含滞后及不确定参数动态过程系统的定量优化方法与应用

许多动态化工系统含有不确定参数。当含不确定参数的过程系统又带有滞后环节时,系统的优化问题就变得非常复杂。对含不确定参数的化工系统的动态过程进行优化,若未考虑滞后环节对动态优化结果的影响,不能保证系统实际操作的优化及安全运行。本文采用改进的有限元正交配置优化算法,较好地解决了含有滞后、不确定参数的化工过程的动态优化问题。最后将一个具有循环返料的反应-分离器系统以及一个绝热反应釜作为案例对该优化方法的应用进行分析,根据案例的研究验证了该优化方法的有效性,从而为含有滞后、不确定参数的动态系统的设计和操作性能优化提供一种有效的定量分析方法和理论依据。     

Initialization strategies for optimization of dynamic systems

For dynamic optimization applications, real-time solution reliability is improved if there is an initialized prior solution that is sufficiently close to the intended solution. This paper details several initialization strategies that are useful for obtaining an initial solution. Methods include warm start from a prior solution, linearization, structural decomposition, and an incremental unbounding of decision variables that leads up to solving the originally intended problem. Even when initialization is not required to solve a dynamic optimization problem, a staged initialization approach sometimes leads to an overall faster solution time when compared to a single optimization attempt. Several challenging optimization problems are detailed that include a high-index differential and algebraic equation pendulum model, a standard reactor model used in many benchmark tests, a tethered aerial vehicle, and smart grid energy storage. These applications are representative of a larger class of applications resulting from the simultaneous approach to optimization of dynamic systems.     

An automatic initialization procedure in parameter estimation problems with parameter-affine dynamic models

This paper proposes an initialization approach for parameter estimation problems (PEPs) involving parameter-affine dynamic models. By using the state measurements, the nonconvex PEP is modified such that a convex approximation to the original PEP is obtained. The modified problem is solved by convex optimization methods yielding an approximate solution to the original PEP. The approximate solution can be further refined by linearizing the original problem around the obtained minimum. An assessment of the distance between the real solution and the one provided by the linearization of the problem around the convex approximation is presented. The optimum obtained by the convex approximation is used to subsequently initialize a simultaneous Gauss–Newton (SGN) approach on the original nonconvex PEP. Comparative results for the SGN with arbitrary initialization and with the proposed approach are presented using three benchmark examples in the chemical and biological fields.     

Joint optimization of number of wells,well locations and controls using a gradient-based algorithm

This paper presents a detailed algorithm for solving the general well-placement optimization problem in which the number of wells, their locations and rates are simultaneously optimized with an efficient gradient-based algorithm. The proposed well-placement optimization algorithm begins by placing a large number of wells in the reservoir, where, the well rates are the optimization variables. During iterations of the algorithm, most of the wells are eliminated by setting their rates to zero. The remaining wells and their controls determine the optimal number of wells, their optimum locations and rates. The well-placement algorithm consists of two optimization stages. In the initialization stage, the appropriate total reservoir production rate (or the total injection rate) for the set of to-be-optimized producers (or injectors) is estimated by maximizing the net-present-value for the specified operational life of the reservoir. In the second stage, a modified net-present-value functional which also considers the drilling cost of the wells is maximized subject to the a total rate constraint determined in the initialization stage. Both stages of the algorithm use gradient projection to enforce the linear and bound constraints, where the required gradients are computed with the adjoint method. The bottomhole pressure constraints on the wells are enforced using a practical approach. The applicability and robustness of our well-placement algorithm is discussed through several example problems.     

A perturbation approach for consistent initialization of index-1 explicit differential-algebraic equations arising from battery model simulations

Estimation of consistent initial conditions is very crucial for the successful solution of differential-algebraic equation (DAE) systems that arise in many fields of science and engineering. In this paper, an efficient perturbation approach for initialization of DAE systems of index-1 is proposed and implemented for DAE models governing batteries. In addition, different existing solvers are compared for consistent initialization of DAE systems. The proposed approach does not necessarily require a nonlinear solver for initialization and builds on the applicability and usability of robust and efficient explicit, linearly implicit and semi-implicit integrators in time. Three different problems are presented wherein the proposed approach is observed to work for a wider range of inconsistent initial conditions compared to other existing generally used routines. It is also observed that the present approach is computationally efficient compared to the other existing approaches in a given environment.     

Design of Chemical Engineering Systems with Chance Constraints

In the design of chemical process under uncertainty in initial information, an important problem is to determine a structure in which the control system will guarantee that all constraints are satisfied despite variations in internal and external factors at the operation stage. A method has been proposed for solving onestage optimization problems with chance constraints in the design of optimal flexible chemical processes. The developed approach makes it possible to avoid multidimensional integration in each of the iterations of problem solving, thus reducing the computational effort. The efficiency of the proposed approach is illustrated by model examples.     

一种求解化工动态优化问题的迭代自适应粒子群方法

智能优化方法因其简单、易实现且具有良好的全局搜索能力,在动态优化中的应用越来越广泛,但传统的智能方法收敛速度相对较慢。提出了一种迭代自适应粒子群优化方法（IAPSO）来求解一般的化工动态优化问题。首先通过控制变量参数化将原动态优化问题转化为非线性规划问题,再利用所提出的迭代自适应粒子群优化方法进行求解。相比传统的粒子群优化方法,该种迭代自适应粒子群优化方法具有收敛速度更快的优点,主要原因是：该算法根据粒子种群分布特性自适应调整参数;该算法通过缩减搜索空间并迭代使用粒子群算法搜索最优解。将提出的迭代自适应粒子群方法应用到多个经典动态优化问题中,测试结果表明,该方法简单、有效,精度高,且收敛速度比传统粒子群算法有显著提升。     

Continuous global optimization of structured process systems models

Nonconvex models for the optimization of process systems in chemical engineering give rise to multiple suboptimal solutions, and a number of complications that often cause failure of standard local optimization techniques. A deterministic branch and bound algorithm is presented in this paper for the global optimization of structured process systems models that include non-convexities introduced by concave univariate, bilinear and linear fractional terms. The proposed branch and contract algorithm relies on a bounds contraction operation, which consists of the solution of a finite sequence of convex bounds-contraction subproblems for the subset of nonconvex variables in a problem. The application of the proposed algorithm is illustrated with several numerical examples, which include heat exchanger networks, chemical reactors, simplified process flowsheets, and waste-water treatment systems. The results show that by executing the contraction operation at selected branch and bound nodes, large portions of the search region over which the objective function takes only values above a known upper bound are eliminated. It is shown that with the proposed approach the total number of nodes in the solution tree is kept relatively small, and for some problems, no branching is required at all.     

化工过程系统优化的分布式并行计算

针对大规模化工过程系统优化计算能力不够的情况 ,讨论用机群系统建构成并行优化计算环境 .在分析并行计算的原理和现状后 ,对优化算法的并行化进行探讨 ,并且深入讨论了大规模优化算法SQP的并行化和如何提高机群系统效率的问题 .通过精馏塔优化算例 ,证明利用机群系统开展并行优化是行之有效的     

厂际氢气网络多周期集成的分步优化方法

厂际氢气系统集成对于化工园区合理配置氢气系统和氢气资源具有重要意义。针对化工园区中多厂氢气网络多周期优化设计的问题,提出了一种三步求解策略优化设计多厂氢气网络的多周期优化设计。该方法首先采用厂际氢气网络的单周期优化模型获取各子周期下的氢气公用工程的传输量,然后采用单厂氢气网络的多周期优化设计模型获得各厂内的氢气系统结构,最后采用厂际氢气系统的多周期优化设计模型确定化工园区中厂际氢气系统的网络结构和氢气调度方案。研究表明,所提出的多厂氢气网络多周期优化设计方法可有效解决厂际氢气网络的优化设计问题,该策略在不增加氢气系统结构复杂度的前提下,可以获得较好的经济性,并可提高优化模型求解的计算效率。     

Improvement of state profile accuracy in nonlinear dynamic optimization with the quasi‐sequential approach

Quasi‐sequential methods are efficient and flexible strategies for the solution of dynamic optimization problems. At the heart of these strategies lies the time discretization and approximation of dynamic systems for nonlinear optimization problems. To address this question, we employ a time derivative analysis within the quasi‐sequential approach and derive a finite element placement strategy. In addition, methods for direct error prediction are applied to this approach and extended with a proposed time derivative analysis. According to the information for current time derivatives, subintervals are introduced that improve accuracy of state profiles. Since this is only done in the simulation layer, the nonlinear programing solver need not be restarted. An efficient gradient computation is also derived for these subintervals; the resulting enhanced accuracy accelerates convergence performance and increases the robustness of the solution to initialization. A beer fermentation process case study is presented to demonstrate the effectiveness of the proposed approach. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Computation of phase and chemical equilibria

A new method is proposed for the computation of simultaneous phase and chemical equilibria by minimization of the Gibbs energy. A non-linear programming approach is used which enables one to determine the number and identity of phases at equilibrium, as well as the compositions of each component in each phase. Any thermodynamic model which predicts fugacities can be incorporated easily in this method. Numerical results of various systems that involve gases, liquids and solids are presented.     

Identification of critical points for the design and synthesis of flexible processes

Optimization problems for the design and synthesis of flexible chemical processes are often associated with highly discretized models. The ultimate goal of this work is to significantly reduce the set of uncertain parameter points used in these problems. To accomplish the task, an approach was developed for identifying the minimum set of critical points needed for flexible design. Critical points in this work represent those values of uncertain parameters that determine optimal overdesign of process, so that feasible operation is assured within the specified domain of uncertain parameters. The proposed approach identifies critical values of uncertain parameters a-priori by the separate maximization of each design variable, together with simultaneous optimization of the economic objective function. During this procedure, uncertain parameters are transformed into continuous variables. Three alternative methods are proposed within this approach: the formulation based on Karush–Kuhn–Tucker (KKT) optimality conditions, the iterative two-level method, and the approximate one-level method. The identified critical points are then used for the discretization of infinite uncertain problems, in order to obtain the design with the optimum objective function and flexibility index at unity. All three methods can identify vertex or even nonvertex critical points, whose total number is less than or equal to the number of design variables, which represents a significant reduction in the problem's dimensionality. Some examples are presented illustrating the applicability and efficiency of the proposed approach, as well as the role of the critical points in the optimization of design problems under uncertainty.     

基于群体智能算法的换热网络同步最优综合

换热网络同步综合方法一般需要建立复杂的混合整数非线性数学规划模型,该模型具有非凸、非线、不连续的特点,属于最难求解的一类NP-hard问题,应用传统的优化算法很难确定其全局最优解,尤其是对大规模换热网络综合问题,甚至无法在合理时间内接近全局最优的局部最优解。针对换热网络同步综合问题,提出基于群体智能算法的分层优化策略,外层采用离散粒子群算法与遗传算法相结合的混合群体智能算法优化换热网络结构,内层在结构变量给定条件下利用改进粒子群算法优化冷热物流分流比与换热负荷。两个典型算例研究证明了该方法能以较高的效率和稳定性得到较好的优化结果。     

Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.     

Simultaneous synthesis of distillation sequences in overall process schemes using an improved minlp approach

This paper describes the synthesis of distillation sequences simultaneously with the synthesis of other process subsystems. An improved MINLP approach is proposed for the synthesis of complex problems. The improvements were made on three major MINLP levels. By postulating the superstructures we propose to use smaller and more compact superstructures of the distillation sequences included in the flowsheet superstructure rather than the usual tree and network representations. In the modelling step a higher degree of simultaneity has been accomplished by the use of simultaneous models of the distillation column and aggregated models of other process units. To facilitate the optimization phase the modified OA/ER algorithm [Kravanja and Grossmann, Ind. Engng. Chem. Res.26, 1869–1880 (1994)], implemented in the computerized synthesizer PROSYN-MINLP, has been used to reduce the effect of nonconvexities. Also, a special initialization and linearization scheme for simultaneous synthesis of HEN has been proposed. The improved method is illustrated by the synthesis of the separation subsystem followed by the simultaneous synthesis of the heat integrated separation system and its heat exchanger network (HEN). Finally, the optimization of the overall process and the simultaneous synthesis of its distillation system and heat integrated HEN is presented.     

New approaches to the integrated synthesis of flexible automated chemical engineering systems

The problems of optimizing the design and operational (control) variables during the integrated design of flexible automated complexes of chemical engineering process (CEP)—automated control systems (ACS) under conditions of the uncertainty of physicochemical, engineering, and economic initial data have been formalized. The selection of the best available version of a flexible automated complex is performed by means of the pairwise comparison of alternative versions of automated complexes using criteria that take into account both the quality of the manufactured products and the characteristics of energy and resource saving, on one hand, and the quality of transient processes in the ACS, on the other hand. A two-stage problem of stoichastic optimization of flexible automated complexes with hard and soft constraints has been stated, and a new approach to its solution has been proposed. An example of the integrated design of a flexible continuous process of azo pigments synthesis and a system of the optimum stabilization of its conditions in the presence of an interval uncertainty of the kinetic coefficients of the chemical reaction and individual engineering variables has been shown.     

Association effects in ternary vapour—liquid equilibria

A thermodynamic model is proposed for the analysis of multicomponent systems capable of homo and heteroassociation between all the chemical species present. Detailed equations have been developed for ternary systems. The method has been applied to the experimental vapour—liquid data obtained for the system formic acid—acetic acid—propionic acid at 760 mm Hg. The calculated activity coefficients were thermodynamically consistent and were correlated using the Redlich—Kister equation. Boiling points, compositions and activity coefficients can be predicted from the vapour—liquid equilibrium data of the three binary systems.     

ESTIMATION AND LOCALIZATION OF MAXIMUM TEMPERATURE IN A TUBULAR CHEMICAL REACTOR BY LUENBERGER STATE OBSERVER

This study deals with an observer built for distributed parameter systems described by nonlinear representations. This observer was applied to a tubular chemical reactor in order to estimate the maximum temperature of the reactant mixture and its position in stationary and transient regimes. This estimation uses a Luenberger observer, while MacCormack's numerical method was used for resolution of the partial differential equations. Furthermore, to take into account the nonlinearity of the system, the gain of this estimator was proposed as a function of the position along the chemical reactor. This observer requires the values of both concentration and temperature at the inlet but only of temperature at the outlet. The convergence and robustness of this estimator were experimentally tested with initialization and modeling errors.     

多目标多级串联系统优化的模糊优选动态规划技术

将模糊优选理论与动态规划技术有机地结合起来,提出多目标多级串联系统优化的模糊优选动态规划技术。为解决化工系统中的多目标多阶段优化问题提供一条新路。最后例举一多级反应器系统最优控制应用算例。