On solving optimal control problems with free initial condition using iterative dynamic programming

For solving optimal control problems where the initial conditions of some of the state variables are not specified, a procedure based on iterative dynamic programming (IDP) is presented. In this procedure, the free initial conditions are taken to be additional control variables for the first time stage only; then the search for the optimal initial conditions and also the optimal control policy is carried out simultaneously using IDP. The procedure is straightforward, and as illustrated with two nonlinear optimal control problems, for each case the optimum performance index is readily obtained.     

基于微粒群优化算法的不确定性调和调度

Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimization problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization （PSO） algorithm is developed for nonlinear optimization problems with both continuous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.     

A Mixed Coding Scheme of a Particle Swarm Optimization and a Hybrid Genetic Algorithm with Sequential Quadratic Programming for Mixed Integer Nonlinear Programming in Common Chemical Engineering Practice

In this paper, mixed integer nonlinear programming (MINLP) is optimized by PSO_GA–SQP, the mixed coding of a particle swarm optimization (PSO), and a hybrid genetic algorithm and sequential quadratic programming (GA–SQP). The population is separated into two groups: discrete and continuous variables. The discrete variables are optimized by the adapted PSO, while the continuous variables are optimized by the GA–SQP using the discrete variable information from the adapted PSO. Therefore, the population can be set to a smaller size than usual to obtain a global solution. The proposed PSO_GA–SQP algorithm is verified using various MINLP problems including the designing of retrofit heat exchanger networks. The fitness values of the tested problems are able to reach the global optimum.     

化工过程综合问题MINLP算法中整型变量的连续化

化工过程系统综合问题需要同时考虑设备结构参数和工艺操作参数,一般用整型变量表示设备的取舍,用连续变量表示操作参数,这就构成一个流程的超结构,在数学形式表现为一个混合整型非线性规划（MINLP）问题。混合整型非线性规划问题的求解成为化工过程综合优化的关键。今根据超结构中整型变量的特征,提出整型变量连续化处理的思路,将MINLP问题简化为NLP问题,然后采用罚函数法求解。最后将该算法运用于加氢脱烷基化（HDA）过程综合的实例研究,结果表明该算法克服了传统方法在处理整型变量时出现的麻烦,为有效快速地进行化工过程综合优化问题提供了一种新的途径。     

Continuous flow operation in emulsion polymerization of styrene

The kinetics of continuous emulsion polymerization of styrene were studied theoretically on the basis of the authors' batch reaction model, and a new reaction model was proposed for continuous operation. The validity of the model was tested by experiments conducted with stirred tank reactors in series. The characteristics of the first reactor used to generate polymer particles were studied in particular detail. It was found that there was an optimum residence time for the first reactor, the value of which was quantitatively predictable from the operating variables. The most suitable combinations of several types of reactors for continuous emulsion polymerization are also discussed.     

A hierarchical approach for the synthesis of batch water network

This work addresses the problem of synthesising cost-effective batch water networks where a number of process sources along with fresh water are mixed, stored, and assigned to process sinks. In order to address the complexity of the problem, a three-stage hierarchical approach is proposed. In the first stage, global targets are identified by formulating and solving a linear transportation problem for minimum water usage, maximum water recycle, and minimum wastewater discharge. These targets are determined a priori and without commitment to the network configuration. Next, a network with minimum number of tanks is synthesised by solving a mixed-integer non-linear program. The bilinear constraints are relaxed to transform the program into a mixed-integer linear program that is globally solvable. The third stage is aimed at simplifying the network configuration by minimising the number of network inter-connections. Insights gained from the water pinch analysis are also incorporated into the approach to further reduce the water flows via the placement of water regeneration unit. A case study is solved to illustrate the effectiveness of the proposed procedure.     

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through integrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.     

Water networks security: A two-stage mixed-integer stochastic program for sensor placement under uncertainty

This work describes a stochastic approach for the optimal placement of sensors in municipal water networks to detect maliciously injected contaminants. The model minimizes the expected fraction of the population at risk and the cost of the sensors. Our work explicitly includes uncertainties in the attack risk and population density, so that the resulting problem involves optimization under uncertainty. In our formulation, we include the location of a number of sensors as first stage decision variables of a two-stage mixed-integer stochastic linear problem; the second stage evaluates the population at risk for the scenario obtained in the first stage and that information is then used to modify the first stage decisions for the next iteration. Since the model is integer in the first stage, a generalized framework based on the stochastic decomposition algorithm allows us to solve the problem in a reasonable computational time. The paper describes the mixed-integer stochastic model and the algorithmic framework, and compares the deterministic and stochastic optimal solutions. The network used as our case study has been derived through the water network simulator EPANET 1.0; four acyclic water flow patterns are considered. Results show a significant effect of uncertainty in sensor placement and total cost.     

FAULT DETECTION AND DIAGNOSIS IN BATCH AND SEMI-BATCH PROCESSES USING ARTIFICIAL NEURAL NETWORKS

The objective of this work is to assess the feasibility of adopting artificial neural networks (ANNs) in fault detection and diagnosis for batch and semi-batch processes. Although there is a large volume of related publications available, most of them used steady-state data to train ANNs and, as such, the task of fault diagnosis can only be implemented in continuous operations. Based upon the concept of analytical redundancy, the framework of a two-stage fault monitoring system is proposed in this paper. In the first stage, a hybrid ANN is adopted to predict the long-term dynamic behaviors of the output variables under normal condition. The occurrence of fault(s) can be detected by inspecting the residuals, i.e. the differences between the measured and the predicted values of outputs. A second feedforward neural network is then used for the purpose of differentiating the residual patterns caused by various faults. In addition to the fact the results of pilot tests are quite satisfactory, it is also demonstrated in our experimental studies that the proposed fault-monitoring system is capable of detecting and diagnosing faults that cannot be described by traditional mathematical models.     

非线性蒸汽动力系统参数优化新方法——改进遗传算法

针对蒸汽动力系统参数优化的整数非线性规划问题（ＮＬＰ）提出一种改进的遗传算法。该算法对连续变量采用连续化遗传算子进行处理,使得算法与原问题的对应更加自然有效。针对常见的提前收敛或局部最小现象提出几种算子。实例表明本方法能对蒸汽动力系统参数准确、迅速地进行优化。     

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.     

One-step approach for heat exchanger network retrofitting using integrated differential evolution

Heat exchanger network (HEN) retrofitting is more important and challenging than HEN synthesis since it involves modifying existing network for improved energy efficiency. Additional factors to be considered include spatial constraints, relocation and re-piping costs, reassignment and effective use of existing heat exchanger areas. The previous studies using stochastic global optimization algorithms are mainly focused on two-level approach: the first level uses a stochastic algorithm for optimizing structure, and the second level uses either a stochastic or a deterministic algorithm for optimizing continuous variables. In this study, we propose and test one-step approach where a stochastic global optimization method, namely, integrated differential evolution (IDE), handles both discrete and continuous variables together. Thus, HEN structure and retrofitting model parameters are simultaneously optimized by IDE, which avoids the algorithm trapping at a local optimum and also improves the computational efficiency. Results on HEN applications show that the proposed approach gives better solutions.     

Global optimization of bilinear process networks with multicomponent flows

This paper deals with the global optimization of networks consisting of splitters, mixers and linear process units and that involve multicomponent streams. Examples include pooling and blending systems and sharp separation networks in which nonconvexities arise in the bilinear equations for the mass balances. A reformulation-linearization technique is first applied to models expressed with compositions and total flows in order to obtain a relaxed LP formulation that provides a valid lower bound to the global optimum. This formulation is used within a spatial branch and bound search. The application of this method is considered in detail for sharp separation systems with single feed and mixed products. Numerical results are presented on 12 test problems involving up to a few hundred variables. It is shown that only a few nodes are commonly required in the branch and bound search.     

Interactions between an electrochemical reactor and associated unit processes

It is shown that in the presence of interactive variables, the optimum operating conditions for a reactor cannot be determined in isolation from its associated unit operations. The argument is illustrated by a process model developed for a continuous electrochemical reactor linked to a distillation unit which recycles unconverted feedstock. The model reveals that if conditions in the distillation unit are ignored a false optimum well removed from the true optimum would be identified.     

一种改进的差分进化算法及其在补料分批式生化反应器动态优化中的应用

动态优化是生物化工过程中的重要课题,求解动态优化问题通常有两种方法:解析法和数值法。基于智能进化算法的数值方法在动态优化中的应用越来越广泛,但是这些方法局部寻优能力不强,容易陷入局部最优,并且求解速度相对较慢。针对这些方法的不足,提出了一种改进的差分进化算法,设计了新的局部寻优算子来增强算法的局部寻优能力,并且采用一种新的控制策略表示方法来求解动态优化问题。通过求解补料分批式生化反应器的动态优化实例,证明了算法的有效性和鲁棒性。通过与其他几种方法进行对比,实验结果表明,所提出的方法在优化结果和计算代价方面都有优势。     

聚丙烯纤维增强水泥砂浆力学性能试验研究

为研究聚丙烯纤维掺入量对不同养护龄期的水泥砂浆试件变形破坏规律的影响,对水泥砂浆试件进行单轴压缩实验,同时利用数字散斑相关方法(DSCM)、扫描电子显微镜(SEM)对试件侧向变形场、断口形貌进行细观观测.结果表明:试件养护龄期相同时,抗压强度随聚丙烯纤维掺量增加呈先增加后减小趋势,在设置的变量梯度范围内,纤维最优掺量为0.5%;掺入聚丙烯纤维的试件峰后表现出明显的塑性特征,峰后广义刚度系数变化量较大;试件侧向变形场演化过程分为四个阶段:均匀阶段、成核阶段、变形局部化阶段、破坏阶段;聚丙烯纤维与水泥砂浆的粘结强度弱于砂粒与水泥的粘结强度,含聚丙烯纤维的试件在破坏形态上表现出"裂而不断"的特点.提出了含聚丙烯纤维水泥砂浆的微观胶结接触模型,模型的力学关系较好的解释了聚丙烯纤维试件峰后塑性提高的特征.     

离散粒子群算法的波纹管优化设计研究

为了解决波纹管所涉及的非线性约束离散变量的优化设计问题,文中尝试将粒子群算法与惩罚函数法相结合,建立新型离散粒子群算法,实现离散变量与连续变量之间的转化。提出了一种新的离散惩罚因子更新策略,以保证离散解的精度及算法的收敛性。通过著名的容器设计算例验证,文中方法优于文献方法。用该方法对波纹管工程实例进行优化设计,优化目标值比在用产品提高了79.96%,且与理论值接近,离散解的精度满足要求,进一步证明了该方法在求解波纹管工程非线性约束离散变量优化设计问题时的有效性。     

Synthesis of Rice Processing Plants. III. Sensitivity Analysis

An optimal process flowsheet for a rice processing plant has been developed. The optimization problem was formulated as a Mixed-Integer Nonlinear Programme, MINLP, consisting of a vector of binary and continuous variables. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determined as the solution of the MINLP problem. Six objective functions were investigated as performance criteria. A sensitivity analysis of each model parameter was conducted to determine its influence on the optimal flowsheet. The MINLP approach is an efficient tool for optimization and the simplified models were adequate for use at the synthesis stage. The solution is insensitive to uncertainty in the models. However, due to the nonconvex nature of MINLPs, the solution was found to depend on the initial starting values, especially for the maximum profit flowsheet.     

Synthesis of Rice Processing Plants. III. Sensitivity Analysis

Abstract

An optimal process flowsheet for a rice processing plant has been developed. The optimization problem was formulated as a Mixed-Integer Nonlinear Programme, MINLP, consisting of a vector of binary and continuous variables. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determined as the solution of the MINLP problem. Six objective functions were investigated as performance criteria. A sensitivity analysis of each model parameter was conducted to determine its influence on the optimal flowsheet. The MINLP approach is an efficient tool for optimization and the simplified models were adequate for use at the synthesis stage. The solution is insensitive to uncertainty in the models. However, due to the nonconvex nature of MINLPs, the solution was found to depend on the initial starting values, especially for the maximum profit flowsheet.     

改进的全息搜索策略及其在化工优化中的应用

引言 基于样本数据估计反应动力学参数是常见的化工优化问题.参数估计的通用规则是偏差最小化,许多经典的序贯类寻优方法都可用于这一目的,例如Powell共轭梯度法、模式搜索法、变度量法等.