Linear Algebra and Minimum Relative Entropy to Investigate Contamination Events in Drinking Water Systems

A two-step approach is proposed to assist forensic investigation of possible source locations following a contaminant detection in drinking water systems. Typically this identification problem is ill posed as it has more unknowns than observations. First, linear algebra is employed to rule out potential contaminant injections. Second, an entropic-based Bayesian inversion technique, the minimum relative entropy method, solves for the remaining variables. This formulation allows for the less committed prior distribution with respect to unknown information and can include model uncertainties and measurement errors. The solution is a space-time contaminant concentration probability density function accounting for the various possible injections that may be the cause of the observed data. Besides, a probability measure quantifying the odds of being the actual location of contamination is assigned to each potential source. Effectiveness and features of the method are studied on two example networks.