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Optimal stochastic fault detection filter. (English) Zbl 1036.93060
Any system under automatic control demands a high degree of system reliability. This requires a heat monitoring system capable of detecting any plant, actuator and sensor faults as they occur and identifying the faulty components. In this paper a fault detection and identification algorithm, called optimal stochastic fault detection filter, is determined. The objective of the filter is to detect a single fault, called the target fault, and block other faults, called the nuisance faults, in the presence of the process and sensor noises. The filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults. Therefore, the residual is affected primarily by the target fault and minimally by the nuisance faults. The transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances. It is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity. The asymptotic behavior of the filter near the limit is determined by using a perturbation method. Filter designs can be obtained for both time-invariant and time-varying systems.

MSC:
93E11 Filtering in stochastic control theory
93B35 Sensitivity (robustness)
93B51 Design techniques (robust design, computer-aided design, etc.)
93B30 System identification
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