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.

许多工程流程都是通过模型参数和操作条件中不确定性的部分微分方程（PDE）建模的。由于其数学和数值复杂性，在不确定性下的受约束PDE的优化仍然是一个挑战。随机PDE系统的优化，该系统将在空间分布的输出变量上施加机会限制，直到现在直到现在。该提议的项目的目的是开发有效的方法，以使用高斯和非高斯分布式不确定性对PDE系统的频率约束优化。首先挑战的任务是通过输入不确定性适当地描述空间分布的输出变量。与偶然的限制一致，将构建适当的正交多项式集，以扩展受约束的输出变量为无限总和。将研究降低策略以截断随机PDE模型的无限维度。第二个目标是开发数学和数值方法，以有效地计算PDE系统的机会约束。将开发多维稀疏技术，以确定随机PDE的确定性转换，并有效地计算出机会约束及其梯度的高维积分。一般而言，对空间分布的机会约束的评估构成了巨大的困难。因此，我们将设计一个可进行的典型且单调的分析近似，以确保先验可行性。为了改善计算负担，将制定和实施适合并行计算的合适策略。总体理论和数值发展将通过有关内源性和外源性不确定性的热力学过程优化的案例研究来证明。