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Control the Fibre Orientation Distribution at the Outlet of Contraction

机译:控制收缩出口处的纤维取向分布

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摘要

A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then, the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness of this idea is that the method is not iterative and it does not need any initial guess of the solution.
机译:研究了造纸机流浆箱中纤维取向分布的二维模型。目的是通过改变其形状来控制收缩出口处的纤维取向分布。数学公式导致了一个优化问题,该问题以线性对流扩散方程的系数控制为状态问题。然后,将该问题表示为由变分形式控制的最优控制问题。通过使用嵌入方法,可允许的形状类别将由一类正Radon量度代替。然后,通过线性规划问题来近似测量空间中的优化问题。表示最佳形状的最佳度量是通过解决此线性规划问题来近似得出的。在本文中,我们证明了嵌入方法(将可允许集合嵌入到度量的子集中)可以成功地应用于一维流浆箱的形状变化设计。这种想法的有用之处在于该方法不是迭代的,并且不需要对解决方案进行任何初始猜测。

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