Integration of design and operation considering parametric uncertainty and dynamic variability for the optimal design of load-flexible processes based on a simultaneous solution approach

传统上，过程首先在稳态基础上设计。然后确定过程控制概念或控制器设计。然而，这并没有考虑到设计和操作是相互依赖的。因此，在稳态操作条件下设计的过程在标称条件下可能具有最小成本，但在输入变量的动态变化、在操作期间违反产品规格或其它边界条件或需要大量干预的情况下不再可操作。此外，还有其他挑战，如模型参数的不确定性以及过程拓扑的二元决策变量。在该项目中，提出了一种同时的方法，它结合了设计和操作在一个优化问题。参数的不确定性描述使用无迹变换，这消除了不确定性下的鲁棒优化的顺序算法的需要。输入变量的可变性使用调幅伪随机二进制序列来生成，以便为这些输入信号覆盖尽可能大的频率和幅度范围。为了解决混合整数部分，一个解决方案的方法，使用一个典型的MINLP算法，以及一个替代的并行化方法，使用最陡梯度。在这方面，我们特别与滑铁卢大学（加拿大）的Ricarcart-Sandoval教授合作。为了确定所需的有限元数，实施了一种启发式算法，该算法评估非配置点处的离散化误差，并在此基础上增加有限元数。在这里，我们与卡内基梅隆大学的比格勒教授密切合作。该框架适用于三个示例过程的复杂性不断增加（由于变量和混合整数变量的数量）的扰动周围的标称操作点，以及灵活性的情况。这些是一个单一的反应器，两个CSTR和一个蒸馏塔（二元决策变量）的组合。该项目的目标是设计一个灵活操作的过程工程过程的框架，对动态干扰的敏感性低，对参数不确定性鲁棒。

vConventionally, processes are first designed on a steady-state basis. This is followed by the determination of the process control concept or the controller design. However, this does not take into account that design and operation are interdependent. A process designed under steady-state operating conditions may therefore have a minimum cost under nominal conditions, but is no longer operable under dynamic variability of the input variables, product specifications or other boundary conditions are violated during operation, or heavy intervention is required. In addition, there are other challenges such as uncertainty of model parameters as well as binary decision variables for the process topology. In the project, a simultaneous approach is proposed, which combines design and operation in one optimization problem. Parametric uncertainties are described using the Unscented Transform, which eliminates the need for sequential algorithms for robust optimization under uncertainties. The variability of the input variables is generated using an amplitude-modulated pseudo-random binary sequence in order to cover as large a frequency and amplitude range as possible for these input signals. To solve the mixed integer part, a solution approach using a typical MINLP algorithm as well as an alternative parallelizable approach using the steepest gradient are proposed. In this aspect, we cooperate in particular with Prof. Ricardez-Sandoval from the University of Waterloo (Canada). In order to determine the necessary number of finite elements, a heuristic is implemented that evaluates the discretization error at non-collocation points and increases the number of finite elements based on this. Here, we collaborate intensively with Prof. Biegler of Carnegie Mellon University. This framework is applied to three example processes with increasing complexity (due to number of variables and mixed integer variables) for disturbances around the nominal operating point as well as for flexibility scenarios. These are a single reactor, a combination of two CSTRs and a distillation column (with binary decision variables). The goal of the project is framework for the design of process engineering processes to be operated flexibly, with low susceptibility to dynamic disturbances and robust to parametric uncertainty.