【作者】 洪伟荣；

【导师】 王树青； Günter Wozny； Pu Li；

【作者基本信息】 浙江大学 ， 控制科学与工程， 2005， 博士

【摘要】 在流程工业领域,基于严格机理模型的开放式方程建模与优化已成为国际上公认的主流技术方向。许多系统工程公司和各大科研机构纷纷投入大量人力物力对系统的模型与优化进行深入细致的研究,企图取得突破性的进展。然而基于严格机理模型的离散化后的优化命题往往具有方程数多、变量维数高、非线性强的特点,这使得变量的存储、计算及命题的求解相当困难。常规的优化算法面对这样的大型问题已无能为力,无论在计算速度、收敛性、初值敏感性等方面都远不能满足现代工业的要求。因此,针对现代工业过程的大规模优化问题,开发出相应的优化算法已成为现代工业过程发展的一个重要研究工作。 大规模动态优化问题的常用算法是基于非线性规划(NLP)的序贯算法(Sequential approach)和联立算法(Simultaneous approach)。序贯算法具有寻优变量少,是可行路径法,可利用现有过程模拟软件等优点。但它不能处理状态变量的路径约束。另外,在寻优过程中不涉及过程模型信息,寻优效率不高。联立算法可以处理路径约束问题,仅仅在最优点处求解一次模型方程。它的缺点是寻优变量多,产生一个非常大的NLP问题,需要特殊的求解策略和数学处理才能保证算法较好的收敛性和收敛速度。本论文在总结序贯算法和联立算法的基础上,提出了一种结合两种算法优点的,基于SQP的动态过程优化算法—拟序贯算法(Quasi-Sequential approach),编写了算法程序QSOPT,并同目前应用最广泛的联合算法及软件IPOPT进行了比较,比较结果显示拟序贯算法非常适合求解强非线性的最优控制问题。由于它在求解NLP时不存在等式约束,对一些在NLP求解过程中等式约束(过程模型方程)值变化剧烈的优化问题求解时显示出较高的计算效率,因此在需要高效率优化算法的非线性模型预测控制和在线优化中具有很好的实际应用价值。论文主要内容包括: 1.提出了一种兼有序贯算法和联合算法优点的动态优化算法—拟序贯优化算法(quasi-sequential approach)。它一方面与联立算法一样,状态变量和控制变量用有限单元配置法同时被离散,这样状态变量的路径约束在配置点处都能够满足,避免了传统序贯算法不能求解状态变量路径约束问题的缺点;另一方面与序贯算法一样,通过模型方程的模拟消去了状态变量和等式约束,这样原问题就变为仅仅包含不等式约束和控制变量的更小规模的优化问题。不像联立算法为了使大规模的优化问题降维,需要复杂的数学推导,拟序贯算法简单易行,是一种易于在工程领域推广应用的动态优化算法。更多还原

【Abstract】 Modelling and optimization based on rigorous mathematical model equations have significantly become a major technology area in the process industries. Many system engineering companies and academic organization have put a lot of research efforts to study in depth on the process modelling and optimization, and hope to make great progress. However, the discretized optimization problems based on rigorous and mathematical model often own the characteristics that are many model equations, multi-variables and high nonlinearity. There exists great difficulty to solve such optimizations, and store such numbers of variables. Solution of this large-scale optimization problem with general optimization approach can be inefficient. Even though the solution could be found, the computation efficiency, convergence rate and initial-value sensitivity were unsuitable for demand of modern process industries. Therefore, it is a crucial research work to develop efficient approach for the large-scale optimization problems in modern process industries.Methods that apply NLP solvers to large-scale dynamic optimization normally can be separated into sequential approach and simultaneous approach. Sequential approaches have some advantages that are few degrees of freedom in NLP, feasible path method and employment of normal simulation solvers. But it cannot handle problems with path constraints efficiently. Simultaneous approach directly couple the solution of model equations with the optimization problem, the model equations are solved only once at the optimal point. Moreover, it has the advantage for problems with path constraints. Its disadvantage arises from the need to solve large nonlinear programming problems, specialized methods and mathematical analyses are required to solve them efficiently. In this dissertation, a novel sequential approach based on SQP, namely quasi-sequential approach, is presented for solving dynamic process optimization problems. It possesses advantages of both the simultaneous and the sequential approach. Furthermore, following the quasi-sequential approach, a program QSOPT is developed. QSOPT is compared with recently developed IPOPT (based on simultaneous approach). The comparative results show that the quasi-sequential approach is well suited for solving highly nonlinear optimal control problems. This is especially the case for highly nonlinear large-scale problems where the dynamic model equations may be violated by large values during the course of NLP solution.The main research works and contributions of this dissertation are as follows:1. A novel sequential approach based on SQP, namely quasi-sequential approach, is proposed for solving dynamic process optimization problems. It possesses advantages of both the simultaneous and the sequential approach. In the quasi-sequential approach, as in the simultaneous approach, both state and control variables are discretized using collocation on finite elements, so that path constraints can be guaranteed inside each element. On the other hand, the state variables are solved in a similar manner as in the sequential approach, this eliminates the discretized differential algebraic equations (DAEs) and state variables, so that the problem is reduced to a smaller problem only with inequality constraints and control variables. Quasi-sequential approach does not need complex mathematics derivation in order to reduce optimization problem to smaller one as simultaneous approach does. It is straightforward optimization approach and easy to be applied in engineering field.2. The different performance of optimization approaches is studied by comparing the solution path and step length of line search. The comparison results show that the quasi-sequential approach is well suitable to solve some process optimization problems, for example optimal control problem. The equality constraints are not included in SQP in the quasi-sequential approach and the merit function for line search only consists of the objective function, so that the strict descent requirement for merit function in line search is relieved. Compared with simultaneous approach, the quasi-sequential method takes larger step length and this leads to fewer SQP iterations. Numerical experiments show that quasi-sequential approach performs better than simultaneous approach while solving highly nonlinear large-scale problems where the dynamic model equations may be violated by large values during the course of solution by NLP. Moreover, quasi-sequential approach has advantage for general inequality constrained problems.3. A criterion, which is used to choose approach for a practical optimization problem, is given by analyzing the arithmetic operations of solution course and computational efficiency. By calculating the arithmetic operations of both quasi-sequential and simultaneous approach for a practical equality constrained optimization problem, the criterion can be used to decide which one is suitable for solving it. The example of CSTR optimal control problem is used todemonstrate its validity.4. The effect of process model structure on computation cost of optimization approach in solving optimization problem is exploited. The optimization approach can be more efficient by considering the sparsity of the DAE system. A program QSOPT based on quasi-sequential approach is developed, and used to calculate two typical chemical engineering examples: One is the CSTR optimal control; the other is optimization operation and parameter estimation of heat-integrated distillation system. From the computational results, it can be concluded that this quasi-sequential approach is able to solve large-scale dynamic optimization problems containing path constraints on state variables quickly.The dissertation is concluded with a summary and prospect of future researches.更多还原