Robust Stacked Probabilistic Latent Variable Model for Fault Isolation of Dynamic Process With Outliers

Modern industrial data is commonly dynamic and contains outliers, which challenges the accurate isolation of faulty variables in abnormal situations. To deal with process dynamics, a robust stacked probabilistic latent variable model is proposed, which is formed by stacking a series of static probabilistic latent variable models. A fault indicator matrix with the Bernoulli-Gaussian prior is constructed to indicate which process variables are faulty. The Bernoulli-Gaussian prior neatly accommodates the stacked structure of the indicator matrix so that rows corresponding to normal variables will shrink to zero. The stacked probabilistic latent variable model is further extended to deal with outliers by introducing an outlier indicator vector with the Beta-Bernoulli prior. The location and magnitude of the outliers can be successfully identified. Based on the robust stacked model, a variational Bayesian inference algorithm is developed to estimate unknown parameters. By using the piecewise affine approximation, the proposed fault isolation method can be extended to deal with nonlinear processes. The effectiveness and superiority of the method are illustrated by application studies to a simulation case and an industrial boiler case.