Data reconciliation: a robust approach using contaminated distribution.
Résumé
On-line optimisation provides a means for maintaining a process around its optimum operating range. This optimisation heavily relies on process measurements and accurate process models. However, these measurements often contain random and possibly gross errors as a result of miscalibration or failure of the measuring instruments. Thus, these measurements do not generally satisfy the process constraints and they need to be reconciled. In the data reconciliation process, data are adjusted to satisfy the process constraints while minimizing the error in the least squares sense. On a mathematical point of view, data reconciliation is generally based on the assumption that the measurement errors have Gaussian probability density function (pdf) with zero mean and known variance. The elimination of the less frequent gross errors is achieved by so called gross error detection. Therefore, simultaneous data reconciliation and gross error detection have emerged as a key issue of on-line optimization. Indeed, in the presence of gross errors, all of the estimates provided by classical data reconciliation methods are greatly affected by such biases and would not be considered as reliable indicators of the state of the process. This paper proposes a data reconciliation strategy that deals with the presence of such gross errors. Instead of constructing the objective function to be minimized on the basis of random errors only, the proposed method takes into account both contributions from random and gross errors using a so-called contaminated Gaussian distribution. It is shown that this approach introduces less bias in the estimation due to its natural property to reject gross errors. An academic application to flowrate and concentration data in mineral processing illustrates the efficiency of the proposed method.