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An Efficient Reachability Analysis Algorithm
 Created: Saturday, 01 November 2008
A document discusses a new algorithm for generating higherorder dependencies for diagnostic and sensor placement analysis when a system is described with a causal modeling framework. This innovation will be used in diagnostic and sensor optimization and analysis tools. Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and insitu platforms. This algorithm will serve as a power tool for technologies that satisfy a key requirement of autonomous spacecraft, including science instruments and insitu missions.
In the causal modeling, the system is modeled in terms of firstorder causeandeffect dependencies; i.e., how the fault propagates from a faulty component to its immediate neighbors. For diagnostic purpose, also global (or higherorder) dependencies are needed, which is the effect of a fault on nonneighbor components. The global dependencies should be inferred from the firstorder dependencies. The method that finds these dependencies is called a reachability analysis algorithm. The result of this algorithm determines at each test point (or sensor position) which of the failure sources can be observed.
The standard reachability analysis algorithm uses a “token propagation” method. The complexity of this algorithm is proportional to the product EN, where E is the number of links (edges) of the graph of the system and N is the number of components. Here a new algorithm is introduced. The complexity of this algorithm is proportional to the product dN, where d is the length of the longest (directed) path in the graph of the system. To compare the performance of these two algorithms, first it is noted that always d ≤ E. But typically, d is of the order of log(E); thus the new algorithm, in general, outperforms the standard algorithm.
This work was done by Farrokh Vatan and
Amir Fijany of Caltech for NASA’s Jet
Propulsion Laboratory.
NPO45797
This Brief includes a Technical Support Package (TSP).
An Efficient Reachability Analysis Algorithm (reference NPO45797) is currently available for download from the TSP library.
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