Hysteresis Modeling in Iron-Dominated Magnets Based on a Multi-Layered NARX Neural Network Approach

Abstract

A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.

Drift-Free Integration in Inductive Magnetic Field Measurements Achieved by Kalman Filtering

“…Some of the aspects on which further work is planned include extending the method to long, slender induction coils such as the ones used to measure the integral field produced by accelerator magnets and developing suitable formulations for non-linear current-to-field relationships (Equation ( 14 )) in order to improve accuracy when only the excitation current can be used. In particular, preliminary investigations showed promising results with respect to the application of recurrent neural networks [ 34 ] or more complex neural architectures [ 35 ] in terms of representing dynamic magnetic phenomena such as eddy currents and hysteresis. The use of high-precision measurements obtained by the Hall probe-based Kalman filter in a controlled laboratory setting is currently being considered for training a network that will then be used to supplement simple current measurement in a real-time operational context.…”