  When faulty sensors are rare in a network, diagnosing sensors individually is
inefficient. This study introduces a novel use of concepts from group testing
and Kalman filtering in detecting these rare faulty sensors with significantly
fewer number of tests. By assigning sensors to groups and performing Kalman
filter-based fault detection over these groups, we obtain binary detection
outcomes, which can then be used to recover the fault state of all sensors. We
first present this method using combinatorial group testing. We then present a
novel adaptive group testing method based on Bayesian inference. This adaptive
method further reduces the number of required tests and is suitable for noisy
group test systems. Compared to non-group testing methods, our algorithm
achieves similar detection accuracy with fewer tests and thus lower
computational complexity. Compared to other adaptive group testing methods, the
proposed method achieves higher accuracy when test results are noisy. We
perform extensive numerical analysis using a set of real vibration data
collected from the New Carquinez Bridge in California using an 18-sensor
network mounted on the bridge. We also discuss how the features of the Kalman
filter-based group test can be exploited in forming groups and further
improving the detection accuracy.
