Spatial prediction of hydrogen sulfide in sewers with a modified Gaussian process combined mutual information

This paper proposes a data driven machine learning model for spatial prediction of hydrogen sulfide (H₂S) in a gravity sewer system. The gaseous H₂S in the overhead of the gravity sewer is modelled using a Gaussian Process with a new covariance function due to constraints of sewer boundaries. The covariance function is proposed based on the distance between two locations computed along the lengths of the sewer network. A mutual information based strategy is used to choose the best k sensor measurements and their locations from among n potential sensor observations and their locations. This provably NP-hard combinatorial sensor selection problem is addressed by maximizing the mutual information between the selected locations and the locations that are not selected or do not have any sensor deployments. A proof-of-concept study was carried out comparing the spatial prediction of H₂S with a complex model currently used by Sydney Water. The proposed approach is shown to be effective in both modelling and predicting the H₂S spatial concentrations in sewers as well as identifying optimal number of H₂S sensors and their locations for a required level of prediction accuracy.