Purpose

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

Design/methodology/approach

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

Findings

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

Originality/value

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

中文翻译：

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基于约束的优化技术来估算吉尔斯-阿瑟顿磁滞模型的物理参数

目的

在模拟铁磁材料时，Jiles-Atherton（JA）磁滞模型的参数不合适会导致非物理磁滞回线。这可以通过在参数拟合优化算法中包含适当的物理约束来解决。本文旨在在亚启发式模拟退火（SA）优化和Nelder-Mead单纯形（NMS）算法中实施约束，以找到产生物理磁滞回线的JA模型参数。使用单板测试仪的现有测量结果模拟了无取向（NO）硅钢板的准静态B（H）特性。将JA模型在修改的逻辑函数和分段三次样条曲线拟合到平均M（H）曲线下收到的磁滞回线与测得的较小和主要磁滞回线进行比较。

设计/方法/方法

物理约束考虑了起点处的迟滞敏感性。这有助于优化决策，在给定的迭代步骤中接受还是拒绝随机生成的参数。全局和局部启发式优化方法的组合用于确定JA滞后模型的参数。首先，应用SA方法，然后在该过程中使用NMS方法。

发现

物理约束的实现提高了参数拟合的鲁棒性，并导致了更多的物理磁滞回线。与适合使用分析函数相比，通过拟合至所测得的主要磁滞回线平均值的样条对无磁化磁化进行建模，可以更好地拟合数据。结果表明，修改后的逻辑函数可以被认为是本文所用的NO硅钢合适的滞后（分析）函数。在高强度激励下，平均M（H）曲线可与测得的磁滞回线正确拟合。但是，对于主磁滞回线有效的参数不能为次磁滞回线产生适当的拟合。

创意/价值

在SA和NMS优化算法中添加了物理约束。优化算法取自GNU科学库，该库可从GNU项目获得。本文描述的方法可用于估算JA磁滞模型的物理参数，特别是对于NO硅钢的单向交替B（H）特性。