Effective control and monitoring of a plant require reliable and frequent real-time information on state variables of the plant. In practice, frequent measurements of all state variables of a process are rarely available, and in such cases, the missing frequent information on the un-measurable state variables can be obtained using a state estimator [1, 2]. Reliable state estimation requires an accurate mathematical model of the plant under consideration. However, in most cases, an accurate mathematical model is rarely available. One way to address this problem is to use a purely data-driven method to conduct the estimation.

In this paper, we present a data-driven approach for state and parameter estimation. The approach is based on Bayesian Belief Network (BBN) theory. In this approach, nodes of a BBN model represent the parameters and state variables of the process under study. The numerical-value-span of interest for each node is divided into equally spaced states. There is no limitation on number of states that can be assigned for each node in BBN theory. However, equal number of states has been considered in this work to achieve as accurate estimation as possible [3]. The necessary conditional probability data set associated with the model that captures correlation between pair of nodes in the model is determined by quantitative batch BBN training procedure [3, 4]. Evidence propagation by junction tree method [5] in the BBN model is used to update probability distribution of nodes representing un-measurable/unavailable process states and parameters. Weighted averaging of updated probability distribution is used to calculate numerical values for such states and parameters. To show the application and performance of the method, two plants, a simple stirred heating tank and the Tennessee Eastman Process [6], are considered. The training data for the first plant is generated by conducting Monte-Carlo simulation of the plant described by a first-principles model. For the second plant, the training data is available for the Tennessee Eastman process [6]. The simulation results show that the proposed method is capable of providing reliable estimates of plant parameters and state variables.

Keywords: data-driven state estimation; data-driven parameter estimation; Bayesian Belief Networks; Tennessee Eastman Process

References

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