Hysteresis Model Based on Neural Network and Consuming Function
Introduction
The computation of steadystate solutions of nonlinear timeperiodic magnetic fields can be performed in the time or the harmonic domain. The solutions in the time domain generally require several periods to reach a steady state, by using a timestepping technique starting from arbitrary initial values. Variables in the electromagnetic field under steadystate excitations can be approximated by the triangular series. The electromagnetic field can be solved directly in the harmonic domain, without a long computational time.
Table 5.13 Comparison of the flux density
Uac(V) 
Bav(T) 
B1(T) 
B2(T) 

^{B}av,dc 
^{B}av,ac 
^{B}1,dc 
^{B}1,ac 
^{B}2,dc 
^{B}2,ac 

240 
0.858 2 
0.918 6 
0.972 7 
0.851 0 
0.868 1 
0.898 5 
368 
0.383 0 
1.416 3 
0.531 8 
1.305 6 
0.4107 
1.386 5 
495 
0.010 0 
1.8909 
0.033 0 
1.873 3 
0.007 2 
1.8744 
However, it is difficult to deal with hysteresis effects in computation of nonlinear magnetic fields. The fixedpoint technique is used in the timestepping finite element method to analyze the hysteretic characteristics and eddy current problems. A smoothing algorithm is proposed to guarantee the stability of the solution in the iterative procedure when the hysteresis model is involved in the numerical computation of the magnetic field [47].
The hysteresis loops of the iron core exhibit symmetric and asymmetric features under sinusoidal and DCbiased magnetizations respectively [43]. The opentype single sheet tester has been developed to measure the static hysteresis loops under DCbiased magnetization [38]. However, it is still difficult to obtain the DCbiasing hysteresis loops of the laminated core directly from the measurement. In addition, there are no proper hysteresis models combined with numerical methods to compute the nonlinear magnetic field under DCbias conditions. The Preisach model requires experimental dynamic hysteresis loops, which is difficult to measure when the DC magnetic flux exists in the laminated core. The JilesAtherton model is not accurate enough to simulate the DCbiasing hysteresis loops [49]. The DCbiasing hysteresis loops are simulated precisely by using the neural network (NN) theory [43]. However, the NN hysteresis model may occasionally predict inaccurate magnetic fields in numerical computation, due to the limited generalization ability.