论文标题
基于模型和离散目录的地区供暖网络的自适应非线性优化
Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs
论文作者
论文摘要
我们提出了一种适应性优化算法，用于固定政权中的操作区供暖网络。使用不可压缩的Euler方程和适当选择的能量方程式对管道网络中热水流的行为进行建模。通过对这些方程式应用不同的简化，我们得出了模型目录。我们的算法基于此目录，并自适应地控制在网络中使用哪些模型的位置。此外，应用离散化的粒度以类似的适应性方式控制。通过这样做，我们能够以低计算成本获得满足规定的公差W.R.T.的最佳解决方案。最准确的建模水平。为了自适应地控制不同级别和离散网格的适应性之间的切换，我们得出了误差度量公式和后验误差测量估计器。在合理的假设下，我们证明自适应算法在有限的许多迭代后终止。我们的数值结果表明，该算法能够为以前无法解决的问题实例生成解决方案。
We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen energy equation. By applying different simplifications to these equations, we derive a catalog of models. Our algorithm is based on this catalog and adaptively controls where in the network which model is used. Moreover, the granularity of the applied discretization is controlled in a similar adaptive manner. By doing so, we are able to obtain optimal solutions at low computational costs that satisfy a prescribed tolerance w.r.t. the most accurate modeling level. To adaptively control the switching between different levels and the adaptation of the discretization grids, we derive error measure formulas and a posteriori error measure estimators. Under reasonable assumptions we prove that the adaptive algorithm terminates after finitely many iterations. Our numerical results show that the algorithm is able to produce solutions for problem instances that have not been solvable before.
