Bayesian approach to contaminant source characterization in water distribution systems: adaptive sampling framework

Abstract

Bayesian analysis can yield a probabilistic contaminant source characterization conditioned on available sensor data and accounting for system stochastic processes. This paper is based on a previously proposed Markov chain Monte Carlo (MCMC) approach tailored for water distribution systems and incorporating stochastic water demands. The observations can include those from fixed sensors and, the focus of this paper, mobile sensors. Decision makers, such as utility managers, need not wait until new observations are available from an existing sparse network of fixed sensors. This paper addresses a key research question: where is the best location in the network to gather additional measurements so as to maximize the reduction in the source uncertainty? Although this has been done in groundwater management, it has not been well addressed in water distribution networks. In this study, an adaptive framework is proposed to guide the strategic placement of mobile sensors to complement the fixed sensor network. MCMC is the core component of the proposed adaptive framework, while several other pieces are indispensable: Bayesian preposterior analysis, value of information criterion and the search strategy for identifying an optimal location. Such a framework is demonstrated with an illustrative example, where four candidate sampling locations in the small water distribution network are investigated. Use of different value-of-information criteria reveals that while each may lead to different outcomes, they share some common characteristics. The results demonstrate the potential of Bayesian analysis and the MCMC method for contaminant event management.