(325e) Constrained Parametric Estimation of Multivariate Probability Density Functions From Normal Operation Data and Its Application to Fault Detection

Identifying faults in processing plants and predicting the probability of possible abnormal situations caused by the faults are of great importance in safe and reliable operation of the plants. Conducting these tasks requires a mathematical model that can provide information on the probabilities of the faults and abnormal situations. Such a model can be obtained by developing a Bayesian network, which allows one to effectively represent complex probabilistic systems consisting of large number of variables with intricate interactions. A Bayesian network has an easy-to-use graphical representation and eases the computationally intensive problem of probabilistic inference by factorizing the system's joint probability density functions (PDFs) into marginal and conditional PDFs describing cause and effect relationships among the variables [1, 2].

 In this work we consider the problem of estimating complete PDFs that include information on probabilities of faults and abnormal situations, from “normal” historical process data that is not representative of all possible faults or abnormal situations, including the probability of their occurrence. This problem becomes more difficult but interesting when an accurate first-principles model is not available. We have developed a method of estimating complete marginal and conditional PDFs from normal historical data. This method makes use of a parametric model whose parameters are estimated from cumulative probability properties. The method has been successfully tested on a set of mathematical and process examples, showing satisfactory performance of the method. This method enables us to build large Bayesian networks with any number of nodes and arbitrary level of complexity in the node-node interactions, with much higher convergence rate, stability and interpretability. The Bayesian networks constructed using this method will then be utilized to dynamically model plant-wide risks and perform real-time plant state assessment analysis and fault detection.

[1] N. Mehranbod, M. Soroush, M. Piovoso, B.A. Ogunnaike, A probabilistic model for sensor fault detection and identification, AIChE Journal 49 (7) (2003) 1787-1802.

[2] S. Verron, J. Li, T. Tiplica, Fault detection and isolation of faults in a multivariate process with Bayesian network, Journal of Process Control 20 (2010) 902–911.