This paper presents a state-based method to address the verification of K-diagnosability and fault diagnosis of a finite-state vector discrete-event system (vector DES) with partially observable state outputs due to l...
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This paper presents a state-based method to address the verification of K-diagnosability and fault diagnosis of a finite-state vector discrete-event system (vector DES) with partially observable state outputs due to limited sensors. vector DES models consist of an arithmetic additive structure in both the state space and state transition function. This work offers a necessary and sufficient condition for verifying the K-diagnosability of a finite-state vector DES based on state sensor outputs, employing integer linear programming and the mathematical representation of a vector DES. Predicates are employed to diagnose faults in a vector DES online. Specifically, we use three different kinds of predicates to divide system state outputs into different subsets, and the fault occurrence in a system is detected by checking a subset of outputs. Online diagnosis is achieved via solving integer linear programming problems. The conclusions obtained in this work are explained by means of several examples.
The diagnosability problem of faults is studied in the framework of vector discrete-event system (VDES). A VDES is a discrete-eventsystem model in which a system state is represented by a vector with integer componen...
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The diagnosability problem of faults is studied in the framework of vector discrete-event system (VDES). A VDES is a discrete-eventsystem model in which a system state is represented by a vector with integer components, and state transitions are represented by integer vector addition. Predicates are employed to verify the fault diagnosability of VDES, since, defined as functions, predicates can conveniently identify particular state sets of interests. Specifically, system states are partitioned into different subsets by predicates, and the fault diagnosability of a system is verified by checking a subset of states. A sufficient condition for fault diagnosability of VDES is presented first. A necessary and sufficient condition is then developed. According to the two conditions, two types of predicates are given to partition the states in a VDES. In this work, a diagnoser or a full state enumeration is not constructed, whose complexity is exponential with respect to the system state size. In order to verify whether a system satisfies the proposed conditions, several polynomial algorithms and an algorithm by constructing a tree automaton are developed. Several examples are provided to illustrate the results obtained in this paper.
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