Experimental Setup and Machine Learning-Based Prediction Model for Electro-Cyclone Filter Efficiency: Filtering of Ship Particulate Matter Emission

Abstract

Ship emissions significantly impact air quality, particularly in coastal and port regions, contributing to elevated concentrations of PM_2.5, and PM₁₀, with varying effects observed across different locations. This study investigates the effectiveness of emission control policies, inland and port-specific contributions to air pollution, and the health risks posed by particulate matter (PM). A regression discontinuity model at Ningbo Port revealed that ship activities show moderate PM_2.5 and PM₁₀ variations. In Busan Port, container ships accounted for the majority of emissions, with social costs from pollutants estimated at USD 31.55 million annually. Inland shipping near the Yangtze River demonstrated significant PM contributions, emphasizing regional impacts. Health risks from PM_2.5, a major global toxic pollutant, were highlighted, with links to respiratory, cardiovascular, and cognitive disorders. Advances in air purification technologies, including hybrid electrostatic filtration systems, have shown promising efficiency in removing submicron particles and toxic gases, reducing energy costs. In this paper, a random forest machine learning model developed to predict particulate concentrations post-cleaning demonstrated robust performance (MAE = 0.49 P/cm³, R² = 0.97). These findings underscore the critical need for stringent emission controls, innovative filtration systems, and comprehensive monitoring to mitigate the environmental and health impacts of ship emissions.

1. Introduction

1.1. The Impact of Ship Particulate Matter Emissions on Air Quality

Research findings on the impact of international shipping on air pollution in Europe indicate that ship emissions significantly affect air quality, especially in coastal regions [1]. The importance of regulating ship emissions to improve air quality and reduce health risks is highlighted in [2]. Primary particulate matter (PPM) is directly emitted during fuel combustion [3]. The sub-components of PPM are ash which contains inorganic residues from fuel combustion, black carbon which absorbs sunlight and contributes to climate warming, and organic carbon, which is formed from the incomplete combustion of fuels. These particulates are fine PM_2.5, and they exert significant health and environmental impacts [4].

A regression discontinuity (RD) model was used to evaluate the effectiveness of ship emission control area (ECA) policies on air quality at Ningbo Port [5]. The study analyzed the impact of ship emissions on concentrations of PM_2.5 and PM₁₀. The results indicate that PM_2.5 and PM₁₀ levels vary with ship activities.

Inland ship emissions significantly contribute to air pollution in China along the Yangtze River in the Nanjing region [6]. The estimated emissions of PM₁₀ and PM_2.5 from September 2018 to August 2019 were 3.8 and 3.3 kt, respectively, with the highest emissions occurring in the summer.

Container ships were identified as the largest contributors to particulate emissions at Busan Port [7]. The average annual emissions from 2015 to 2019 were PM_2.5 (0.05%) and PM₁₀ (0.05%). The total social costs of air pollutants emitted from ships at Busan Port in 2019 were estimated to be between USD 11.06 million and USD 100.64 million, depending on the valuation method used. The base case estimate was USD 31.55 million.

International shipping significantly impacts air quality [8,9], particularly in coastal regions. Effective regulation of ship particulate emissions is crucial to reduce health risks and environmental damage. Emission control policies show promise, but challenges remain, especially with inland emissions and economic costs at major ports [10,11].

1.2. The Impact of Ship Emissions of Particulate Matter on Human Health

Air pollution was the fourth leading risk factor for early deaths globally in 2019, contributing to 6.67 million premature deaths. Particulate matter (PM), especially fine particulate matter (PM_2.5), is a major toxic exposure risk, causing more than two million hospital admissions and premature deaths annually. PM is a major risk factor for mortality, causing 4.2 million deaths and 103.1 million disability-adjusted life-years (DALYs) globally [12,13,14,15,16]. The International Agency for Research on Cancer classifies PM as a group 1 carcinogen due to its toxicity. PM exposure is linked to adverse health effects such as pulmonary inflammation, bronchoconstriction, and chronic respiratory diseases like asthma and COPD. Epidemiological studies show that PM contributes significantly to the global disease burden, particularly in developing countries.

Air pollutants such as particulate matter can trigger inflammation in the brain, leading to cognitive decline [15,16,17,18,19]. Increased production of reactive oxygen species (ROS) can damage brain cells. Pollutants may disrupt the blood–brain barrier, allowing harmful substances to enter the brain. Air pollution can impair blood flow to the brain, affecting cognitive function. Even low levels of PM can lead to increased mortality and morbidity, affecting both adults and children. Short-term exposure is linked to respiratory and cardiovascular diseases. The effects are more pronounced in vulnerable groups such as the elderly, children, and individuals with preexisting cardiovascular and respiratory conditions. PM consists of a complex mixture of solid and liquid particles, including combustion particles, secondary inorganics, and crustal-derived particles. Fine particles (PM_2.5) and ultrafine particles (less than 0.1 μm) are primarily produced by fossil fuel combustion. These particles can penetrate deep into the lungs and enter the bloodstream, causing systemic health effects.

Air pollution, especially PM_2.5, is a major global health risk, causing millions of premature deaths and severe health issues like respiratory and cardiovascular diseases and cognitive decline. The impact is particularly severe in developing countries and vulnerable populations. Reducing PM emissions is essential to improve global health.

1.3. Efficiency, Efficiency Factors and Lifetime of Different Technologies of Removing Particulate Matter from Air

Initial results of a holistic performance assessment showed that duct-type electrostatic precipitators (ESPs) used in heating, ventilation, and air conditioning (HVAC) systems with dielectric coatings (L1-IFD) displayed enhanced removal efficiency of submicron particles compared to ESPs without dielectric coatings [20]. The initial filtration efficiency for submicron particles was higher for ESPs with dielectric coatings, with overall efficiencies comparable to F7 filters but with 85% lower energy consumption. The pressure drop across ESPs increased with face velocity, and the resistance of L1-IFD was higher than that of ESPs without dielectric coatings due to the smaller gap between the collecting plates. Dust loading reduced the filtration efficiency of all ESPs, with L1-IFD showing a relatively large efficiency attenuation of 33.6%. Post-washing filtration efficiency of ESPs improved but did not fully recover to initial levels, indicating incomplete removal of dust on the surface. The maximum quality factor attenuation caused by dust loading was 55.3%, and the maximum attenuation after washing was 17.5%. The ozone emission rates (OERs) were significantly higher for ESPs without dielectric coatings compared to L1-IFD. The OERs for ESPs without dielectric coatings were approximately 2–7 times higher than for L1-IFD.

The investigation into the performance and degradation of cylindrical corona electrodes in electrostatic precipitators (ESPs) showed that the collection efficiency of the ESPs is influenced by both the diameter and pitch of these electrodes [21]. Thinner electrodes result in higher collection efficiency due to stronger electric fields and larger ionization regions. A shorter pitch between electrodes also leads to higher collection efficiency because of the increased number of electrodes. The collection efficiency varies nonlinearly and inversely with the diameter of the electrodes, suggesting an optimal diameter for maximum efficiency. There is a trade-off between achieving high collection efficiency and maintaining the longevity of the electrodes. Stronger electric fields improve collection efficiency but accelerate electrode degradation due to oxidation. It is suggested that optimizing the pitch and diameter of the electrodes would balance collection efficiency and electrode life.

High-efficiency particulate air filters (HEPA) and electrostatic precipitators (ESP) have limitations such as high energy consumption and low filtration efficiency, respectively [22]. Electrostatic-assisted air filtration systems combine HEPA and ESP to achieve high filtration efficiency and low energy consumption. The presence of the PMMA tank has a minimal effect on the V-I characteristics. When the applied voltage is 20 kV, the relative error of the total current value between the cases with and without the dielectric tank is only 3%.

Jian Li et al. presented a novel air purification filter designed to efficiently remove fine particulate matter (PM_2.5) from the air. The filter is based on a coaxial core–shell structure composed of CuO@NH2-MIL-53(Al) nanowire arrays grown on a copper mesh. This design leverages both local and external electric fields to enhance the removal efficiency of pollutants [23]. The filter achieves a PM_2.5 removal rate of 98.72% with an external electric field and 44.41% without it. The filter maintains stable air pollution removal efficiency after repeated filtration and cleaning cycles, demonstrating its reusability. The filter is constructed using a copper mesh for its excellent electrical conductivity and rigidity, with CuO nanowires providing a high surface area for pollutant capture. The NH2-MIL-53(Al) layer enhances the filter’s ability to adsorb toxic gases. The filter operates through a combination of long-range electrostatic interactions (enhanced by an external electric field) and short-range electrostatic interactions (local electric field), which together improve the capture of PM_2.5.

Air temperature and humidity impact the performance of electric precipitators used for air purification [24,25]. When the electric filter is powered by a constant voltage, the electric current (discharge current) increases as the air temperature goes up. When using pulsed voltage (a type of voltage that turns on and off rapidly), the discharge current stays almost the same regardless of the temperature. With constant voltage, the discharge current decreases as the air gets more humid. With pulsed voltage, the discharge current remains stable even as humidity changes. Pulsed voltage generates a higher discharge current compared to constant voltage making the filter more effective. Pulsed voltage makes the filter less affected by changes in temperature and humidity, ensuring consistent performance [26].

Hybrid electrostatic filtration systems are developed and applied in such a way so as to address the limitations of conventional filtration methods [27], particularly in removing submicrons and nanoparticles from exhaust gases. High temperatures (>1000 K) in industrial processes limit the use of bag filters, and cyclones are ineffective for PM_2.5 removal. Electrostatic precipitators have a “penetration window” where efficiency drops below 50% for particles in the 100 nm to 1 µm range. The solution is to combine electrostatic devices (e.g., electrostatic precipitators, pre-chargers, agglomerators) with mechanical filters (e.g., fibrous filters, cyclones). Hybrid systems show significant improvements in collection efficiency for PM_2.5 particles [28]. The observed system achieves a PM_2.5 collection efficiency of over 99.999%, with a significantly slower increase in pressure drop across the bag filter compared to conventional systems. Electrically energized filters and hybrid electrostatic filters reduce the pressure drop across the filter media. This is achieved by charging the particles which enhances their deposition on the filter fibers and reduces the buildup of a dense dust cake. Lower pressure drop translates to reduced energy consumption for maintaining airflow through the filters, thereby lowering operational costs. Hybrid systems can handle high-temperature exhaust gases by using components like cyclones and electrostatic precipitators that are resistant to high temperatures, followed by cooling stages before mechanical filtration. Hybrid electrostatic filtration systems offer a highly efficient solution for exhaust gas cleaning, particularly for fine and ultrafine particles.

Advancements in electrostatic precipitators (ESPs) and hybrid filtration systems enhance air purification efficiency and reduce energy consumption. ESPs with dielectric coatings improve submicron particle removal and lower ozone emissions. Hybrid systems combining ESPs with mechanical filters achieve high PM_2.5 removal rates. Novel filters using CuO@NH2-MIL-53(Al) nanowire arrays effectively remove fine particulates and toxic gases. These innovations provide more effective and sustainable air purification solutions.

1.4. Modelling of ESPs

The investigation into the optimization of electrode structures in electrostatic precipitators (ESPs) to enhance dust removal efficiencies compared wire–plate, plate–hole, and hole–hole configurations through experiments and simulations. Key findings revealed that the hole–hole structure achieves higher peak currents and better dust removal efficiency for particles larger than 1 μm compared to other configurations. Simulations showed that hole–hole structured electrodes increase electric field intensity at openings and reduce surface charge density, mitigating reverse corona phenomena [29]. Additionally, perforations in collection plates helped manage ion wind effects, improving the capture of fine particulate matter. The research concluded that the hole–hole electrode structure significantly enhances ESP efficiency, particularly for smaller particles, by optimizing electric and flow fields and reducing secondary dust re-entrainment.

The investigation into the effect of high-voltage electrostatic precipitator dust collection plate structure on collection efficiency explored how changes in the structure of dust collection plates affect the flow field and electric field distribution in electrostatic precipitators (ESPs). A multi-physics coupled numerical model was used to analyze linear flat plates and folded plates with different pole configurations [30]. Results showed that the folded plate design improves the near-plate electric field and flow field, reducing particle re-entrainment and enhancing dust removal efficiency. The folded plate structure decreases the flow velocity near the dust collection plate by approximately 20% compared to traditional linear flat plates, particularly at an inlet velocity of 0.5 m/s. This reduction in flow velocity increases particle residence time, improving dust collection efficiency.

A new time-dependent model was developed to simulate continuous DC supply with impulse voltage supply, highlighting that impulse mode not only saves energy but also enhances precipitation efficiency, building on previous steady-state models [31]. The results indicated that during the “ON” state of impulse voltage, particles are effectively charged and precipitated, while during the “OFF” state, charged particles continue to precipitate due to residual charge.

Accurate long-term modelling is essential for optimizing ESP performance, particularly in multi-zone configurations where different sections of the precipitator experience vary in conditions and require tailored rapping cycles and energization strategies [32].

Optimizing electrode structures in electrostatic precipitators (ESPs) significantly enhances dust removal efficiency [33]. The hole–hole configuration outperforms wire–plate and plate–hole setups, achieving higher peak currents and better efficiency for particles larger than 1 μm [34]. Perforated electrodes improve electric field intensity and reduce reverse corona effects, while folded plate designs enhance near-plate electric and flow fields, reducing particle re-entrainment [35]. Additionally, impulse voltage supply increases precipitation efficiency and energy savings [36]. Accurate long-term modeling is crucial for optimizing ESP performance, especially in multi-zone configurations with varying conditions [37].

The aim of this study is to develop and validate a machine learning model, specifically a random forest regressor, to predict the particle concentration after cleaning in an experimental electro-cyclone filter system. The aim of the model is to accurately simulate and forecast the filter’s performance under various conditions without the need for extensive physical experiments. By leveraging experimental data on particle size, dosage speed, voltage, and airflow rate, the model should provide reliable predictions of filtering efficiency, thereby aiding in the optimization and practical application of electro-cyclone filters in managing particulate matter emissions.

2. Materials and Methods

The data for the model for predicting the efficiency of our experimental prototype electro-cyclone filter system were gathered from the conducted experiments. The gathered data were used for model training and validation, implementing machine learning (ML) modelling of the filtering efficiency of particulate matter. The experimental setup featured a gas flow generation and management system designed to deliver a gas output with air flow rate levels ranging from 67 to 411 m³/h. Flow regulation was achieved using a frequency converter adjustable between 10 and 60 Hz with a precision of 0.05–0.10 Hz [38]. The system’s innovative architecture included a multi-channel helical cyclonic filter that integrated three separate deposition zones within a single housing. To introduce controlled particulate matter, a Palas RGB 1000 mobile particulate generator, manufactured by Palas GmbH, Karlsruhe, Germany, was utilized, enabling precise aerosol feeding into the air duct just after the fan and before the cleaning system. Primary particulate matter from ship emissions, closely resembling test particles (density range 1.80–2.56 g/cm³, refractive index range 0.45–1.52), were used for the experiments, whereby the particle concentration and size were measured using a Palas Welas Digital 3000 light-scattering spectrometer (Palas GmbH, Karlsruhe, Germany) with a measurement range of 0.2 μm to 10 μm. A detailed grain composition of the tested particulate matter is presented in

Table 1. Composition of the tested particulate matter.

PM diameter, µm	0.2	0.5	1	3	5	8	10
% under for full sample	0.8	1.2	5.2	19.8	29.5	39.3	44.8

.

The setup also included a low-voltage electrostatic air filter featuring components such as a flow equalizer, aerodynamic test points, and particle concentration test points, located before and after the cleaning process. The pipe diameter of the upstream (input) airflow was 140 mm. The downstream (output) pipe diameter was 250 mm.

The experimental results were validated with the experimental study of Šabanovič et al. [39], and the data were reformatted to a model training dataset excel file. The dataset sample of the first ten rows is shown in Appendix A. The columns in the appendix provide the following information: the first column is the particle size that our measurement devices are able to count; the second column states the dosage speed of the particles—the bigger the number, the more particulate matter is being injected into the incoming airflow; the third column states the input voltage that goes to power our electric air filter part; the fourth column states the airflow into which the particulate matter is inserted; the fifth column states the particle concentration before air cleaning, this concentration enters our filter with the incoming airflow; the sixth column states the particle concentration after air cleaning, this is the concentration which comes out of the filter after the cyclone and electric air filtering; and the seventh column states the manually calculated efficiency of the air filtering process—this directly corresponds with the difference of particle concentration before and after the cleaning process.

As mentioned above, our goal was to develop a machine-learning model to predict particle concentration after cleaning based on these parameters. This is valuable because it allows one to simulate and forecast filter performance under different conditions without running all possible experiments. We trained the model on the data where the speeds of the dosage device feed piston that controls the feeding intensity of the particles being fed into the airflow before air cleaning (dosage speed) were 2, 4, and 16 mm/h, while the reserved data with a dosage speed of 8 mm/h was used as the test set. Dosage speeds of 2, 4, 8, and 16 mm/h correspond to 0.13, 0.26, 0.51, and 1.02 mg/s of particulate matter per unit time, respectively. However, to not make the simulation too complex, we used the initial units of mm/h. This allowed us to validate the model’s predictive accuracy on an intermediate dosage speed that was not used in training.

A random forest regressor was selected as our model. This choice was based on several advantages, such as the model’s ability to capture complex relationships in the data, which is useful since filtering efficiency is not purely linear [40]. Random forests provide insights into which features are most influential in making predictions, and the approach handles noisy data well, which is important in experimental setups with some variability [41]. Random forests differ fundamentally from iterative algorithms such as neural networks because of how they are built and optimized. A random forest is an ensemble of decision trees. Each decision tree is grown independently from a bootstrap sample (randomly selected subset with replacement) of the training data. Each tree is trained to completion in a single step by recursively splitting the data into branches to minimize a chosen criterion (e.g., mean squared error for regression). Unlike neural networks, random forests do not involve iterative steps to improve their parameters (like weights in a neural network). Instead, each tree is constructed once and remains static, and the randomness in data sampling and feature selection (at each tree split) contributes to the diversity of the ensemble, which improves generalization. In random forests, the main hyperparameter controlling its power is the number of trees (n_estimators). More trees generally improve performance (up to a point) by reducing variance through averaging their predictions. While adding trees can be thought of as a “progression”, it is not an iterative process like epochs in neural networks, where the entire model is re-trained with adjustments in weights after every pass over the data.

A multi-step data cleaning process was implemented to ensure the integrity and reliability of the dataset [42]. No missing values were observed in the dataset as the data was collected directly from controlled experiments with real-time monitoring. Data points were reviewed for potential noise caused by equipment fluctuations or external factors. Measurements that deviated significantly from the expected operating ranges (e.g., abrupt drops or spikes in particle concentrations unrelated to dosage speed) were flagged and excluded. The dataset was checked for duplicate rows resulting from repeated logging events, and these were removed to prevent over-representation of specific measurements.

Outliers were identified using both visual inspection (scatter plots) and statistical methods (e.g., z-score thresholds and interquartile range analysis) [43]. Outliers were defined as data points falling more than three standard deviations from the mean or beyond the 1.5 × IQR range. Outliers were not automatically removed; instead, for each outlier, the corresponding experimental conditions were reviewed. If an outlier resulted from an equipment malfunction (e.g., voltage fluctuations), it was removed. The random forest algorithm was selected partly because of its robustness to outliers. Outliers that were not caused by experimental anomalies, but represented extreme yet plausible conditions, were retained to ensure the model learned from the full range of data variability.

The target variable (particle concentration after cleaning) was directly measured during experiments, ensuring that labels were not inferred or subject to manual annotation errors. The feature set (particle size, dosage speed, voltage, airflow) was also derived directly from instrumentation outputs, requiring no additional labeling. Given that random forest models are not sensitive to feature scaling, normalization of the dataset was not required. However, feature distributions were inspected to ensure that features such as particle size and voltage spanned consistent ranges without drastic imbalances. Input values for each feature were checked for unit consistency (e.g., ensuring that all particle sizes were in micrometers, airflow in m³/s, etc.) [44].

The Python script was prepared for modeling. The script imports the dataset and extracts the necessary data, such as features (particle size, dosage speed, voltage, and air flow rate) and targets (particle concentrations after air cleaning). The dataset is split into training data (where the dosage speeds were 2, 4, and 16 mm/h) and testing data (with the dosage speed of 8 mm/h). The script initializes a random forest regressor model. The model is trained on the training set features (X_train) to predict the target variable (Y_train). Predictions (Y_pred) are generated for the test set using the trained model. Performance metrics such as Mean Absolute Error (MAE) and R² are calculated.

We used the test data after training (dosage speed of 8 mm/h) to evaluate the model’s performance. This step provided insight into the model’s ability to generalize to unseen data. We calculated two key metrics: MAE and R². The MAE is a measure of the average absolute error between actual and predicted values. It quantifies the model’s accuracy by measuring how close the predictions are to the actual observations, regardless of whether the errors are positive or negative [45].

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|y_i-{\widehat{y}}_i\right|,$$

(1)

where $y_i$ is the actual value (experiment data), ${\widehat{y}}_i$ is the predicted value, and $n$ is the total number of predictions.

The R² score (coefficient of determination) measures how well the model explains the variance in the target variable. It is a metric commonly used for regression models and ranges from 0 to 1, where values closer to 1 indicate a better fit.

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{\sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}},$$

(2)

where $\overline{y}$ is the mean of the actual values.

The residuals are the differences between the actual values and the predicted values. They help to assess model accuracy and can be used to analyze patterns in errors.

$$\mathrm{Residual}=y_i-{\widehat{y}}_i.$$

(3)

In random forest regression, the final prediction for each input is the average of predictions made by each individual tree in the forest. The formula for each prediction is:

$$\widehat{y}={\displaystyle \frac{1}{T}}\sum _{t=1}^T{\widehat{y}}_t.$$

(4)

These formulas form the backbone of our approach to assessing model accuracy and interpreting results.

3. Results

The scatter plot (Figure 1) shows the relationship between the actual and predicted particle concentrations after cleaning with data points color-coded by dosage speed.

Most points are tightly clustered around the red dashed line of perfect prediction ($y=x$). Each dosage speed (2, 4, 8, and 16 mm/h, or 0.13, 0.26, 0.51 and 1.02 mg/s of particulate matter per unit time) shows a similar clustering behavior. For smaller dosage speeds (e.g., 2 mm/h and 4 mm/h), the predictions are almost indistinguishable from the actual values. At higher dosage speeds (e.g., 8 mm/h and 16 mm/h), there are slightly larger deviations for higher concentration values. As particle concentrations increase (>20 P/cm³), deviations from the perfect prediction line become more noticeable, particularly for the higher dosage speeds (yellow points). The average model prediction deviation is 28%.

Figure 2 shows a line plot of actual vs. predicted concentration by particle dosage speed. For all dosage speeds, the solid lines (actual) and dashed lines (predicted) closely overlap across the range of particle sizes.

Concentration decreases steeply for particles smaller than 2 μm and stabilizes for larger particles (plots are not continued further). Larger particles are more efficiently removed by the cyclone section of the filter leading to lower concentrations after cleaning. At higher speeds (8 mm/h and 16 mm/h) there is a slight separation between actual and predicted values for smaller particles. The main case is the actual vs. predicted values of concentration for the dosage speed of 8 mm/h and it shows an average difference between the actual and predicted values of 6.34%.

The residuals by dosage speed plot (Figure 3) show that actual–predicted values are symmetrically distributed around zero, indicating no systematic bias in the model.

Residuals for 8 mm/h show a slightly larger variability. Outliers are more frequent for higher speeds (e.g., 8 mm/h and 16 mm/h), particularly for positive residuals (model underpredicting). Across all speeds, residuals are small relative to the scale of the particle concentrations (±2 P/cm³). In general, the percentage of residual points within the acceptable limits for each dosage speed and is as follows: 2 mm/h—67.81%; 4 mm/h—75.38%; 8 mm/h—75.92%; 16 mm/h—75.38%.

Model performance metrics (

Table 2. Model performance metrics.

Dosage Speed (mm/h)	MAE	R2
2	0.196	0.995
4	0.232	0.994
8	0.491	0.967
16	0.156	0.993

) show that predictions deviate by an average of less than 0.5 particles per cubic centimeter from actual values. The R² value is 0.97.

4. Discussion

4.1. Model Performance Evaluation

Since most points are tightly clustered around the perfect prediction line (Figure 1) and the slight deviations are distributed symmetrically, it means that there is no systematic underprediction or overprediction bias. It also indicates that the model accurately predicts the particle concentration after cleaning.

For smaller dosage speeds (e.g., 2 mm/h and 4 mm/h), the predictions are almost indistinguishable from the actual values. At higher dosage speeds (e.g., 8 mm/h and 16 mm/h), there are slightly larger deviations for higher concentration values, likely due to the greater complexity of particle interactions at these conditions.

Limitations in capturing dynamic behaviors of particle accumulation in the cyclone or measurement noise in experimental data may reflect the deviations from the perfect prediction line becoming more noticeable as particle concentrations increase. The high accuracy across dosage speeds and concentration ranges validates the generalizability of the random forest model. Small deviations at higher concentrations highlight areas where model refinement could improve precision, such as accounting for dust resuspension effects in the cyclone. The average deviation in model predictions is reasonably low.

The solid lines (actual) and dashed lines (predicted) aligning closely across all dosage speeds and particle sizes indicate that the model accurately captures the filtration efficiency of the cyclone for particles of varying sizes. Concentration drops sharply for particles under 2 μm and stabilizes for larger ones, as the cyclone filter more effectively removes larger particles, resulting in lower post-cleaning concentrations. At higher speeds (8 mm/h and 16 mm/h), a slight separation between actual and predicted values for smaller particles suggests more pronounced particle accumulation or dust resuspension effects. The model effectively captures particle concentration patterns across all speeds, demonstrating robustness in representing the electro-cyclone filter’s behavior. Deviations at higher speeds and smaller particle sizes suggest potential for improvement through fine-tuning, such as accounting for particle size and flow rate interactions. The primary case involves comparing the actual and predicted concentration values for a dosage speed of 8 mm/h, revealing a very small difference, which is lower than 7%.

The residuals are symmetrically distributed around zero across all speeds, indicating no systematic bias in the model. Residual spread is consistent, though slightly larger at 8 mm/h due to its intermediate nature and complex particle behaviors. Outliers, more frequent at higher speeds, suggest unmodelled phenomena such as dust resuspension. Overall, the low residual range (±2 P/cm³) confirms the model’s strong predictive performance, with outliers offering insights for further refinement. The proportion of residual points falling within acceptable limits for each dosage speed.

The model’s MAE of 0.49 P/cm³ highlights its accuracy, with deviations averaging less than 0.5 P/cm³ across a concentration range up to 30 P/cm³. Its R² of 0.97 confirms that the model captures 97% of the variance, effectively reflecting complex interactions among particle size, dosage speed, voltage, and airflow.

Particles of >2 μm are effectively filtered, resulting in lower post-cleaning concentrations, consistent with the cyclone filter’s expected performance. Higher speeds (e.g., 16 mm/h) show increased residuals and deviations likely due to dynamic effects such as resuspension or turbulence. Concentration decreases with increasing particle size across all speeds, demonstrating the system’s efficiency in capturing larger particles.

Addressing outliers at higher speeds by integrating factors such as dust resuspension dynamics or advanced flow modeling could boost accuracy. Reducing experimental noise through preprocessing, such as filtering extreme data points, can further enhance model reliability.

The random forest model performs exceptionally well in predicting particle concentrations after cleaning with strong alignment between actual and predicted values across different dosage speeds and particle sizes. The insights gained from the residuals and deviations provide actionable areas for refinement, but the overall performance metrics (MAE = 0.49, R² = 0.97) confirm the model’s robustness and reliability for practical use.

4.2. Comparison of the Proposed Model with Existing Models

Unlike traditional models that primarily rely on empirical or numerical approaches (e.g., finite differences, finite volume, or analytical models), the proposed model incorporates a random forest machine learning (ML) framework to predict post-cleaning particle concentrations. This allows the model to generalize across various experimental conditions and reduce dependency on extensive physical testing.

The study integrates a multi-channel helical cyclonic filter with electrostatic filtration, combining mechanical and electrical deposition mechanisms. This hybrid approach addresses the limitations of traditional ESPs, such as their inefficiency in removing mid-sized particles (e.g., 0.1–1 µm) and “penetration window” issues.

The model evaluates sensitivity across particle sizes and dosage speeds, providing a fine-grained understanding of filtration efficiency for particles as small as 0.198 µm, which is often overlooked in previous models.

By withholding data at 8 mm/h dosage speed during training, the model demonstrates its ability to generalize, improving reliability for untested operating conditions.

The random forest regressor achieves a Mean Absolute Error (MAE) of 0.49 P/cm³ and an R² of 0.97, reflecting robust predictions and high reliability. This surpasses many traditional models, which often lack real-time adaptability and predictive performance across varying parameters.

The model shows a clear advantage in predicting performance for a wide range of particle sizes (0.2–10 µm), particularly for mid-sized particles where traditional ESPs and cyclonic systems struggle.

By simulating filtration efficiency without the need for exhaustive physical experimentation, the proposed model enables significant time and cost savings, especially for industrial applications.

Deviations in predictions (e.g., at higher speeds or mid-sized particles) are systematically analyzed, indicating areas for improvement, such as accounting for dust resuspension or turbulence effects, which many earlier models do not address comprehensively.

Traditional ESP models (e.g., Deutsch-Anderson, Lagrangian particle tracking) focus on deterministic numerical simulations of electrostatic field interactions. Recent hybrid filtration models combine ESPs with fibrous or bag filters but lack robust predictive capabilities for dynamic conditions or real-time scenarios.

The random forest approach allows the model to anticipate filtration outcomes under varied conditions without recalculating field interactions for each scenario.

The experimental setup operates at 5 kV, significantly reducing energy consumption compared to high-voltage systems in earlier studies while maintaining high deposition efficiency (84.9% average).

The integration of mechanical and electrostatic deposition mechanisms improves efficiency for a wider particle size range, particularly addressing the “penetration window” challenges in traditional ESPs.

The model was validated on unseen data (8 mm/h dosage speed) to assess generalizability. Deviations were minimal, highlighting the model’s reliability for intermediate conditions.

Sensitivity analysis identified potential areas for refinement, such as accounting for dust resuspension and flow turbulence at higher speeds.

5. Conclusions

The random forest model developed in this study demonstrated strong predictive performance for particle concentrations after cleaning in an electro-cyclone filter system. The model achieved a Mean Absolute Error (MAE) of 0.49 P/cm³ and an R² of 0.97, accurately capturing 97% of the variance in the experimental data. Residuals were symmetrically distributed around zero, with acceptable limits achieved for 67.81% of points at 2 mm/h, 75.38% at 4 mm/h, 75.92% at 8 mm/h, and 75.38% at 16 mm/h dosage speeds. Larger particles (>2 μm) were filtered with greater efficiency, aligning with the cyclone filter’s design. Deviations between actual and predicted values were minimal, with an average difference of 6.34% at 8 mm/h, confirming the model’s reliability for practical applications. This work highlights the potential for machine learning to optimize air filtration systems, enabling efficient particulate matter reduction with minimal experimentation.

These results indicate that the proposed model is robust and reliable for predicting electro-cyclone filter efficiency under varying conditions. The model could be used to optimize the design and operation of electro-cyclone filters in industrial settings such as manufacturing plants and power stations, where particulate matter emissions are a concern. Industries could adjust operational parameters to maximize efficiency and comply with environmental regulations by predicting the filter’s performance under different conditions. Environmental agencies could use the model to predict the effectiveness of air filtration systems in reducing particulate matter in urban areas. Improved air filtration systems could significantly reduce the concentration of harmful particulate matter in the air, thereby improving air quality and reducing health risks associated with air pollution. By predicting filter performance without the need for extensive physical testing, the model could help in developing cost-effective air filtration solutions. This could be particularly beneficial for small and medium-sized enterprises that may not have the resources for comprehensive experimental setups. Overall, the model’s robustness and reliability make it a valuable tool for predicting and optimizing electro-cyclone filter performance in practical applications.