On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Abstract

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

Decentralized and distributed active fault diagnosis: Multiple model estimation algorithms

“…The cost function can represent true economic costs of the missed detection, false alarm and incorrect fault isolation. If these costs are not available in a particular problem, they can be regarded as tuning parameters that shape the behavior of the active fault detector (Punčochář and Šimandl, 2014).…”

“…where σ : G → M and γ : G → U are unknown functions. The detection cost function for the perfect state information model equivalent to L d in ( 9) can be shown (Punčochář and Šimandl, 2014) to satisfy…”

Parametric Fault Diagnosis of an Active Gas Bearing

“…One of the systems represents the healthy system while the others represent the system subject to one of the possible faults. Extensive effort has been put into defining the framework and the optimal input for the diagnosis of such a problem statement [14][15][16][17][18][19][20]. Another approach for defining the effect of the fault has been proposed in [21].…”

Active Fault Diagnosis via Reachable Set Separation using Interval Methods

“…This may result in undesirable delays in in detecting and/or isolating faults, possibly leading to more severe consequences or propagation to major failures in the system. As explained in [2], many different methods and scenarios have been proposed under the umbrella of AFD, considering deterministic [3], [4] or stochastic uncertainties [5], [6], hybrid stochastic-deterministic approaches [7], [8], and finite or infinite AFD auxiliary control sequences [9].…”