Maximum likelihood data rectification: Steady‐state systems

A maximum likelihood rectification (MLR) technique that poses the data‐rectification problem in a probabilistic framework and maximizes the probability of the estimated plant states given the measurements is proposed. This approach does not divide the sensors into “normal” and “gross error” classes, but uses all of the data in the rectification, each sensor being appropriately weighted according to the laws of probability. In this manner, the conventional assumption of no sensor bias is avoided, and both random errors (noise) and systematic errors (gross errors) are removed simultaneously. A novel technique is introduced that utilizes historical plant data to determine a peior probability distribution of the plant states. This type of historical plant information, which contains the physical relationships among the variables (mass balances, energy balances, thermodynamic constraints), as well as statistical correlations among the variables, has been ignored in prior data‐rectification schemes. This approach can use the historical plant information to solve a new class of data‐rectification problems in which there are no known model constraints. The MLR method is demonstrated on data from a simulated flow network and a simulated heat‐exchanger network. The MLR technique provides considerably improved performance over existing data‐reconciliation schemes in these examples.