Optimal and Robust Operations of Complex Processes withNon-Gaussian Distributed Uncertain Variables under ChanceConstraints - Extension to Model Predictive Control of Parabolic Partial Differential Equation Systems

机会约束下非高斯分布不确定变量复杂过程的最优鲁棒运行——抛物型偏微分方程系统模型预测控制的推广

基本信息

批准号：
182502969
负责人：
Professor Dr.-Ing. Pu Li
金额：
--
依托单位：
Institut für Automatisierungs- und Systemtechnik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/182502969?language=en
关键词：
Optimal Robust Operations Complex Processes

项目摘要

Many engineering processes are modeled by partial differential equations (PDEs) with uncertainties both in model parameters and in operating conditions. Optimization of constrained PDEs under uncertainties remains a challenge due to its mathematical and numerical complexity.Optimization of stochastic PDE systems where chance constraints are to be imposed on spatially distributed output variables has not been properly investigated until now. The objective of this proposed project is to develop efficient approaches to chance constrained optimization of PDE systems with Gaussian and non-Gaussian distributed uncertainties. The firstchallenging task is to appropriately describe spatially distributed output variables through the input uncertainties. Consistent with chance constraints, proper sets of orthogonal polynomials will be constructed for the expansion of the constrained output variables into infinite sums.Dimension reduction strategies will be investigated to truncate the infinite dimensionality of the stochastic PDE model. The second target is to develop mathematical and numerical methods for efficient computation of chance constraints of the PDE systems. Multidimensional sparsegrid techniques will be developed for deterministic transformation of stochastic PDEs as well as for efficiently computing high-dimensional integrals of chance constraints and their gradients.In general, the evaluation of spatially distributed chance constraints poses enormous difficulties. Hence, we will design a tractable and monotonic analytic approximation for chance constraints which guarantees a priori feasibility. In order ameliorate computational burdens suitable strategiesfor parallel computing will be developed and implemented. The overall theoretical and numerical development will be demonstrated through case studies on optimization of thermodynamic processes with endogenous and exogenous uncertainties.

许多工程过程都是通过偏微分方程 (PDE) 建模的，模型参数和操作条件都存在不确定性。由于数学和数值的复杂性，不确定性下受约束 PDE 的优化仍然是一个挑战。对空间分布输出变量施加机会约束的随机 PDE 系统的优化迄今为止尚未得到适当的研究。该项目的目标是开发有效的方法来对具有高斯和非高斯分布不确定性的偏微分方程系统进行机会约束优化。第一个具有挑战性的任务是通过输入不确定性来适当地描述空间分布的输出变量。与机会约束一致，将构造适当的正交多项式集，以将受约束的输出变量展开为无限和。将研究降维策略以截断随机 PDE 模型的无限维数。第二个目标是开发数学和数值方法来有效计算偏微分方程系统的机会约束。多维稀疏网格技术将被开发用于随机偏微分方程的确定性变换以及有效计算机会约束及其梯度的高维积分。一般来说，空间分布机会约束的评估带来了巨大的困难。因此，我们将为机会约束设计一个易于处理且单调的解析近似，以保证先验可行性。为了减轻计算负担，将开发和实施适当的并行计算策略。整体理论和数值发展将通过具有内生和外生不确定性的热力学过程优化的案例研究来论证。