-vector.

H = evaluate_H(this, Bin, kstep)

Evaluates H with the given B, at the given time-step, and updates the state of this.

H = evaluate_H(this, Bin, false)

The same as above, but skip state-update.

* evaluate_H_scalar Evaluate scalar model.

H = evaluate_H_scalar(this, Bin)

Evaluates scalar H with the input scalar time-series Bin.

* evaluate_differential_reluctivity Evaluate differential reluctivity.

dHdB = evaluate_differential_reluctivity(this, Bin, kstep)

Evaluates the differential reluctivity dH/dB using numerical differentiation.

* evaluate_shape_function Evaluates the scalar shape functions.

Hout = evaluate_shape_function(this, pnorm, m)

* evaluate_vector_hysteron Evaluate vector hysteron value.

Pout = evaluate_vector_hysteron(this, B, m)

Evaluates the hysteron m with the given input flux density (2xN vector) and the current hysteron state, AND update the current hysteron states.

Pout = evaluate_vector_hysteron(this, B, m, false)

The same as above, but don’t update current state.

* fit_model_with_least_squares Fit given model using non-negative

least-squares.

model = fit_model_with_least_squares(model, loops) fits the given model to measured BH loops.

  • model : a HysteronModel

  • loops : an array of structs with the fields .B and .H

IMPORTANT: the given loop data should span one entire major BH loop, not more and not less.

Fitting is is performed by feeding the given B-data to the model, and fitting its output to the measured H, using monotonic non-negative least-squares fitting on the shape function nodal values.

* initialize Initializes the model.

initialize(this, Binit) initializes the model to the given initial flux density vectors, using linear ramping.

* ndof Number of free nodes in shape function.

n = ndof(this, m)

* nodes Nodes of shape function.

bs = nodes(this, m)

* sample_scalar_hysteron Evaluate scalar hysteron for series input.

bout = sample_scalar_hysteron(this, Bin, m) evaluates the m:th scalar hysteron for the input time-series Bin.

* set_new_step Increment step.

set_new_step(this, kstep) sets the current candidate state (p_cand, B_cand) as the previous state (p_previous, B_previous)

* set_shape_function_data Set shape function nodes from fitted vector.

set_shape_function_data(this, coeffs)

set_shape_function_data(this, cs, plot_results)

* simulate_measured_loop Simulate H-values.

H = simulate_measured_loop(this, Bmeas)

Bmeas should consist of exactly one period of B.