Detection of incipient failures by geometric methods

The problem of detecting anomalous operating conditions in systems subject to deterioration is tackled by means of geometric tools, which provide sharp necessary and sufficient conditions for its exact solution. According to an approach often adopted, the observation problem is turned into the more congenial control problem by means of duality arguments. Hence, an extension of the well-known geometric conditions for noninteracting controls is introduced, which, when transferred to the observation context, enables detection of anomalies in the behavior of the monitored system by processing recorded sequences of the outputs. The algorithm herein proposed is particularly suitable and effective in condition monitoring of single-throw mechanical systems (railway switch machines, lifts, mechanical presses, automatic doors and barriers, etc.). A minimal-norm solution, which can be used when the geometric conditions are not satisfied is also presented.