Distributionally Robust Optimal Sensor Placement Method for Site-Scale Methane-Emission Monitoring

Recent research in deterministic sensor placement optimization technologies has improved the capability of monitoring large-scale field environments with a limited budget. In traditional stochastic mixed-integer linear programming formulations, minimizing the expectation of detection time can lead to a detector placement with good average behavior but unexpected worst case behavior. The uncertainty factors in the complex environment and sensor system significantly challenge the effects of the placement strategy provided by stochastic programming (SP). These factors include unknown leakage rate and location, sensor delay, and primary uncertainty of wind conditions. This article introduces a distributionally robust optimization (DRO) formulation of sensor placement under the uncertainty of wind conditions and improves a sensor network’s detection robustness. The method is demonstrated using the atmospheric simulation with site-specific methane-emission scenarios that capture partial natural wind conditions and emission characteristics. DRO techniques are employed to determine sensor locations that minimize the detection time expectation of the emission scenarios with a significantly better worst case behavior. Experiment results show that the proposed DRO method outperforms the sensor placement methods based on SP.