Selecting proper uncertainty model for steady-state data reconciliation – Application to mineral and metal processing industries

Data reconciliation is widely applied in mineral and metal processing plants to improve information quality. Imprecision, unreliability and incompleteness of measurements are common problems motivating the implementation of the technique. Current practices rely on mass and energy conservation constraints to estimate the underlying steady-state values of process variables. Typically, the Gaussian context is assumed and a Maximum-Likelihood estimator is selected. The performance of such an estimator depends on the covariance matrices used to characterize model and measurement uncertainties. In practice, determining these covariance matrices is a challenging task that is often overlooked. Using inappropriate uncertainty models, based on simplistic or improper hypotheses, can lead to unexpected underperformances. The objective of the paper is to illustrate the impact of correctly selecting uncertainty covariance matrices for steady-state data reconciliation. Different case-studies involving a combustion chamber, a hydrocyclone, a flotation circuit, and a separation unit are used for investigating the sensitivity of the algorithm to the structure of covariance matrices. An example based on Monte-Carlo simulations is presented to assess the importance of assigning right values to variance terms. Simulation results show that the adjustment of uncertainty covariance matrices has a significant influence on the precision of estimates and reveal that some common tuning practices can have detrimental effects.