Compressive Sensing in Fault Detection

Randomly generated tests are used to identify faulty sensors in large-scale discrete-time linear time-invariant dynamical systems with high probability. It is proved that the number of the required tests for successfully identifying the location of the faulty sensors (with high probability) scales logarithmically with the number of the sensors and quadratically with the maximum number of faulty sensors. It is also proved that the problem of decoding the identity of the faulty sensors based on the random tests can be cast as a linear programming problem and therefore can be solved reliably and efficiently even for large-scale systems. A numerical example based on automated irrigation networks is utilized to demonstrate the results