Rare Events Monte Carlo Sampling for Contamination Warning Systems (CWS) Evaluation

Contamination warning systems (CWS) are being designed to protect water distribution systems against deliberate terrorist contamination intrusions. To test the performance of a contamination warning system, contamination intrusion events need to be selected. Since contamination injections can occur at any node at any time, even for a moderate size of a network the theoretical number of possible injection events is enormous, and grows exponentially with system size. To cope with this difficulty a Cross Entropy algorithm, which originates from Rare Event simulation methodologies, is proposed. The suggested algorithm is able to sample efficiently a predefined rare sub-set (i.e., a sub-set of events with a small probability to occur, but with an extreme impact) of the entire set of contamination events (e.g., all the events whose contamination exposure to public are greater than a specific value). The methodology is demonstrated on two growing complexity water distribution systems examples.