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An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

机译：动态优化问题的改进有限元网格划分策略

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摘要

The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.
机译：有限元正交配置法广泛用于微分代数方程（DAE）的离散化，而离散策略则显着影响结果的准确性和效率。在这项工作中，提出了一种在非配置点上带有误差估计的有限元网格划分方法，并研究了几种情况。首先，基于有限元的同时策略被用来将微分和代数优化问题（DAOP）转化为大规模非线性规划问题。然后，通过用固定的控制变量进行模拟来获得反应过程的状态变量。引入非并置点以计算在非并置点的状态变量的误差估计。最后，为了提高有限元的计算精度，采用了移动有限元策略来动态地动态调整有限元的长度，以满足设定的误差范围。所提出的策略适用于两个经典的控制问题和大规模的反渗透海水淡化过程。计算结果表明，所提出的策略可以有效地减少动态优化问题的计算量，并具有满意的精度。

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  • 来源
    《Mathematical Problems in Engineering》 |2017年第7期|4829195.1-4829195.10|共10页
  • 作者

    Gong Minliang; Jiang Aipeng; Zhang Quannan; Wang Haokun; Hu Junjie; Lin Yinghui;

  • 作者单位

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

    Hangzhou Dianzi Univ, Sch Automat, Hangzhou 310018, Zhejiang, Peoples R China;

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