An analysis of model parameter uncertainty on online model-based applications



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It is important to predict the behavior of an engineering process accurately and timely. The predictions are usually achieved using a first-principles-based model that describes the complex phenomena embodied in the process. However, no model is an exact representation of the complex process for multiple reasons. The primary goal of this research is to investigate one of the possible reasons, the uncertainty of the model parameters from the viewpoint of their effect on the accuracy of the model’s predictions. Other secondary goals of this research are updating the uncertain parameter values and determination of robust estimates of the uncertain parameters to improve the accuracy of a model.

The methodologies applied to understand propagation of the uncertain parameters through a model are Latin hypercube sampling coupled with Hammersley sequencing (LHHS). These methods are selected because of their efficiency and effectiveness when there are multiple uncertain parameters in a model.

Real processes experience unmeasured and unplanned disturbances. Even though a model may come arbitrarily close to estimating the output of the process, because of these types of disturbances there always will be process/model mismatch. This study addresses this issue by investigating updating of the model uncertain parameters to minimize this mismatch. The updating methods designed in this research come from the class of particle filters (also referred to as sequential Monte Carlo filters); they include a Markov chain Monte Carlo filter and an ensemble Kalman filter.

As the number of uncertain parameters increase so does the computational burden. While updating is one solution to improve model accuracy another potential solution is to determine a robust estimate of the uncertain parameter using the theory of robust statistics. This research will provide the theoretical proof that the maximum likelihood estimate is the best statistic to provide a robust estimate.

The operational side of this research focuses on online model-based applications such as model-based control and monitoring with processing of uncertain model parameters. To demonstrate these research concepts, we employ simulations of a continuous reactor system and an oil producing reservoir system. The results are analyzed and discussed.