Marco Propato

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.

A sensor location model to detect contaminations in water distribution networks

Real-time continuous water quality monitoring could provide an increased barrier to protect consumers against contaminations. Among several challenges to be faced to successfully build such a system, there is the sensor location problem that should be designed to satisfy several requirements. A general simulation framework describes the computational tasks necessary to assess consumer exposure from contamination event scenarios. A mixed integer linear program is proposed to identify optimal sensor locations to detect random contaminations occurring in drinking water systems under unsteady hydraulic conditions. Such problem formulation is flexible to accommodate dierent design objectives whose mathematical dierences are only the coecient values while the number of variables and constraints remains identical. Such feature reduces the computational eort required to determine the tradeo solutions and it makes more straightforward results analysis and comparison. To optimize problem coecients calculation, several computational tasks are decoupled. In particular, for large contamination event ensembles, concentration dynamics at consumer nodes can be calculated using a linear input/output model without requiring to execute a water quality model simulation for every contamination scenario.

Monitoring design for source identification in water distribution systems.

The design of sensor networks for monitoring contaminants in water distribution systems is currently an active area of research. Much of the effort has been directed at the contamination detection problem and the expression of public health protection objectives. Monitoring networks once they are in place, however, are likely to be used to gather monitoring data for source inversion as well. Thus, the design of these networks with the unique objectives associated with source inversion problems in mind is a necessity. Source inversion problems in water distribution systems are inherently underdetermined and exhibit solution nonuniqueness; and moreover, the structure of the errors associated with a solution are a function of monitoring observations. Optimal inverse experiment design is investigated as an approach for improving solution quality. The approach involves the selection of monitoring locations that are best suited to the generation of a well-conditioned source identification inverse problem. The m...

SLOW TRANSIENT PRESSURE DRIVEN MODELING IN WATER DISTRIBUTION NETWORKS

A Pressure Driven Model is presented for inclusion within a slow transient model (rigid water column) in water distribution networks. Special emphasis is made to consider the available pressure in calculating the resulting consumption. Nevertheless, integrity pressure constraints are also discussed and solved. Differently from conventional approaches, a formulation involving not only inertia terms for head at free level tank nodes and flow rates at links but also for head at fixed demand nodes, is proposed. With this extension, it is not possible anymore, as in a conventional demand driven analysis, to reduce the system so that it is loop-based nor even node-based. Nevertheless, the approach can be related to hybrid methods for steady states and extended period simulations. It is well known that numerical instability can appear due to initial conditions far from working mode, small diameter pipes, valve closures, pumping turn off/on, deficient water resources. This paper presents an efficient method for numerically integrating this stiff ordinary differential equation. A convenient Lyapunov function allows the reduction of time stepsize when possible.

Integrated Control and Booster System Design for Residual Maintenance in Water Distribution Systems

Booster disinfection is a spatially distributed strategy to maintain chlorine residuals throughout a drinking water distribution system. Such technique can reduce the total disinfectant application and can be more effective in maintaining a more homogeneous spatiotemporal distribution of chlorine residuals at nodes of consumption. However, the lack of reliable real-time feedback control algorithms to regulate chlorine injections and the need to develop secure methods to place actuators (booster stations) and sensors, is limiting its implementation in real distribution systems. Here an integrated approach is proposed for flow-paced chlorine injections. The input/output dynamical behavior can be expressed as a discrete-time linear system with unknown coefficients. An indirect adaptive control scheme is developed to identify and track slow time variations of the input/output plant parameters and the task in managing fast variations is assigned to the wise selection of actuator and sensor locations. To take advantage of the periodic properties of the hydraulic dynamics, a periodic adaptive control scheme is proposed. System-wide control performance is improved by optimally selecting the set of input and output locations. The design problem is formulated as a bi-level non-linear optimization problem.