Monitoring Sensor Network Design for Water Distribution Source Inversion Problems

Monitoring network design for the detection of contaminants in water distribution systems is currently an active area of research. Much of the effort has been directed at the contamination detection sub-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 in mind is a necessity. Source inversion problems in water distribution systems are inherently under-determined and exhibit solution non-uniqueness. Judicious monitoring design is one approach for addressing these difficulties. Herein, discrete linear inverse theory is applied to the monitoring sensor network design problem; in particular, a quantitative description of solution existence, uniqueness, stability, and resolution is developed using singular value decomposition.