Air-Dispersion-Model-Based Identification and Sparse Regression Inversion of Radon Sources in Uranium-Mine Roadways

Abstract

Source identification in confined underground ventilation systems is essential for hazardous-gas monitoring, and uranium-mine radon provides a representative case in which release locations and strengths must be inferred from limited concentration measurements. This presents an underdetermined, ill-posed inverse problem whose solvability under different sparse-regression strategies and roadway configurations remains poorly understood. In this study, a computational fluid dynamics (CFD) forward model is coupled with sparse regression. The ventilation flow field and radon advection–diffusion process are solved in OpenFOAM to construct a source–sensor contribution matrix, and source recovery is formulated as a sparse linear inverse problem. Four methods—LASSO, LASSO with non-negative least-squares (NNLS) refitting, Elastic Net, and Elastic Net with NNLS refitting—are compared, and the contribution matrix is characterized by its mutual coherence, condition number, and singular-value spectrum. Numerical tests were conducted for single- and multiple-source scenarios in single-main and main–branch roadway models. The results indicate that inversion performance depends on the spatial information and local identifiability provided by the sensor configuration rather than on sensor number alone. LASSO and Elastic Net exhibited varying degrees of source-strength shrinkage or dispersion, whereas NNLS refitting reduced these effects when the first-stage support contained the dominant source candidates. In the prescribed three-source case, denser sensor coverage improved dominant-source localization and reduced the post hoc condition number of the prescribed-source submatrix, although the full-matrix condition number increased. This finding indicates improved local identifiability for the tested source combination rather than a general sensor-count effect. Because the synthetic observations and the inversion operator were derived from the same CFD response matrix, the results represent a controlled model-consistent proof of concept rather than an estimate of field-level performance.