磁化曲线的连续可导拟合方法

Magnetization Curve Fitting Based on the Function-chain Neural Network

为了满足磁场储能迭代计算的需要,提出了磁化曲线的连续可导拟合方法。磁化曲线具有高度非线性,难以用一个函数来逼近,根据其特点,提出了线性插值和二次插值相结合的方法,分为三段来拟合。根据曲线连接点处的约束关系,通过求解约束方程获得拟合函数的待定系数,保证了整条曲线的连续可导。由拟合结果给出了磁导率随磁通密度的函数关系及其导函数关系。最后给出了一个具体的拟合算法实例,验证了拟合精度。

To meet the need of iteractive calculation of the magnetic field energy, the continuous derivable fitting method of the magnetization curve is proposed. The magnetization curve is seriousy nonlinear, it can not be fitted by one function. According to its characteristic, the magnetization curve is divided in three parts, seprately fitted by linear interpolations and quadratic interpolation. By the constraint relation at the connection point, the constraint equations is established, and the undetermined coefficients of the fitting function is solved, which ensured the continuous and differentiable of the curve. By the fitting results, the function of the magnetic permeability and the flux density is provided, and its derived function is given. At last, a fitting example is proposed, and the fitting precision is confirmed.