⚡ electrical engineering

Prediction of spray dust suppression time for blasting dust in tunnel using CFD and Operon symbolic regression

This study demonstrates that the Operon symbolic regression algorithm provides a highly accurate, efficient, and interpretable explicit expression for predicting spray dust suppression time in tunnel blasting, outperforming various other machine learning and regression methods while significantly reducing computational costs.

Original authors: Zheng Chen, Chun Guo, Xuting Zheng

Published 2026-10-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zheng Chen, Chun Guo, Xuting Zheng

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When a tunnel is blasted open through solid rock, the air fills with a thick, choking cloud of dust. This is not just a nuisance; it is a serious hazard for the workers who must enter the space to continue construction. To clear the air, engineers use high-pressure water sprays that turn into a fine mist, catching the dust particles and weighing them down so they fall to the ground. The challenge is knowing exactly how long to keep the water running. If the spray stops too soon, dangerous dust remains. If it runs too long, valuable time and water are wasted. In the past, figuring out the perfect duration required running thousands of complex computer simulations, a process that was accurate but incredibly slow and expensive.

A team of researchers set out to find a faster way to predict this critical timing. They focused on a single railway tunnel in China, where the rock is a hard type of granite known as gneissic granodiorite. Instead of relying solely on slow computer models, they combined real-world measurements with a new kind of mathematical discovery tool. This tool, known as symbolic regression, acts like a scientist that can look at a pile of data and write down the exact mathematical sentence that explains it, rather than just guessing a number. The goal was to create a simple, clear formula that engineers could use immediately to know how long to spray water after a blast, ensuring the air is safe without wasting resources.

The researchers began by watching a real blasting event in the tunnel. They placed sensors along the floor to measure how the dust moved and how long it took to clear. They found that the dust concentration spiked twice, with a dip in between, reaching a dangerous peak of 2100 milligrams per cubic meter. The wind inside the tunnel was moving slowly, at about 0.2 meters per second. To understand the physics behind this, they built a detailed computer model of the tunnel. This model simulated the air, the water droplets, and the dust particles interacting with each other. They tested different sizes of nozzles, different water pressures, and different angles for the spray to see how each change affected the time it took for the air to become safe.

To make sense of the vast amount of data generated by these simulations, the team designed a structured experiment. They tested five different factors: the size of the first nozzle, the pressure of the second nozzle, the angle of the second nozzle, the distance between spray rings, and the volume of air being forced into the tunnel. They ran 25 different combinations of these settings. The most important factor turned out to be the volume of air being forced into the tunnel, followed by the angle of the spray nozzle. The distance between the spray rings mattered the least. They found that the best setup for their specific tunnel involved a nozzle diameter of 1.6 millimeters, a spray pressure of 5 megapascals, a spray angle of 40 degrees, a spacing of 60 meters between rings, and an air supply of 28 cubic meters per second.

With this data in hand, the researchers turned to the symbolic regression algorithm, a method that searches for the best mathematical expression to describe the relationship between the spray settings and the time it takes for the dust to clear. They compared this method against many other common computer learning techniques, such as random forests and support vector machines. While those other methods were very good at memorizing the training data, they failed to predict new situations accurately, a problem known as overfitting. The symbolic regression method, specifically a tool called Operon, performed the best. It found a formula that balanced accuracy with simplicity, achieving a prediction accuracy that was significantly higher than the other methods when tested on new data.

The final result was a specific equation that predicts the dust suppression time based on the spray settings. The researchers noted that the equation had some wiggles and fluctuations, which they explained by the fact that the dust does not clear evenly everywhere in the tunnel at the same time. In some spots, dust lingers in pockets, while in others, it clears quickly. The formula captures this uncertainty. When they tested their best-performing equation, it predicted that the dust would be cleared in about 459 seconds on average for the optimal setup, with the worst-case scenario taking around 710 seconds. In their simulations, the water droplets stabilized within 100 seconds, and the larger droplets settled near the middle of the tunnel while the finer mist reached further down the line.

This study provides a practical tool for tunnel engineers. Instead of running hours of complex computer simulations for every new project, they can now use this formula to estimate how long to run their water sprays. The researchers emphasize that this approach moves beyond simple data fitting to actually discovering the underlying rules that govern the dust clearing process. While the current model is based on specific conditions in one type of railway tunnel, the method offers a path toward faster, more reliable predictions for complex tunnel environments in the future. The work demonstrates that by combining physical simulations with intelligent mathematical discovery, it is possible to turn a slow, expensive engineering problem into a quick, solvable calculation.

Technical Summary: Prediction of Spray Dust Suppression Time for Blasting Dust in Tunnels Using CFD and Operon Symbolic Regression

Problem Statement
Spray dust suppression is a critical measure for controlling blasting dust in tunnel engineering, particularly in railway tunnels where dust properties and cross-sectional shapes differ from coal mine environments. While numerical simulations (CFD) are widely used to optimize suppression parameters, they incur high computational costs, especially as models become more refined. Existing prediction methods, such as response surface methods or neural networks, often suffer from large prediction errors in high-dimensional relationships or lack interpretability ("black-box" nature). There is a specific need for a method that can rapidly determine the optimal spray dust suppression time while providing an explicit, interpretable mathematical expression that balances accuracy with physical plausibility.

Methodology
The study employs a hybrid approach combining field testing, numerical simulation, and machine learning:

Field Data and Numerical Inversion:
- Field tests were conducted in a single-tube railway tunnel (Grade III gneissic granodiorite) using a CCZ3000 dust monitor. The data revealed a maximum dust concentration of 2100 mg/m³ and a characteristic diameter of 16.561 μm.
- A gas-liquid-solid coupled CFD model was established and validated against field data. The model utilized a medium grid (1,023,576 elements) to simulate dust migration and spray interaction.
Orthogonal Experimental Design:
- An orthogonal experiment was designed to investigate five influencing factors: No. 1 nozzle orifice diameter (A), No. 2 nozzle spray pressure (B), No. 2 nozzle spray angle (C), spray ring spacing (D), and forced-air duct air supply rate (E).
- The evaluation index was the time required for the sectional average dust concentration to drop below the safety limit of 4 mg/m³ within a 200 m range.
- A supplementary "Test 26" was added to verify the optimal combination derived from the orthogonal analysis.
Variable Engineering and Dimensional Analysis:
- Initial importance analysis (SHAP values) indicated that the air supply rate (E) was the most significant factor, while spray ring spacing (D) was the least.
- To address dimensional inconsistencies and improve regression accuracy, the authors constructed new dimensionless variables ( $X_1, X_2, X_3$ ) based on physical parameters (air density, droplet size, dust size, and ventilation time).
Symbolic Regression (Operon):
- The Operon algorithm, a high-performance symbolic regression framework based on tree-based genetic programming, was used to derive an explicit mathematical expression for the dust suppression time.
- Operon was compared against 12 other algorithms, including PySR, GpGomea, SVR, Random Forest, XGBoost, and various regression combinations.
- The model selection criterion was the SCORE metric, which balances the coefficient of determination ( $R^2$ ) and equation complexity.

Key Results

Factor Sensitivity: The range analysis of the orthogonal experiments ranked the factors affecting dust suppression time in descending order of influence: Air supply rate (E) > No. 2 nozzle spray angle (C) > No. 2 nozzle spray pressure (B) > No. 1 nozzle diameter (A) > Spray ring spacing (D).
- The optimal combination identified was: No. 1 diameter 1.6 mm, No. 2 pressure 5 MPa, No. 2 angle 40°, spacing 60 m, and air supply 28 m³/s.
Numerical Simulation Insights: In the optimal Test 26, the maximum safety time recorded was close to 710 s (with a mean of 459 s), representing the lowest mean and narrowest spread among all trials. In contrast, Test 9 yielded the longest safety time in the dataset at approximately 1,780 s. The simulation showed that droplets stabilized by 100 s. Large droplets (>50 μm) were concentrated between 50–110 m, while finer droplets (<50 μm) were found below 120 m. Dust particles (<10 μm) primarily occupied the middle-upper zones. By 600 s, most dust was captured, and by 800 s, tunnel dust was almost entirely captured or discharged beyond the 200 m section.
Algorithm Performance:
- Operon demonstrated the best generalization ability among all tested algorithms. While many complex models (e.g., TPS, KNN, GPR+SVR+RF) achieved near-perfect fits on the training set ( $R^2 \approx 1.0$ ), they suffered from severe overfitting on the test set ( $R^2$ dropped to 0.15–0.34).
- Operon achieved the highest test set $R^2$ of 0.58 among all algorithms, followed by GpGomea, SVR, PySR, and others which ranged between 0.15 and 0.35. Operon maintained short training times and controlled complexity, with a predicted maximum $R^2$ capability of approximately 0.85 in specific configurations.
- The final derived equation (Eq. 13) expresses the dust suppression time $T$ as a function of the new variables, incorporating trigonometric and square root terms to capture non-linear relationships.

Significance and Claims
The paper claims to provide a practical tool for estimating the duration of spray dust suppression under similar tunnel blasting conditions without the need for extensive, time-consuming CFD simulations for every scenario. By utilizing the Operon symbolic regression algorithm, the study successfully bridges the gap between data-driven prediction and physical interpretability.

The authors emphasize that this method offers a "white-box" alternative to neural networks, yielding an explicit mathematical expression that engineers can analyze and apply directly. The study concludes that while the derived equation reflects the uncertainty inherent in limited-range dust suppression data (evidenced by oscillations in the fitting surface), it represents a significant step toward moving symbolic regression from simple "data fitting" to "knowledge discovery" in complex tunnel environmental systems. Future work is proposed to integrate deep learning and physical constraints to further refine these prediction equations.

Technical Summary: Prediction of Spray Dust Suppression Time for Blasting Dust in Tunnels Using CFD and Operon Symbolic Regression

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