The Jiles-Atherton (J-A) model, as a classical model, plays an important role in the study of ferromagnetic materials. However, its classical rendition, coupled with conventional identification algorithms, falls short in achieving both precision and computational efficiency. To scrutinize the hysteresis characteristics of silicon steel sheets with greater efficacy, this study pioneers the application of the field separation and loss separation method. This approach constructs a relationship between each magnetic field component and loss component. By incorporating eddy current losses and anomalous losses stemming from dynamic processes into the static Jiles-Atherton hysteresis model, we redefine the energy balance formula. Deriving the formulae for the model enhancement, we establish the dynamic J-A hysteresis model. Concurrently, we employ an adaptive inertia weight particle swarm optimization algorithm, augmented with a contraction factor, to identify model parameters. Comparative analysis of model fitting results against experimental data substantiates the efficacy of the enhanced algorithm in model parameter extraction. Through this algorithm, parameters in the dynamic model are extracted with an identification error not exceeding 8%, yielding B-H curves under diverse magnetic field variables. These outcomes underscore the accuracy and effectiveness of both the validated model and the improved algorithm as proposed in this paper.