Key Takeaways & Executive Findings
- •• • PSO-NM coupled algorithm outperforms GA, NM, and other hybrids on Shubert, Hartmann, and Shekel functions, achieving mean values closest to theoretical optima with minimal standard deviation, ensuring reliable convergence in multi-dimensional, multi-extremum optimization. • • Single-point SF6 source inversion yields source strength relative deviations of -27.1% to 38.5% (mean absolute relative deviation <30%) and positional errors <10 m, demonstrating high accuracy and repeatability for rapid emission source identification. • • Multi-point source inversion shows stability but lower accuracy (deviations typically >30%); low-release sources achieve source strength relative deviations of 37.3%-70.4%, while high-release sources range from -71.4% to 161.8%, indicating the need for source-specific constraints. • • Positional parameter inversion errors remain below 50 m in most multi-point scenarios, with low-release sources achieving x0 deviations of -1.6 to 8.2 m, yet y0, z0, and distance parameters are less accurate, highlighting the impact of source interference and meteorological variability.
Abstract
Accurate identification of pollutant emission source parameters is critical for effective pollution response. This study evaluates the performance of genetic algorithm (GA), Nelder-Mead simplex (NM), particle swarm optimization (PSO), and their coupled variants on multi-dimensional, multi-extremum benchmark functions, and develops a source parameter inversion technique integrating PSO-NM with a Gaussian dispersion model. Validation via sulfur hexafluoride (SF6) single-point and multi-point release experiments demonstrates that PSO-NM achieves mean values closest to theoretical optima on Shubert, Hartmann, and Shekel functions, with superior stability and precision. In single-point source experiments, the relative deviation of source strength (Q) inversion ranges from -27.1% to 38.5%, with positional errors below 10 m, indicating robust convergence and repeatability. Multi-point source inversion exhibits stability across two scenarios but with reduced accuracy compared to single-point cases. When source strength is unknown, inversion accuracy for low-release sources (relative deviation 37.3%-70.4%) surpasses that for high-release sources; when position is unknown, positional deviations generally remain below 50 m, with low-release sources yielding better x0 deviations (-1.6 to 8.2 m) but slightly worse y0, z0, and distance parameters. Inversion errors primarily stem from meteorological non-stationarity, inter-source interference, algorithmic local optima, low-concentration measurement noise, and model assumptions. Future improvements may incorporate real-time meteorological correction and source-specific constraints to enhance accuracy and robustness in complex scenarios. The findings provide technical support for precise source tracing, monitoring, and refined management of pollutant emissions at microscale in industrial parks and enterprises.
1. Introduction
Accidental releases of hazardous chemicals from production, storage, and transportation frequently lead to sudden atmospheric pollution events, where emission source parameters—such as source strength and location—remain unknown or uncertain. Traditional source estimation methods, including maximum likelihood estimation and nonlinear least squares, require gradient information of the objective function, which is computationally intensive and often fails for nonlinear inversion problems. Probabilistic approaches, while providing uncertainty quantification, demand high prior knowledge and suffer from slow sampling, hindering rapid response. These bottlenecks underscore the need for direct optimization algorithms that balance global and local search capabilities to achieve fast and accurate source parameter inversion.
This study addresses these limitations by coupling particle swarm optimization (PSO) with the Nelder-Mead simplex (NM) algorithm, integrating it with a Gaussian dispersion model to construct a robust inversion framework. The PSO-NM hybrid leverages PSO's global exploration and NM's local refinement, overcoming premature convergence and enhancing precision. Validated through controlled SF6 release experiments, the technique demonstrates high accuracy in single-point scenarios and acceptable performance in multi-point cases, offering a practical solution for microscale emission tracing in industrial settings.
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CUI Jixian, BAI Zishuo, SUN Lei, HONG Ningning, PENG Shitao, YE Yin, ZHANG Guangming (2026). Precision Source Parameter Inversion for Typical Air Pollutant Emissions at Microscale: An Integrated PSO-NM Algorithm and Gaussian Dispersion Model Approach. Chinese Journal of Environmental Engineering. https://doi.org/10.12030/j.cjee.202509072
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Frequently Asked Questions
What are the specific advantages of the PSO-NM algorithm over standalone PSO or NM in terms of convergence speed and accuracy for multi-dimensional optimization?
PSO-NM combines PSO's global search with NM's local refinement, triggered at fixed intervals. In benchmark tests (Shubert, Hartmann, Shekel), PSO-NM achieved mean values closest to theoretical optima with the smallest standard deviation, indicating superior stability and precision. This hybrid approach mitigates premature convergence and enhances local exploitation, leading to faster and more reliable convergence compared to standalone algorithms.
How does the inversion accuracy vary between single-point and multi-point source scenarios, and what are the primary sources of error?
Single-point source inversion yields source strength relative deviations of -27.1% to 38.5% and positional errors <10 m, demonstrating high accuracy. Multi-point inversion shows stability but lower accuracy, with deviations typically >30%. Errors arise from meteorological non-stationarity, inter-source interference, algorithmic local optima, low-concentration measurement noise, and model simplifications. These factors compound in multi-source scenarios, reducing precision.
What is the impact of source strength magnitude on inversion accuracy when the source strength is unknown?
When source strength is unknown, low-release sources achieve relative deviations of 37.3%-70.4%, whereas high-release sources show deviations ranging from -71.4% to 161.8%. This indicates that low-release sources are inverted with better relative accuracy, likely due to lower concentration gradients and reduced interference, while high-release sources may suffer from nonlinear effects and measurement saturation.
How does the inversion technique perform under varying meteorological conditions, and what future improvements are suggested?
The technique shows robust performance under typical conditions, but extreme meteorological conditions slightly degrade accuracy. Future improvements include real-time meteorological correction, source-specific constraints, and multi-model fusion to account for non-stationary wind fields and atmospheric stability, thereby enhancing robustness in complex real-world scenarios.
What are the practical implications of this research for industrial emission monitoring and regulatory compliance?
The technique enables rapid and accurate identification of emission sources, facilitating timely intervention and mitigation. With positional errors below 10 m in single-point cases and below 50 m in multi-point cases, it supports precise source attribution in industrial parks, aiding compliance with emission standards and improving environmental management efficiency.
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