Le Tung, Hadjicostis Christoforos N
Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
IEEE Trans Syst Man Cybern B Cybern. 2007 Dec;37(6):1607-21. doi: 10.1109/tsmcb.2007.906977.
In this paper, we study the application of the max-product algorithm (MPA) to the generalized multiple-fault diagnosis (GMFD) problem, which consists of components (to be diagnosed) and alarms/connections that can be unreliable. The MPA and the improved sequential MPA (SMPA) that we develop in this paper are local-message-passing algorithms that operate on the bipartite diagnosis graph (BDG) associated with the GMFD problem and converge to the maximum a posteriori probability (MAP) solution if this graph is acyclic (in addition, the MPA requires the MAP solution to be unique). Our simulations suggest that both the MPA and the SMPA perform well in more general systems that may exhibit cycles in the associated BDGs (the SMPA also appears to outperform the MPA in these more general systems). In this paper, we provide analytical results for acyclic BDGs and also assess the performance of both algorithms under particular patterns of alarm observations in general graphs; this allows us to obtain analytical bounds on the probability of making erroneous diagnosis with respect to the MAP solution. We also evaluate the performance of the MPA and the SMPA algorithms via simulations, and provide comparisons with previously developed heuristics for this type of diagnosis problems. We conclude that the MPA and the SMPA perform well under reasonable computational complexity when the underlying diagnosis graph is sparse.
在本文中，我们研究最大积算法（MPA）在广义多重故障诊断（GMFD）问题中的应用，该问题由组件（待诊断）以及可能不可靠的警报/连接组成。我们在本文中开发的MPA和改进的顺序MPA（SMPA）是局部消息传递算法，它们在与GMFD问题相关联的二分诊断图（BDG）上运行，并且如果该图是无环的，则收敛到最大后验概率（MAP）解（此外，MPA要求MAP解是唯一的）。我们的模拟表明，MPA和SMPA在相关BDG中可能存在循环的更一般系统中表现良好（在这些更一般的系统中，SMPA似乎也优于MPA）。在本文中，我们给出了无环BDG的分析结果，并评估了这两种算法在一般图中特定警报观测模式下的性能；这使我们能够获得关于相对于MAP解进行错误诊断概率的分析界限。我们还通过模拟评估了MPA和SMPA算法的性能，并与先前针对此类诊断问题开发的启发式方法进行了比较。我们得出结论，当基础诊断图稀疏时，MPA和SMPA在合理的计算复杂度下表现良好。
