Nonlinear Gaussian Belief Network based fault diagnosis for industrial processes

A Nonlinear Gaussian Belief Network (NLGBN) based fault diagnosis technique is proposed for industrial processes. In this study, a three-layer NLGBN is constructed and trained to extract useful features from noisy process data. The nonlinear relationships between the process variables and the latent variables are modelled by a set of sigmoidal functions. To take into account the noisy nature of the data, model variances are also introduced to both the process variables and the latent variables. The three-layer NLGBN is first trained with normal process data using a variational Expectation and Maximization algorithm. During real-time monitoring, the online process data samples are used to update the posterior mean of the top-layer latent variable. The absolute gradient denoted as G-index to update the posterior mean is monitored for fault detection. A multivariate contribution plot is also generated based on the G-index for fault diagnosis. The NLGBN-based technique is verified using two case studies. The results demonstrate that the proposed technique outperforms the conventional nonlinear techniques such as KPCA, KICA, SPA, and Moving Window KPCA.