Improving Efficiency of the Bayesian Approach to Water Distribution Contaminant Source Characterization with Support Vector Regression

Abstract

There are multiple sources of uncertainties in urban water-distribution systems, e.g., nodal water demand and sensor measurement error. All of these uncertainties increase the complexity of contaminant source identification in a sparse sensor network. The large number of attributes (e.g., contaminant source location, magnitude, injection starting time, and duration) of a contaminant event profile cannot be identified given limited sensor data. Instead, the uncertainties in the contaminant event profile need to be characterized. Markov chain Monte Carlo (MCMC) methods for Bayesian analyses allow for the characterization of the uncertainty in the contamination event profile. To account for stochastic water demands, which has been shown in some circumstances to be necessary if the contaminant event is to be properly characterized, the evaluation of the likelihood function is the most computationally expensive part of the MCMC implementation. Previous work applied Monte Carlo methods for error propagation (MCEP). The research reported in this paper investigates the application of support vector regression (SVR) to speed the likelihood evaluation. This coupled MCMC-SVR approach enables probabilistic inference of the contaminant event. An SVR model, which maps from the contaminant event space to the likelihood space, is built for each node in the network to evaluate the likelihood function during the MCMC chain evolution. For the case study investigated, MCMC-SVR is computationally feasible and robust in inferring the contaminant event. A comparison between MCMC-SVR and MCMC-MCEP reveals that there is no substantial difference between the inferences provided by the two models, whereas the former is more computationally efficient.