A Mixed Integer Nonlinear Optimization Based Approach to Simultaneous Data Reconciliation and Bias Identification

The problem of data reconciliation and the detection and identification of gross errors, such as measurement bias, are closely related and permits a solution within a mixed integer optimization framework. A mixed-integer linear programming (MILP) approach has been previously investigated by Soderstrom et al. (2001), where the process model was described by a set of linear equations. This paper outlines an extension of that technique when the model contains only bilinear terms as well as general nonlinear ones, requiring the solution of a mixed integer nonlinear program (MINLP). Several solution methods were compared including the outer approximation / equality relaxation algorithm implemented in GAMS, genetic algorithms, and Tabu Search. These methods were tested on several challenging test problems, showing an improvement over other published methods for bias detection.