Non-smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes

转换平流扩散过程互补公式的非光滑方法

• 批准号: 314147871
• 负责人: Professor Dr. Christian Kirches
• 金额: --
• 依托单位: Institut für Mathematische Optimierung
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/314147871?language=en
• 关键词: Non; smooth; Methods; Complementarity; Formulations

Organic Rankine Cycle (ORC) processes are established in process engineering for energy recovery from an exhaust heat source. They run a cyclically operated advection-diffusion process to transfer energy from exhaust heat into a working medium using a boiler. The working medium in steam phase is expanded to harness energy, while the working medium, now in fluid phase, is fed back to the boiler by way of condenser and pump.We take interest in the temporal and spatial dynamics of the isobaric phases of an ORC under transient boundary conditions described by exhaust flow and temperature. The problem is described by an advection-diffusion process modeled by instationary partial differential-algebraic equations in 1D or 2D with distributed phase-dependent medium parameters. Due to the large scale of process models and significant perturbations of the process by external load-point changes on a time scale considerably smaller than the process' time constant, the non-smooth behavior of the process is non-periodic and shows nontrivial patterns. Optimal operation of the transient behavior is key to making the concept practically worthwhile, and is a highly challenging task for classical control concepts.The proposed research project develops theory and efficient numerical methods for optimization of advection-diffusion processes with phase changes described by instationary nonlinear PDAEs.Theory and methods shall combine the state of the art in reduced approaches for PDE-constrained optimization, a modeling approach for non-smoothness that makes use of discrete-valued controls and a partial outer convexification approach to mixed-integer optimal control combined with a decomposition approach for constraints on the non-smooth parts of the problem. In particular, we develop:- a simultaneous optimization framework is chosen in which the discretized model equations enter the optimization problem as nonlinear constraints;- discrete and non-smooth phenomena are modeled in a partial outer convexification framework. Using adaptive discretizations in space and time, this gives rise a non-convex constraint structure imposed on the simplex of indicator controls;- a decomposition approach for the resulting MIOCP into an MPVC and the use of a SUR algorithm. The approach shall be used to decouple the PDE optimization task from the combinatorial task of identifying an optimal switching structure;- a theoretical framework for the class of advection diffusion processes that relates the non-smooth result of the SUR algorithm to the to the solution of the non-smooth problem. Such relations shall be shown in the spaces of controls and of PDE states, and in terms of bounded loss of feasibility and bounded suboptimality, and shall be related to the choice of discretizations- a reduced semi-smooth Newton-type framework is used to solve the non-smooth nonlinear programming problems that result from the discretization of model equations and controls.

有机朗肯循环（ORC）过程在过程工程中建立，用于从废热源回收能量。它们运行循环运行的平流扩散过程，使用锅炉将废热中的能量转移到工作介质中。蒸汽相工质通过膨胀利用能量，而流体相工质通过冷凝器和泵返回锅炉，研究了在排气流量和温度描述的瞬态边界条件下ORC等压相的时空动态特性。该问题由一维或二维非定常偏微分-代数方程组描述，介质参数为分布相控。由于大规模的过程模型和显着的扰动过程的外部负载点变化的时间尺度上大大小于过程的时间常数，非光滑的行为的过程是非周期性的，并显示出非平凡的模式。瞬态行为的优化操作是使概念实际上有价值的关键，并且是经典控制概念的高度挑战性的任务。所提出的研究项目为具有由非平稳非线性PDAE描述的相变的对流扩散过程的优化发展理论和有效的数值方法。理论和方法将联合收割机结合PDE约束优化的简化方法的最新技术水平，非光滑的建模方法，利用离散值控制和部分外凸化方法的混合整数最优控制结合的分解方法的约束的非光滑部分的问题。特别是，我们开发：-选择一个同时优化框架，其中离散模型方程作为非线性约束进入优化问题;-离散和非光滑现象在部分外凸化框架中建模。使用自适应离散化在空间和时间，这会产生一个非凸约束结构的指标控制的单纯形;-分解方法所产生的MIOCP到一个MPVC和使用的SUR算法。该方法将被用来解耦的PDE优化任务从确定一个最佳的开关结构的组合任务;-对流扩散过程的类的理论框架，涉及到非光滑的结果的SUR算法的非光滑问题的解决方案。这种关系应显示在控制和PDE状态的空间中，并在可行性和有界次优性的有界损失方面，并应与离散化的选择有关-一个简化的半光滑牛顿型框架用于解决模型方程和控制的离散化所产生的非光滑非线性规划问题。