A method to incorporate bounds in data reconciliation and gross error detection—I. The bounded data reconciliation problem

Abstract Data reconciliation and gross error detection techniques can be improved by exploiting information from bounds on process variables. In this paper a new approach is proposed for incorporating upper and lower bounds on process variables in data reconciliation and gross error detection. Bounds on process variables are directly incorporated as constraints in data reconciliation and the resulting problem is solved using an efficient quadratic programming algorithm. More importantly, a method to obtain the statistical distributions of measurement residuals and constraint residuals has been developed which is useful for gross error detection. Gross error detection methods based on this approach are described in Part II of this series (Comput. chem. Engng 17, 1121–1128).