## 4 Results and Discussions
### Simulation and Prediction of Magnetic Field Effect with Different Particle Sizes  
In both magnetic field and non-magnetic-field environments, at a working voltage of 50 kV and a flue gas flow rate of 0.5 m/s, the variation in particle classification dust removal efficiency with particle size can be observed at different temperatures (473 K, 673 K, and 873 K), as depicted in Figure 8. We can summarize our findings as follows:  
1. Irrespective of the consideration of changes in magnetic field and temperature, the efficiency of grade PM2.5 dust-removal gradually increases with the increase in particle size, eventually reaching a plateau.
2. In the presence or absence of a magnetic field, the efficiency of grade dust-removal gradually decreases with the increasing temperature, and this downward trend becomes less pronounced over time.
3. At the same temperature, the introduction of a magnetic field improves the grade dust-removal efficiency, and the extent of improvement gradually increases with the increase in temperature; this indicates that the effect of magnetic field on grade dust-removal efficiency becomes more obvious as the temperature rises.  
Figure 7: Comparison of the grade efficiency.  
By utilizing the grade efficiency data under different temperatures (both with and without a magnetic field) as training data, the BPNN and PSO-SVM models are employed to predict the grade efficiency at 0.25 Tesla and 473 K. The comparison between these models is shown in Figure 9. It is found that both the BPNN and the PSO-SVM models have satisfactory prediction capabilities when compared with the simulation results. Notably, the curve predicted by the PSO-SVM model closely aligns with the original simulated data, indicating that the PSO-SVM model possesses higher prediction accuracy than the BPNN model.  
Based on the comparison of the curves and the subsequent analysis, the relative error and 45\({}^{\circ}\) line comparative chart of the two models are obtained, as shown in Figure 10. It can be seen that the predicted values by the PSO-SVM have a smaller error than those of the BPNN, thereby verifying the superior prediction accuracy of the PSO-SVM model. The PSO-SVM prediction data points are closer to the 45\({}^{\circ}\) line, as shown in Figure 10, which further indicates that the PSO-SVM model is more accurate in predicting the magnetic field effect with R-R size distribution.  
Upon comprehensive comparison of Figures 8 and 9, it is not difficult to find that the PSO-SVM model has a higher prediction accuracy. To further verify this conclusion, the data from Figure 8 are used as training samples to predict the grade efficiency under 673 K and 0.25 T conditions using the PSO-SVM model. A comparison is then conducted, as illustrated in Figure 11. Figure 11 clearly demonstrates that the predicted values of PSO-SVM for the grade efficiency under 673 K and 0.25 T are better matched with the actual simulated data, indicating that the prediction results of the PSO-SVM are more objective. Furthermore, as depicted in Figure 11, the relative errors of the PSO-SVM model predominantly remain below 1%, which also proves that the PSO-SVM model has a high prediction accuracy under a magnetic field with R-R size distribution.  
Figure 8: Grade efficiency with or without magnetic field at different temperatures.  
Figure 9: Comparison of grade efficiency between simulated data and predicted values.