Prediction and Comparative Analysis of the Inﬂuence of Magnetic Field Effect on PM2.5 Trapping Efﬁciency in Electrostatic Precipitator (ESP) under Different Temperatures

: Charged particles have high momentum under high-temperature conditions, which helps to promote their movement towards a dust collector in a magnetic ﬁeld environment, making it possible to improve the efﬁciency of the high-temperature wire-plate electrostatic precipitator (ESP) in this environment. A multi-ﬁeld coupling model was established to numerically simulate PM2.5 dust-removal efﬁciency in an ESP under different working conditions. Combining the particle swarm optimization (PSO) algorithm with the support vector machine (SVM) model, the PSO-SVM prediction model is presented. Simulated data were used as training data, and PSO-SVM and back-propagation (BP) neural network models were utilized to predict collection efﬁciency under different working conditions, respectively. The results show that introducing a magnetic ﬁeld can effectively improve the PM2.5 collection efﬁciency of wire-plate ESP, and the effect of a magnetic ﬁeld on the dust-removal efﬁciency is more obvious at higher temperatures and higher ﬂue gas velocities. When changing the working conditions, the predicted results of the magnetic ﬁeld effect conform to simulated ones, and the PSO-SVM predicted values have a smaller relative error than those of the BP model, which can better adapt to different working conditions. All of the above conclusions can be utilized as a simple and adequately efﬁcient example of the ESP model for follow-up research.


Introduction
With the rapid development of industry, coal, as a dominant energy source in China, is increasingly being used for combustion.Coal burning has driven the development of technology and also brought a series of environmental issues.Since 2013, many countries around the world have had successive smog weather, largely brought about by the smoke produced by coal burning.Particularly, Northern China has suffered a long-term haze and fog cover.To reach a steady ecological balance, on 5 March 2021, China proposed the "3060 Target", which means that China will strive for carbon dioxide emissions to peak before 2030 and to achieve carbon neutrality before 2060 [1].Wang et al. used Beijing as an example to evaluate the health and economic impact of PM2.5, and the results showed that PM2.5 not only had adverse health effects but also brought about huge economic losses.Replacing traditional cars with new energy vehicles can significantly reduce PM2.5 emissions.Yildiz et al. [2] conducted numerical simulations on urban driving cycles to analyze the impact of regenerative electronic stability control (RESC) systems to compare the energy consumption performance of powertrain architecture and found that, compared with all other systems, the studied powertrain significantly reduces the energy consumption of HFCEV, providing new ideas for the development of new energy vehicles.At present, the total dust-removal rate of conventional dust-removal equipment, including the electrostatic precipitator (ESP), reaches more than 97%, but the dust collection effect for PM2.5 is not as ideal as expected.So, in response to the national environmental governance policy, for the study on the change rule of PM2.5 under different parameters, the effective measures to improve the dust-removal efficiency and reduce the concentration of PM2.5 emissions have become urgent problems in environmental governance research [3].Jia et al. [4] conducted a bibliometric analysis of the existing publications on PM2.5 exposure over the past three decades and analyzed the current state and historical trends.They found that the number of publications on PM2.5 exposure has been increasing at an accelerating rate.Wu et al. [5] proposed a quantitative modeling and prediction method for sustained rainfall-PM2.5removal modes on a micro-temporal scale, citing the reasonableness and effectiveness of the proposed method.
This work established a magnetic field environment to add the magnetic effect on the basis of ESP to control the tiny particles whose principle is to attach an external magnetic field to the wire-plate ESP.Therefore, the charged PM2.5 particles would generate Lorentz force under the action of the magnetic field and realize the control of the motion trajectory of the charged particles, so as to achieve the purpose of dust collection.Cumming et al. [6] created a high-flue-gas condition to capture fine particles, and the experimental results showed that the fine magnetic particles could be successfully caught in a high-gradient magnetic field environment.Lawson et al. [7] studied particle dynamics in a magnetic field environment and constructed a trajectory equation for particles in incompressible viscous fluids based on magnetic field force, viscous force, and gravity.Huang et al. [8] simulated the critical path line, indicating the magnetic collection threshold position through the numerical evaluation of particle velocity contours; they found that particle size was one of the most important parameters determining ESP dust collection efficiency under the magnetic effect.Zhang [9] proposed a mathematical model of the motion of magnetic abrasive particles (MAPs) and studied the factors affecting the adsorbed instantaneouseffective abrasive particle (IEPA) through simulation analysis and experiments, which showed that with the increase in flue gas velocity and the growth rate of IEPA, arrest slowed down.Mahesh et al. [10] put forward a new mathematical model to calculate the nanoparticle heat generation in the tissues under an alternating magnetic field, and the corresponding temperature distribution was predicted.Du et al. [11] not only tested the inlet and outlet particulate matter emissions of 26 wet electrostatic precipitators (WESPs) of ultra-low-emission units but also analyzed the removal effect of the wet electrostatic precipitator process on PM10 and PM2.5 so as to obtain the effects of inlet particulate matter concentration, flue gas velocity, residence time, and droplet removal effect on the particulate matter removal effect, emission factors, and removal energy consumption of a wet ESP.These results showed that the concentrations of PM10 and PM2.5 in the flue gas can be controlled within 10 mg/m 3 and 3 mg/m 3 , respectively, by the WESP, which can realize the requirements of ultra-low soot emission.In view of the problems of low collection efficiency and large area occupied by fine particles in existing ESPs, Shen et al. [12] introduced a new type of horizontal electrode dust collector.Eboreime et al. [13] applied numerical methods to build the first two-dimensional cross-flow ESP model for airflow and particle capture by developing and implementing user-defined functions (UDFs) in ANSYS Fluent computational fluid dynamics (CFD) software.
Since the beginning of the twenty-first century, the use of back-propagation neural networks (BPNNs) to establish prediction models in different fields has been widely utilized in China.While the use of BPNNs to predict ESP efficiency is rare, Wang et al. [14] proposed a pork supply prediction method based on an improved mayfly optimization algorithm and back-propagated artificial neural network.Jiang et al. [15] established a mixed interval time-series prediction model to achieve the high-precision interval PM2.5 concentration prediction by considering the daily variation in pollutant concentrations.Considering the problem of the unstable prediction results of BPNNs, the optimization of the PSO-SVM prediction model emerged.The PSO-SVM predictive model is a new type of model for prediction made by introducing the PSO algorithm to the SVM prediction model.Song et al. [16] applied the radar target detection algorithm based on the SVM classifier to the problem of high-resolution distance profiles.Their results indicated that the radar target detection algorithm for SVM classifier can successfully detect targets in different clutter environments and had excellent performance.Sun et al. [17] combined an SVM and BPNNs to predict the computing amount of cloud-computing physical machines in an effort to improve the working efficiency of physical machines and the service quality of cloud computing.The result showed that, compared with the traditional SVM model, the PSO-SVM model not only improves the accuracy of prediction compared with the traditional SVM model, but also effectively detects abnormal problem domains [18].In order to categorize the deformation brought on by the extrusion of surrounding rock, Huang et al. [19] constructed an SVM-BP combination model.They then examined the impact of distinctive factors on the prediction outcomes and the accuracy of predictions made by various models.Using partial least squares discriminant analysis SVM algorithm and attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy, Song et al. [20] built a discriminant model to differentiate between aflatoxin-contaminated and uncontaminated peanut oil and optimized the SVM penalty and the kernel function parameters.Pan et al. [21] created a composite model that included a numerical SVM model of the catalyst layer to anticipate usage, increasing the robustness and generalization of the SVM discrimination approach.In order to address the issue of smart meter degradation being hard to predict under complicated variable situations, Wang et al. [22] developed a simple SVM-based error prediction approach.Yan et al. [23] raised the fast global optimization feature using the PSO, adjusted the SVM regression model's parameters, and used the combination model.They then compared the predicted outcomes with the measured values of the BPNN.The PSO algorithm was utilized by Wang et al. [24] to optimize the SVM model's parameters.The optimal parameter combination was determined to be penalty factor c = 1.42 and kernel parameter σ = 1.15.The optimal parameter combination was then substituted into the SVM model to create the PSO-SVM, which was then employed in the quantitative assessment of landslide susceptibility in the study area.The SVM optimization approach was the focus of Wang et al.'s analysis [25], which demonstrated the algorithm's high intrusion detection accuracy.An SVM-based image segmentation approach based on the texture and color of the picture as feature vectors was proposed by Aimin et al. [26].In order to increase the SVM robustness to measurement uncertainty, Wahb et al. [27] concentrated on evaluating the impact of each parameter's uncertainty on the forecast accuracy of the SVM.Zhang et al. [28] proposed a novel combinatorial neural network algorithm for the prediction of PM10 and PM2.5.The algorithm incorporates the use of the PSO technique to optimize the parameters of the neural network model.
In summary, there has been little research on the systematic numerical simulation of the dust-removal efficiency of high-temperature wire-plate ESP in magnetic field environments.Additionally, there are no reports on the prediction of ESP magnetic field effects under different working conditions using the PSO-SVM and BP neural network models.Therefore, this article conducted numerical simulations to evaluate the dust-removal efficiency of high-temperature wire-plate ESP under various operating conditions in a magnetic field environment.The simulation data were then combined with the PSO-SVM and BP neural network models to predict the magnetic field effect under different operating conditions.The obtained results can serve as a reference for further enhancing the dust-removal performance of ESP and utilizing intelligent algorithms to predict the capture performance of PM2.5 in ESP.

Analysis of Applied Magnetic Field Mechanism
The simplified two-dimensional model of wire-plate ESP is shown in Figure 1.When an external magnetic field is applied to the moving charged particles in the wire-plate ESP, the particles will spiral under the action of electromagnetic fields.The charged particles in ESP have parabolic motion under the action of electric field forces and circular motion under the Lorentz force generated by magnetic fields.The coupling effect of these two makes them move in a spiral motion, prolonging the residence time in ESP and making it easier to trap in order to improve the dust-removal efficiency [29].
The simplified two-dimensional model of wire-plate ESP is shown in Figure 1.When an external magnetic field is applied to the moving charged particles in the wire-plate ESP, the particles will spiral under the action of electromagnetic fields.The charged particles in ESP have parabolic motion under the action of electric field forces and circular motion under the Lorentz force generated by magnetic fields.The coupling effect of these two makes them move in a spiral motion, prolonging the residence time in ESP and making it easier to trap in order to improve the dust-removal efficiency [29].

Inlet Outlet
Corona wire Analysis mechanism of a wire-plate ESP under magnetic field.
During the calculations, the external magnetic field is added as a uniform one in the wire-plate ESP to reduce the error and facilitate the solution, and the method of controlling variables is adopted in this study.The uniform magnetic field is evenly distributed throughout the entire space and remains unaffected by fluctuations caused by the external environment.Therefore, its magnitude and direction remain constant and do not change.As a result, the solution does not involve solving Maxwell's equations.

Temperature Mechanism Analysis
When the flue gas enters the ESP under a magnetic field, the charged fine particles are not only affected by electric field force and Lorentz force, but also exhibit a certain degree of sensitivity to temperature.The influence of temperature on the capture process of fine particles in the wire-plate ESP is usually achieved by the flue gas density.It should be noted that the flue gas density in a specific area differs at different temperatures, thus leading to changes in the flow field inside the ESP.The above two steps are combined to complete the process of temperature influence on the particle dynamic field.From a quantitative point of view, how the temperature affects the changes in flue gas density and flue gas viscosity is, respectively, given as During the calculations, the external magnetic field is added as a uniform one in the wire-plate ESP to reduce the error and facilitate the solution, and the method of controlling variables is adopted in this study.The uniform magnetic field is evenly distributed throughout the entire space and remains unaffected by fluctuations caused by the external environment.Therefore, its magnitude and direction remain constant and do not change.As a result, the solution does not involve solving Maxwell's equations.

Temperature Mechanism Analysis
When the flue gas enters the ESP under a magnetic field, the charged fine particles are not only affected by electric field force and Lorentz force, but also exhibit a certain degree of sensitivity to temperature.The influence of temperature on the capture process of fine particles in the wire-plate ESP is usually achieved by the flue gas density.It should be noted that the flue gas density in a specific area differs at different temperatures, thus leading to changes in the flow field inside the ESP.The above two steps are combined to complete the process of temperature influence on the particle dynamic field.From a quantitative point of view, how the temperature affects the changes in flue gas density and flue gas viscosity is, respectively, given as where ρ gk is density of flue gas (kg/m 3 ), M gk is air quality (kg), V gk is air volume (m 3 ), µ k is the flue gas dynamic viscosity coefficient (kg/(m•s)), b ik is the correlation coefficient, and As a result of the irregular thermal motion and mutual collisions between ions and particles, the change in particle charge quantity decreases with increasing temperature, leading to a reduction in the electric field force.Consequently, temperature influences the diffusion of charge and, in turn, affects the electromagnetic field.
Moreover, in the wire-plate ESP, the total charge of the particles can be expressed as in which ε 0 is the vacuum permittivity, K 0 is the Boltzmann constant (1.38•10 −23 J/K), D i is the particle size (µm), q e is the electron charge (1.6•10 −19 C), N 0 is average ion number density per unit volume, t is the time for the particles to move in an electric field (s), and m ion is the ionic mass (kg).The temperature field in ESP is assumed to be uniformly distributed and does not change with time, namely, it does not involve solving the temperature field equations.

Multi-Field Coupling Analysis
The wire-plate ESP in this work contains both a fluid field and a particle dynamic field inside, which are controlled by the external magnetic field and temperature field.It is necessary to explain that these fields are not independent but rather exhibit a certain coupling relationship internally.The electric field affects the fluid field by altering the wind speed of the ion wind.The modified fluid field, in turn, reacts to the electric field through ion convection, exerting forces such as aerodynamic drag and ion wind on the particle dynamic field.In addition, the particle dynamic field is also influenced by Lorentz force generated through magnetic field and electric field force, respectively.Conversely, the particle dynamic field also influences the electric field through space charge, thereby altering the distribution of the electric field.The fluid field, in a reverse manner, is influenced by the gas-solid two-phase coupling.A multi-field coupling model, considering the influence of the temperature field on the flow field, particle dynamic field, and electromagnetic field, is established [31], as depicted in Figure 2.

BPNN Prediction Model
A typical BPNN is divided into three levels: input layer, hidden layer, and output layer.The training of BPNN is a type of supervised one, which contains the forward propagation of signals and the reverse propagation of errors.Figure 3 shows the specific prediction process of the BPNN.

BPNN Prediction Model
A typical BPNN is divided into three levels: input layer, hidden layer, and output layer.The training of BPNN is a type of supervised one, which contains the forward propagation of signals and the reverse propagation of errors.Figure 3 shows the specific prediction process of the BPNN.
Figure 3 illustrates the specific prediction process of the BPNN.It can be observed that the BPNN prediction process is a training process where signal forward propagation and error back propagation occur iteratively.The whole process can be divided into four parts: forward propagation, back propagation, memory training, and learning convergence.Among them, the network's layers are updated sequentially, while back propagation involves layer-by-layer correction.
In this section, the prediction model based on the BPNN was utilized to predict the capture performance of PM2.5 in the wire-plate ESP under the influence of a magnetic field.The specific parameters were set as follows: the number of hidden layer nodes is 6, the target error is 0.001, the learning rate is 0.01, and the number of iteration steps is 5000.

BPNN Prediction Model
A typical BPNN is divided into three levels: input layer, hidden layer, and output layer.The training of BPNN is a type of supervised one, which contains the forward propagation of signals and the reverse propagation of errors.Figure 3 shows the specific prediction process of the BPNN.

PSO-SVM Prediction Model
For seeking the mapping relationship between input and output, SVM is employed as a learning machine based on the statistical learning theory and the principle of structural risk minimization.The SVM possesses excellent computational capabilities and strong generalization ability, making it suitable for the simulation requirements of this study.The core concept of SVM involves transforming the input variables into a high-dimensional space through a nonlinear transformation and subsequently identifying the optimal linear classification surface.This process is primarily accomplished by defining various kernel functions.
Different kernel functions have different characteristics, and for arbitrary function, h(x) and ψ(x) can be written as where the kernel function G(x, y) is an inner product in the feature space.The commonly used kernel function in this work refers to the Gaussian radial one, which can be expressed as where θ is the telescopic scale and γ is a kernel function parameter.PSO is a simple algorithm with strong global search ability, which can be used as an intelligent optimization algorithm for swarm algorithms to optimize the SVM parameters, resulting in the creation of the PSO-SVM prediction model.This model combines the global search capability of the PSO algorithm with the ability of the optimized SVM to avoid complex genetic operations.The formulas for the PSO algorithm are presented below: x id = x id + v id (8) where i = 1, 2, . . ., D; d = 1, 2, . . ., D; c 1 and c 2 are learning factors, whose values are generally non-negative; r 1 and r 2 are random constants, ranging from 0 to 1; and The specific calculation process of the PSO-SVM prediction model is illustrated in Figure 4.

Numerical Solution of Capture Performance
Figure 5 shows the calculation flowchart of two-dimensional wire-plate ESP in this work, and the detailed simulation process is described as follows: (1) Modeling is achieved through the DM module in ANSYS and exported in IGS format.
The whole numerical solution process is shown in Figure 6.First, create a two-dimensional model in the DM module and save it as the IGS format, which is designed to adapt to the import format of Gambit software.

Numerical Solution of Capture Performance
Figure 5 shows the calculation flowchart of two-dimensional wire-plate ESP in this work, and the detailed simulation process is described as follows: (1) Modeling is achieved through the DM module in ANSYS and exported in IGS format.
The whole numerical solution process is shown in Figure 6.First, create a twodimensional model in the DM module and save it as the IGS format, which is designed to adapt to the import format of Gambit software.When partitioning the grid of the wire-plate ESP, considering that the voltage in the electrode discharge area is relatively large compared with other calculation areas, in order to ensure the accuracy of the simulation results, the corona areas near the three electrodes are subjected to grid refinement processing, totaling 48,260 grids.The entire two-dimensional wire-plate ESP model generates minimal distortion during grid division, resulting in high grid quality and convergence of iterative calculations.When partitioning the grid of the wire-plate ESP, considering that the voltage in the electrode discharge area is relatively large compared with other calculation areas, in order to ensure the accuracy of the simulation results, the corona areas near the three electrodes are subjected to grid refinement processing, totaling 48,260 grids.The entire two-dimensional wire-plate ESP model generates minimal distortion during grid division, resulting in high grid quality and convergence of iterative calculations.When partitioning the grid of the wire-plate ESP, considering that the voltage in the electrode discharge area is relatively large compared with other calculation areas, in order to ensure the accuracy of the simulation results, the corona areas near the three electrodes are subjected to grid refinement processing, totaling 48,260 grids.The entire two-dimensional wire-plate ESP model generates minimal distortion during grid division, resulting in high grid quality and convergence of iterative calculations.

Reliability Verification of Dust-Removal Efficiency Model
The dust collection area in the ESP can be divided into N + 1 sections.When the particle size distribution of the dust particles injected into the ESP follows an R-R distribution, the dust-removal efficiency under each particle size is referred to as the grade dust-removal efficiency.If n represents the collection efficiency of the i-th particle size in the j-th section, the graded dust-removal efficiency n can be calculated as follows: where M i,j is the concentration of the i-th particle size dust in the spatial area corresponding to section j.When j = 1, M i,j = M i,1 represents the i-th particle concentration at the inlet of the electrostatic precipitator.
Obtaining the grade efficiency of the three corona zones in a two-dimensional wireplate ESP for different particle sizes can be easily achieved by exporting the calculated data and fitting them under the specified operating conditions, as depicted in Figure 7.It is evident that the numerical simulation findings in this study exhibit a consistent overall trend with those reported in the literature [31].Moreover, the average discrepancy between them remains within 5%, thereby confirming the reliability of the dust-removal efficiency model and the subsequent numerical simulation techniques employed in this investigation.

Reliability Verification of Dust-Removal Efficiency Model
The dust collection area in the ESP can be divided into N + 1 sections.When the particle size distribution of the dust particles injected into the ESP follows an R-R distribution, the dust-removal efficiency under each particle size is referred to as the grade dust-removal efficiency.If n represents the collection efficiency of the i-th particle size in the j-th section, the graded dust-removal efficiency n can be calculated as follows: , , i , where , i j M is the concentration of the i-th particle size dust in the spatial area corre- sponding to section j.When j = 1, represents the i-th particle concentration at the inlet of the electrostatic precipitator.
Obtaining the grade efficiency of the three corona zones in a two-dimensional wireplate ESP for different particle sizes can be easily achieved by exporting the calculated data and fitting them under the specified operating conditions, as depicted in Figure 7.It is evident that the numerical simulation findings in this study exhibit a consistent overall trend with those reported in the literature [31].Moreover, the average discrepancy between them remains within 5%, thereby confirming the reliability of the dust-removal efficiency model and the subsequent numerical simulation techniques employed in this investigation.

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

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.
increase in temperature; this indicates that the effect of magnetic field on grade dustremoval efficiency becomes more obvious as the temperature rises.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° 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° 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.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.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° 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° 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.Based on the comparison of the curves and the subsequent analysis, the relative error and 45 • 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 • 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.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.

Simulation and Prediction of Magnetic Field Effect under Different Flue Gas Velocities
The working voltage is set as 60 kV, in the environment with and without magnetic field; Figure 12 shows the variation curves of PM2.5 grade efficiency under different flue gas velocities and temperatures, and it is not difficult to observe the following: (1) With or without a magnetic field, as well as considering the changes in flue gas flow rate and temperature, the efficiency of PM2.5 grade efficiency and dust-removal increases with the increase in particle size, and the gradient of the increase gradually decreases.
(2) Regardless of the influence of magnetic field, the grade efficiency of particles declines as the flue gas velocity ascends, gradually reduces with the increase in temperature, and the decreased gradient drops.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.

Simulation and Prediction of Magnetic Field Effect under Different Flue Gas Velocities
The working voltage is set as 60 kV, in the environment with and without magnetic field; Figure 12 shows the variation curves of PM2.5 grade efficiency under different flue gas velocities and temperatures, and it is not difficult to observe the following: (1) With or without a magnetic field, as well as considering the changes in flue gas flow rate and temperature, the efficiency of PM2.5 grade efficiency and dust-removal increases with the increase in particle size, and the gradient of the increase gradually decreases.
(2) Regardless of the influence of magnetic field, the grade efficiency of particles declines as the flue gas velocity ascends, gradually reduces with the increase in temperature, and the decreased gradient drops.

Simulation and Prediction of Magnetic Field Effect under Different Flue Gas Velocities
The working voltage is set as 60 kV, in the environment with and without magnetic field; Figure 12 shows the variation curves of PM2.5 grade efficiency under different flue gas velocities and temperatures, and it is not difficult to observe the following: (1) With or without a magnetic field, as well as considering the changes in flue gas flow rate and temperature, the efficiency of PM2.5 grade efficiency and dust-removal increases with the increase in particle size, and the gradient of the increase gradually decreases.
(2) Regardless of the influence of magnetic field, the grade efficiency of particles declines as the flue gas velocity ascends, gradually reduces with the increase in temperature, and the decreased gradient drops.(3) Whether there is a change in flue gas velocity and temperature or not, the grade efficiency in the magnetic field environment is higher compared with that in the absence of a magnetic field, which indicates that the magnetic field can effectively promote the capture of particles.(4) Regardless of the magnetic field, the difference in grade efficiency at different temperatures becomes smaller as the flue gas velocity increases, which shows that the temperature has less influence on the grade efficiency at high flue gas velocity.(5) In the presence or absence of a magnetic field, the higher the temperature, the lower the weakened gradient of the flue gas velocity on the grade efficiency, which suggests that the increase in temperature reduces the influence of the flue gas velocity on the grade efficiency.
atures becomes smaller as the flue gas velocity increases, which shows that the temperature has less influence on the grade efficiency at high flue gas velocity.(5) In the presence or absence of a magnetic field, the higher the temperature, the lower the weakened gradient of the flue gas velocity on the grade efficiency, which suggests that the increase in temperature reduces the influence of the flue gas velocity on the grade efficiency.To gain a clearer understanding of the relationship between magnetic field and flue gas velocity, the grade efficiency with and without a magnetic field at 873 K and at different flue gas velocities can be obtained based on Figure 10, as shown in Figure 13: (1) At the same temperature, the difference in grade efficiency among different flue gas velocities gradually decreases and flattens with the increases in particle size, indicating that the magnetic field has a more pronounced effect on enhancing the grade efficiency of smaller particle sizes.(2) The larger the flue gas velocity, the greater the increased magnitude of magnetic field on the grade efficiency, showing that the magnetic field effect becomes more significant at a higher flue gas velocity.
(3) The grade efficiency achieved when the flue gas velocity increases by 2.0 m/s is roughly equivalent to that obtained when a 0.5 Tesla magnetic field is applied.This indicates that, although the increase in the flue gas velocity reduces the dust-removal efficiency, the introduction of a magnetic field makes up for the weakening resulting from flue gas velocity.To gain a clearer understanding of the relationship between magnetic field and flue gas velocity, the grade efficiency with and without a magnetic field at 873 K and at different flue gas velocities can be obtained based on Figure 10, as shown in Figure 13: (1) At the same temperature, the difference in grade efficiency among different flue gas velocities gradually decreases and flattens with the increases in particle size, indicating that the magnetic field has a more pronounced effect on enhancing the grade efficiency of smaller particle sizes.(2) The larger the flue gas velocity, the greater the increased magnitude of magnetic field on the grade efficiency, showing that the magnetic field effect becomes more significant at a higher flue gas velocity.(3) The grade efficiency achieved when the flue gas velocity increases by 2.0 m/s is roughly equivalent to that obtained when a 0.5 Tesla magnetic field is applied.This indicates that, although the increase in the flue gas velocity reduces the dust-removal efficiency, the introduction of a magnetic field makes up for the weakening resulting from flue gas velocity.The simulated data of Figure 12-representing the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) and temperatures (473 K, 673 K, and 873 K) with magnetic field strengths of 0.0 T and 0.5 T-are selected as the training data, and the PSO-SVM and the BPNN models are then used to predict the grade efficiency.Comparing the predicted values of the two models with the simulated data, as depicted in Figure 14, the following can be found: (1) No matter what the flue gas velocity is, the variation law of the curves predicted by the BPNN and the PSO-SVM models is basically consistent with that of simulated ones, indicating that the two models possesses a certain level of reliability in predicting the magnetic field effect under different flue gas velocities.(2) Under two different flue gas velocities, the PSO-SVM model outperforms the BPNN The simulated data of Figure 12-representing the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) and temperatures (473 K, 673 K, and 873 K) with magnetic field strengths of 0.0 T and 0.5 T-are selected as the training data, and the PSO-SVM and the BPNN models are then used to predict the grade efficiency.Comparing the predicted values of the two models with the simulated data, as depicted in Figure 14, the following can be found: (1) No matter what the flue gas velocity is, the variation law of the curves predicted by the BPNN and the PSO-SVM models is basically consistent with that of simulated ones, indicating that the two models possesses a certain level of reliability in predicting the magnetic field effect under different flue gas velocities.(2) Under two different flue gas velocities, the PSO-SVM model outperforms the BPNN model in terms of the agreement degree between the predicted values and simulated data, as well as the proximity of the predicted curves to the simulated ones, indicating that the PSO-SVM model has a higher accuracy.The simulated data of Figure 12-representing the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) and temperatures (473 K, 673 K, and 873 K) with magnetic field strengths of 0.0 T and 0.5 T-are selected as the training data, and the PSO-SVM and the BPNN models are then used to predict the grade efficiency.Comparing the predicted values of the two models with the simulated data, as depicted in Figure 14, the following can be found: (1) No matter what the flue gas velocity is, the variation law of the curves predicted by the BPNN and the PSO-SVM models is basically consistent with that of simulated ones, indicating that the two models possesses a certain level of reliability in predicting the magnetic field effect under different flue gas velocities.(2) Under two different flue gas velocities, the PSO-SVM model outperforms the BPNN model in terms of the agreement degree between the predicted values and simulated data, as well as the proximity of the predicted curves to the simulated ones, indicating that the PSO-SVM model has a higher accuracy.Based on the data in Figure 14, a comparative chart with a 45° line is depicted in Figure 15 to compare the predicted values of the two models under different flue gas velocities.It is not difficult to find that no matter how the flue gas velocity changes, the predicted values of the PSO-SVM model are closer to the 45° line compared with those of the BPNN model, especially at 1.0 m/s.These findings further emphasize the higher accuracy Based on the data in Figure 14, a comparative chart with a 45 • line is depicted in Figure 15 to compare the predicted values of the two models under different flue gas velocities.It is not difficult to find that no matter how the flue gas velocity changes, the predicted values of the PSO-SVM model are closer to the 45 • line compared with those of the BPNN model, especially at 1.0 m/s.These findings further emphasize the higher accuracy of the PSO-SVM model in predicting the magnetic field effect at different flue gas velocities.By analyzing Figures 14 and 15, it can be seen that the PSO-SVM model demonstrates a higher prediction accuracy for the grade efficiency under different flue gas velocities at 473 K. Based on this, using the same training data as in Figure 14, the PSO-SVM model is used to predict the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) at 673 K with a magnetic field strength of 0.25 Tesla.Figure 16 shows the comparison and relative error between the predicted results and the simulated data.The following can be seen: (1) Under two different flue gas flow rates, the PSO-SVM prediction curve effectively describes the changes in grade efficiency and exhibits a high degree of consistency with the simulation data, as shown in Figure 16.This confirms the strong applicability of the PSO-SVM model in predicting the magnetic field effects under different flue gas flow velocities.By analyzing Figures 14 and 15, it can be seen that the PSO-SVM model demonstrates a higher prediction accuracy for the grade efficiency under different flue gas velocities at 473 K. Based on this, using the same training data as in Figure 14, the PSO-SVM model is used to predict the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) at 673 K with a magnetic field strength of 0.25 Tesla.Figure 16 shows the comparison and relative error between the predicted results and the simulated data.The following can be seen: (1) Under two different flue gas flow rates, the PSO-SVM prediction curve effectively describes the changes in grade efficiency and exhibits a high degree of consistency with the simulation data, as shown in Figure 16.This confirms the strong applicability of the PSO-SVM model in predicting the magnetic field effects under different flue gas flow velocities.(2) The relative errors of the predicted values of the two flue gas velocities are all less than 3%, and they are even below 2% when the flue gas velocity is 3 m/s, as shown in Figure 16, proving that the PSO-SVM model has high accuracy in predicting the magnetic field effect at different flue gas velocities.By analyzing Figures 14 and 15, it can be seen that the PSO-SVM model demonstrates a higher prediction accuracy for the grade efficiency under different flue gas velocities at 473 K. Based on this, using the same training data as in Figure 14, the PSO-SVM model is used to predict the grade efficiency under different flue gas velocities (1.0 m/s, 3.0 m/s) at 673 K with a magnetic field strength of 0.25 Tesla.Figure 16 shows the comparison and relative error between the predicted results and the simulated data.The following can be seen: (1) Under two different flue gas flow rates, the PSO-SVM prediction curve effectively describes the changes in grade efficiency and exhibits a high degree of consistency with the simulation data, as shown in Figure 16.This confirms the strong applicability of the PSO-SVM model in predicting the magnetic field effects under different flue gas flow velocities.(2) The relative errors of the predicted values of the two flue gas velocities are all less than 3%, and they are even below 2% when the flue gas velocity is 3 m/s, as shown in Figure 16, proving that the PSO-SVM model has high accuracy in predicting the magnetic field effect at different flue gas velocities.

Conclusions
In this study, the dust-removal efficiency of PM2.5 in a high-temperature wire-plate ESP under different working conditions in a magnetic field is numerically simulated.The simulated data are used as training data for the prediction model, and the PSO-SVM and the BPNN models are used to predict the magnetic field effect under different working conditions.The conclusions are as follows: (1) Regardless of the particle size and flue gas velocity, the dust-removal efficiency of PM2.5 in the wire-plate ESP shows a nonlinear decreasing trend with the increase in temperature, and it gradually slows down.(2) Under the same working conditions, the introduction of a magnetic field significantly enhances the particle grade efficiency compared with that in the absence of a magnetic field; further, the magnetic effect has a more obvious improvement in the dust-removal efficiency of fine particle sizes.At high temperatures and high flue gas flow velocities, the effect of an external magnetic field on improving the dust-removal efficiency of PM2.5 particles is more evident.(3) Both the BPNN and the PSO-SVM models are capable of describing the variation law of PM2.5 dust-removal efficiency under different working conditions; moreover, the predicted curves are generally close to the simulated points.(4) Compared with the BPNN model, the predicted values of the PSO-SVM model are more consistent with the simulated data, and the PSO-SVM model also has a higher prediction accuracy, showing a better prediction ability and adaptability to dustremoval efficiency under various working conditions.

Figure 1 .
Figure 1.Analysis mechanism of a wire-plate ESP under magnetic field.

Figure 2 .
Figure 2. Schematic diagram of multi-field coupling relationship inside high-temperature ESP.

Figure 2 .
Figure 2. Schematic diagram of multi-field coupling relationship inside high-temperature ESP.

Figure 2 .
Figure 2. Schematic diagram of multi-field coupling relationship inside high-temperature ESP.

Figure 3
Figure 3 illustrates the specific prediction process of the BPNN.It can be observed that the BPNN prediction process is a training process where signal forward propagation and error back propagation occur iteratively.The whole process can be divided into four

( 2 )
Import the obtained model into Gambit and save it in .mshformat to complete grid refinement processing and facilitate subsequent calculations.The purpose of saving the generated mesh model in .mshformat is to return it to the Fluent module of the ANSYS software for setting boundary conditions and calculation.(3)Import it into FLUENT for calculation and set boundary conditions, fluid phase, and

Figure 7 .
Figure 7.Comparison of the grade efficiency.

Figure 7 .
Figure 7.Comparison of the grade efficiency.

Figure 8 .
Figure 8. Grade efficiency with or without magnetic field at different temperatures.

Figure 9 .
Figure 9.Comparison of grade efficiency between simulated data and predicted values.

Figure 8 .
Figure 8. Grade efficiency with or without magnetic field at different temperatures.

Figure 8 .
Figure 8. Grade efficiency with or without magnetic field at different temperatures.

Figure 9 .
Figure 9.Comparison of grade efficiency between simulated data and predicted values.

Figure 9 .
Figure 9.Comparison of grade efficiency between simulated data and predicted values.

Figure 10 .
Figure 10.Comparison of relative error and 45° line between two models.

Figure 11 .
Figure 11.Comparison and relative error between predicted values and simulated data of grade efficiency.

Figure 10 .Figure 10 .
Figure 10.Comparison of relative error and 45 • line between two models.

Figure 11 .
Figure 11.Comparison and relative error between predicted values and simulated data of grade efficiency.

Figure 11 .
Figure 11.Comparison and relative error between predicted values and simulated data of grade efficiency.

Figure 12 .
Figure 12.Grade efficiency at different temperatures and flue gas velocities with and without magnetic field.

Figure 12 .
Figure 12.Grade efficiency at different temperatures and flue gas velocities with and without magnetic field.

Figure 13 .
Figure 13.Grade efficiency at 873 K with and without magnetic field.

Figure 13 .
Figure 13.Grade efficiency at 873 K with and without magnetic field.

Figure 13 .
Figure13.Grade efficiency at 873 K with and without magnetic field.

Figure 14 .
Figure 14.Comparison between predicted values and simulated data of grade efficiency.

Figure 14 .
Figure 14.Comparison between predicted values and simulated data of grade efficiency.

Figure 15 .
Figure 15.Comparison of predicted and simulated values with a 45° line for different models.

Figure 15 .
Figure 15.Comparison of predicted and simulated values with a 45 • line for different models.

Figure 15 .
Figure 15.Comparison of predicted and simulated values with a 45° line for different models.

Figure 16 .
Figure 16.Comparison and relative error between the predicted values and the simulated data of grade efficiency.

Figure 16 .
Figure 16.Comparison and relative error between the predicted values and the simulated data of grade efficiency.