Research On Moving Finite Elements For Dynamic Optimization

Optimization is a significant technology for industries to save energy and reduce emissions. In recent years, with the increasing requirement of optimization in industry and the development of computer technology, dynamic optimization problem is becoming an important issue in process system engineering. In simultaneous approach, the continuous dynamic optimization problems are discretized into NLP problems. Simultaneous approach has the advantage of more efficiency and high stability. Compared to other methods, simultaneous approach has better prospect on development and application. However, current simultaneous approach still has some issues such as the accuracy after discretization and the optimality of solution and real time requirement for online application. They need to be discussed when used to solve dynamic optimization problem. Based on the simultaneous approach, this thesis focuses on the three issues above. Dynamic optimization problem of chemical process and high temperature gas cooled reactor pebble bed module (HTR-PM) are studied.The main research contents and contributions are as follows:1. Simultaneous approach based on orthogonal collocation finite elements is studied. The property of different orthogonal collocation points are analyzed. An then, non-singular optimal control problem and singular optimal control problem in chemical process are presented.2. Finite elements are utilized to discretize the dynamic optimization problems in simultaneous approach. For the accuracy after discretization and the optimality of solution and determination of breakpoints in discontinuous optimal control trajectory, different moving finite element (MFE) methods are analyzed and compared with each other in detail. At last, disadvantages of moving finite element method are elaborated.3. There are still some shortcomings in current algorithm of MFE. Firstly, more constrained and different NLPs need to be solved in MFE and the NLP problem may fail to converge if large problems are encountered. Secondly, MFE is designed for the single instance of dynamic optimization problem. It cannot satisfy the requirement of different state transition. A random sampling moving finite element (RSMFE) method based on bi-level structure is proposed. Results are compared with the MFE method.4. In order to satisfy the real time requirement for online process of HTR-PM load transition, simplified moving finite element (S-MFE) strategy is proposed based on the phenomenon obtained offline. S-MFE strategy correlates the power change level with finite element configuration. A regress model based on offline data is built to provide finite elements configuration for online application.