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    孙少超, 黄道, 宫艳雪. 过失误差识别和数据校正的MILP模型的新视角[J]. 华东理工大学学报(自然科学版), 2011, (1): 95-99.
    引用本文: 孙少超, 黄道, 宫艳雪. 过失误差识别和数据校正的MILP模型的新视角[J]. 华东理工大学学报(自然科学版), 2011, (1): 95-99.
    SUN Shao-chao, HUANG Dao, GONG Yan-xue. Novel Perspective to Mixed Integer Linear Programming Model for Gross Error Identification and Data Rectification[J]. Journal of East China University of Science and Technology, 2011, (1): 95-99.
    Citation: SUN Shao-chao, HUANG Dao, GONG Yan-xue. Novel Perspective to Mixed Integer Linear Programming Model for Gross Error Identification and Data Rectification[J]. Journal of East China University of Science and Technology, 2011, (1): 95-99.

    过失误差识别和数据校正的MILP模型的新视角

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

    • 摘要: 混合整数线性规划(MILP)方法成功地应用于同时识别过失误差和协调数据,使过程数据满足物料平衡、能量平衡和其他约束条件。然而,在混合整数线性规划的框架下,模型的扩展十分困难。采用公式推导的方式证明了数据校正的MILP模型可以等价地表示成非线性规划模型,因而该模型不仅可以用混合整数线性规划算法求解而且可以用非线性迭代算法求解,两种算法求解的一致性也验证了该结论的正确性。此外,在非线性规划的框架下,模型容易进行扩展,在不增加算法复杂度的前提下,扩展模型保证了在不存在过失误差的情况下模型为最大似然估计。两个应用实例验证了本文的观点。

       

      Abstract: 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.

       

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