Fault Identification via Non-parametric Belief Propagation

We consider the problem of identifying a pattern of faults from a set of noisy linear measurements. Unfortunately, maximum a posteriori probability estimation of the fault pattern is computationally intractable. To solve the fault identification problem, we propose a non-parametric belief propagation approach. We show empirically that our belief propagation solver is more accurate than recent state-of-the-art algorithms including interior point methods and semidefinite programming. Our superior performance is explained by the fact that we take into account both the binary nature of the individual faults and the sparsity of the fault pattern arising from their rarity.

💡 Research Summary

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The paper addresses the problem of identifying a sparse binary fault pattern from noisy linear measurements, a task that naturally arises in many engineering domains such as aerospace systems, industrial process control, and automotive diagnostics. Formally, there are (n) possible faults, each represented by a binary variable (x_s\in{0,1}). The prior probability that a fault occurs is small ((p_s\ll 1)), reflecting the rarity of faults. A set of (m) real‑valued measurements (y\in\mathbb{R}^m) is obtained through a linear model
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