基于模型与离散化目录的区域供热网络自适应非线性优化
Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs
AI总结：
针对区域供热网络稳态运行优化问题，提出基于模型与离散化目录的自适应算法，通过自适应选模型与调离散粒度，以低成本获满足精度的最优解，可求解此前不可解的实例。
摘要：
我们提出一种用于稳态工况下区域供热网络运行的自适应优化算法。管网中热水流动的特性采用不可压缩Euler方程与恰当选取的能量方程建模。通过对这些方程施加不同的简化，我们推导得到一个模型目录。我们的算法基于该目录，可自适应控制在网络的不同位置使用对应模型；此外，所采用的离散化粒度也以类似的自适应方式调控。通过这种方式，我们能够以较低的计算成本获得最优解，且该解相对于最精确的建模层级满足预设的容差要求。为了自适应控制不同层级间的切换以及离散化网格的适配，我们推导了误差度量公式与后验误差度量估计器。在合理假设下，我们证明了该自适应算法会在有限次迭代后终止。我们的数值实验结果表明，该算法能够求解此前无法求解的问题实例。
英文摘要：
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.
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