Novel Perspective to Mixed Integer Linear Programming Model for Gross Error Identification and Data Rectification

Mixed integer linear programming (MILP) approach can simultaneously achieve the gross error detection and data reconciliation, and makes the process data attain the balance of material and energy, and other constrains. However, it is quite difficult for the expansion of model under the MILP framework. In this paper, it is proven that the MILP model for data reconciliation is equivalent to a nonlinear programming model. Hence，the MILP model for data reconciliation can be resolved by utilizing MILP method or nonlinear iterative method, which is verified by the consistency of solutions via the two algorithms. Besides, under the nonlinear programming framework, the expansion of model is easily attained. When the computational complexity is not increased, the proposed extension model ensures that the model is the maximum likelihood estimate under without gross error. Finally, two examples are given to validate the point of view proposed by this paper.