A hysteresis model, based on the enhanced neural network with parallel strategy, is put forward for the prediction of the accurate magnetic behavior of electrical steel sheets (ESSs). Aimed at overcoming the drawbacks such as low convergence rate and convenient to trap into local optimum in the conventional back-propagation neural network (BPNN), a novel collaborative BPNN learning algorithm is introduced according to the error back propagation mechanism and particle swarm optimization (PSO). The reasonable selection of the test point set by the uniform design of experiment methodology, has the potential of lowering the measurement cost, together with guaranteeing the accuracy of the hysteresis modeling. A parallel strategy, which is based on the fast Fourier transformation (FFT), is applied for enhancing the train efficiency of BPNNs. The proposed algorithm is applied for the purpose of modeling the vector hysteresis behavior of ESS. Together, the comparison of the measured and predicted results of H-locus and core loss is discussed as well. INDEX TERMS Back-propagation neural network, collaborative algorithm, design of experiment, parallel strategy, particle swarm optimization, vector hysteresis model.

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