An algorithm for the efficient placement of air quality sensors in underground mines

Air quality sensor installation best practices are typically poorly defined in underground mines. Current approaches rely on the perspectives and experiences of ventilation engineers and health and safety professionals, but this reliance leads to disagreement when installing air quality monitors for ventilation and health and safety monitoring. While a nonrandom sampling approach is useful for initial investigation and area monitoring of airborne contamination, this alone is not ideal. By optimizing monitor installation location with a constrained number of air quality sensors, monitors can be used to their fullest extent and provide coverage of the largest area possible. Background The installation of underground air quality monitors has been relatively static. Atmospheric monitoring systems (AMSs) employed in underground coal mining operations have gone through minimal regulatory changes since August 2004, with minor changes to sensor spacing requirements going into effect at the end of 2009. For more than 15 years, there has been no change in US 30 CFR 75.351(e)(1) or 75.351(f), which establishes maximum AMS sensor separation along beltways in coal mines. AMSs are purpose-built, with the intention of monitoring carbon monoxide generation as a precursor to or indicator of spontaneous combustion of coal. Despite the lack of progress with AMSs, these systems remain the blueprint for large-scale, real-time air quality monitoring practices in underground mines, regardless of the purpose of installation or commodity type. Fig. 1 Example of Voronoi tessellation. While AMSs are well-established features in underground coal mines in the United States, there exist no further regulations prescribing real-time air quality monitoring outside of beltways. There exist no agreed-upon industry best practices for the installation of air quality monitors, despite an obvious desire to expand monitoring capacity, especially in the face of an uncertain regulatory environment for particulate matter hazards. By developing an algorithm that prioritizes an even spacing of air quality sensors that respects ventilation behavior (such as airflow direction, turbulence and diffusion effects), it is possible to paint a clearer picture of airborne contamination dynamics with existing real-time area monitoring technologies. Methods We present an algorithm for the efficient placement of air quality sensors (EPAQS). It is a polynomial time algorithm that relies on a computational geometry approach to approximate a solution to the capacity-constrained centroidal Voronoi diagram (CCCVD) problem, a subclass of the NP-complete optimal set partition problem. Overall, Voronoi diagrams can be thought of as an extension of the nearest neighbor method, dividing an area into cells based on a proximity to a certain “seed” (sensor) location (Fig. 1). This division of the area and corresponding cells constitute a Voronoi tessellation. The goal of the CCCVD problem is to determine a set of sensor locations such that each sensor sits at the centroid of its corresponding cell in the Voronoi tessellation. EPAQS uses a graph realization of the mine, which is distinct from typical graph theory network modeling approaches used in mine ventilation. Instead of realizing airways as edges within the graph, discrete locations within the mine are realized as vertices of the graph, with edges representing the statistical “cost” from one location to the next under airflow constraints. This allows EPAQS to consider airflow effects when placing sensors. Previously developed algorithms for the CCCVD problem rely on a known density or weight function for the calculation of centroids, but this is not an option in underground ventilation where airflow conditions are nonlinear and nonuniform across the mine. Otherwise stated, contaminant transport effects cannot be described as a function over the original existing mine geometry. This ultimately requires the graph realization to facilitate determination of relevant centroids, allowing EPAQS to suggest sensor installation locations. Results and discussion The EPAQS algorithm iteratively compares potential installation locations by considering the amount of overlap between any two installation locations when requiring each sensor covers the same amount of area in the mine, thereby fulfilling the capacity constraint. It is important to note that the centroid of the Voronoi cell, or the sensor’s region of influence is not necessarily at the geometric center of the cell because of airflow effects. This allows for a region of influence around the sensor that accurately reflects the statistical relevance of a sensor’s ability to reflect conditions upwind or downwind of the sensor. As such, these Voronoi cells display larger areas of influence downwind of the sensor than upwind of the sensor. Fig. 2 Optimized sensor installation regime using EPAQS algorithm to guide the installation of 10 air quality monitors. Compared to a naive approach involving random selection of installation locations, EPAQS presents a significant improvement in even sensor spacing. In the case of sensor placement in a portion of an underground room-and-pillar coal mine, EPAQS starts with a naive distribution of sensors, and iteratively selects the most promising installation locations by rejecting locations that lead to large overlaps with other sensors. In the case of 10 sensors, EPAQS can provide an installation regime that has a mean overlap of three percent of the fixed Voronoi cell capacity (Fig. 2). When compared to random installation, there is a significant improvement in the spacing of air quality sensors, with EPAQS providing a far lower overlap between Voronoi cells. Conclusion The EPAQS algorithm aims to provide a new option to support the installation of air quality monitors in underground mines, especially with the lack of industry-accepted best practices. With a lack of federal regulation to guide installation regimes in nonregulatory areas as is prescribed for underground coal AMSs in US 30 CFR 75.351(e)(1) and 75.351(f), EPAQS gives mining operations a new method to ensure monitoring programs provide a comprehensive picture of real-time air quality conditions. By removing outright reliance on experience, EPAQS uses a physics-informed approach to consider airflow effects while suggesting installation locations. As an approximation algorithm, EPAQS approximates a solution to the CCCVD problem in polynomial time, representing a steep improvement when compared to existing genetic algorithm methods. As the first algorithm developed for air quality sensor installation that prioritizes the spatial distribution of sensors explicitly for the purpose of reliable air quality monitoring data that covers the largest part of the mine as possible, EPAQS is a strong basis for future sensor placement methods to support real-time air quality monitoring. The EPAQS algorithm is available as a Windows program at no cost to the user upon reasonable request. References A list of all references is available in the full paper.

An algorithm for the efficient placement of air quality sensors in underground mines

Authored by: Kate Brown Requist and Moe Momayez

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