摘要
In multivariate statistical process monitoring, fault isolation is an important step that identifies the process variables critical to the detected abnormality. Conventionally, contribution plots are the most popular tools for fault isolation, but they often suffer from the smearing effect and give misleading results. Reconstruction analysis is another commonly used technique. Despite its effectiveness, the original reconstruction analysis method relies on the impractical requirement of a sufficient amount of historical fault data or the complete information of candidate fault directions. Recently, the reconstruction analysis technique has been integrated with the least absolute shrinkage and selection operator (Lasso) to overcome its inherent shortcoming. In that research, the task of reconstruction analysis is reformulated as a Lasso problem, and the faulty variables are indicated by the nonzero point estimates of the Lasso coefficients. As well known, a point estimate does not provide any information about its accuracy and is likely to be affected by the quality of the collected data. In this paper, a Bayesian Lasso approach is utilized to solve the problem mentioned above, which assigns independent Laplace (a.k.a. double exponential) priors to the Lasso coefficients and derives the interval estimates by Gibbs sampling from the Bayesian posterior distribution. Such interval estimates can guide fault isolation by conducting statistical hypothesis tests. In addition, the Bayesian framework facilities the tracking of fault propagation path, thereby benefiting the subsequent root-cause diagnosis step.