Nonparametric Density Estimation of Hierarchical Probabilistic Graph Models for Assumption-Free Monitoring

Abstract

Probabilistic graphical models, such as Bayesian networks, have recently gained attention in process monitoring and fault diagnosis. Their application, however, is limited to discrete or continuous Gaussian distributed variables, which results from the difficulty in efficiently estimating multivariate density functions. This article shows that decomposing the graphical model into a hierarchical structure reduces estimating a multivariate density function to the estimation of low-dimensional/conditional probabilities. These conditional density functions can be effectively estimated from data using a nonparametric kernel method and the low-dimensional densities can be estimated using a kernel density estimation (KDE). On the basis of the estimated densities, anomalous process behavior can be detected and diagnosed by examining which probability is lower than its corresponding confidence limit. Applications to simulated examples and an industrial blast furnace iron-making process show that the proposed metho...