A Bayesian sparse reconstruction method for fault detection and isolation

Abstract

This article develops a Bayesian method for fault detection and isolation using a sparse reconstruction framework. The normal/training data is assumed to follow a signal‐plus‐noise model, and an indicator matrix is used to show whether the test data is from a faulty process. The distribution of the indicator matrix is modeled by a Laplacian distribution, which forces the indicator matrix to be a sparse one, and a Gibbs sampler is derived to obtain the estimation/reconstruction of the indicator matrix, the unobserved signals, and other parameters like signal mean, covariance, and noise variance. The faulty variables can then be detected and isolated by inspecting whether corresponding rows of the indicator matrix are zero. The proposed Bayesian approach is data driven; it allows for simultaneous fault detection and isolation. A simulation study and an industrial case study are used to test the performance of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.