Optimal design of large‐scale chemical processes under uncertainty: A ranking‐based approach

An approach for the optimal design of chemical processes in the presence of uncertainty was presented. The key idea in this work is to approximate the process constraint functions and model outputs using Power Series Expansions (PSE)‐based functions. The PSE functions are used to efficiently identify the variability in the process constraint functions and model outputs due to multiple realizations in the uncertain parameters using Monte Carlo (MC) sampling methods. A ranking‐based approach is adopted here where the user can assign priorities or probabilities of satisfaction for the different process constraints and model outputs considered in the analysis. The methodology was tested on a reactor–heat exchanger system and the Tennessee Eastman process. The results show that the present method is computationally attractive since the optimal process design is accomplished in shorter computational times when compared to the use of the MC method applied to the full plant model. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3243–3257, 2014     

基于多变量预测控制技术的丙烯精馏塔控制系统

精馏是化工中的重要过程,具有强耦合性、不确定性、非线性和大滞后等特征,且存在着苛刻的约束条件,控制难度大,长期以来都是各种先进控制与优化方案的实验对象。预测控制、内模控制、推断控制、模糊控制、神经元控制等多种控制策略都曾应用于精馏过程。选取了丙烯精馏塔作为研究对象,利用APC-Hiecon软件对其进行了基于多变量预测控制的研究。通过先进控制实施效果对比表明,方案实施后,过程变量运行平稳,有效保障了产品质量及精馏过程的稳定,达到了预期控制要求。     

A real‐time process optimization system for injection molding

The proposed real‐time intelligent model for the injection molding process control consists of the initial parameters setting and online defects correction. First, preliminary optimization based on a simplified simulation model is used for the initial setting. This simplified model adopts a geometric approximation of the original part by a rectangular edge‐gated plate. Then, the molding trial will be run on the molding machine by using the initial process parameters. And a fuzzy inference model based on expert knowledge is developed for correcting defects during the molding trial. This defects correction procedure will be repeated until the part quality is found satisfactory. A corresponding intelligent system has been developed that is integrated with the injection machine by communicating with the controller. The system can be used to optimize process parameters real time. Experimental studies have been carried out for verification. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers.     

Probability bounds analysis for nonlinear dynamic process models

Dynamic process models frequently involve uncertain parameters and inputs. Propagating these uncertainties rigorously through a mathematical model to determine their effect on system states and outputs is a challenging problem. In this work, we describe a new approach, based on the use of Taylor model methods, for the rigorous propagation of uncertainties through nonlinear systems of ordinary differential equations (ODEs). We concentrate on uncertainties whose distribution is not known precisely, but can be bounded by a probability box (p‐box), and show how to use p‐boxes in the context of Taylor models. This allows us to obtain p‐box representations of the uncertainties in the state variable outputs of a nonlinear ODE model. Examples having two to three uncertain parameters or initial states and focused on reaction process dynamics are used to demonstrate the potential of this approach. Using this method, rigorous probability bounds can be determined at a computational cost that is significantly less than that required by Monte Carlo analysis. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Optimization of circulating cooling water systems based on chance constrained programming

Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained under deterministic conditions may not be stable and economical. This paper studies the optimization of circulating cooling water systems under uncertain circumstance. To improve the reliability of the system and reduce the water and energy consumption, the influence of different uncertain parameters is taken into consideration. The chance constrained programming method is used to build a model under uncertain conditions, where the confidence level indicates the degree of constraint violation. Probability distribution functions are used to describe the form of uncertain parameters. The objective is to minimize the total cost and obtain the optimal cooling network configuration simultaneously. An algorithm based on Monte Carlo method is proposed, and GAMS software is used to solve the mixed integer nonlinear programming model. A case is optimized to verify the validity of the model. Compared with the deterministic optimization method, the results show that when considering the different types of uncertain parameters, a system with better economy and reliability can be obtained (total cost can be reduced at least 2%).     

Simultaneous model selection and parameter estimation for lithium‐ion batteries: A sequential MINLP solution approach

Equivalent circuit model (ECM) is a practical and commonly used tool not only in state of charge (SOC) estimation but also in state of health (SOH) monitoring for lithium‐ion batteries (LIBs). The functional forms of circuit parameters with respect to SOC in ECM are usually empirical determined, which cannot guarantee to obtain a compact and simple model. A systematical solution framework for simultaneous functional form selection and parameter estimation is proposed. A bi‐objective mixed‐integer nonlinear programming (MINLP) model is first constructed. Two solution approaches, namely the explicit and implicit methods, are then developed to balance model accuracy and model complexity. The former explicitly treats the model complexity as a constraint and the latter implicitly embeds the model complexity into the objective as a penalty. Both approaches require sequential solution of the transformed MINLP model and an ideal and nadir ideal solutions‐based criterion is utilized to terminate the solution procedure for determining the optimal functional forms, in which ideal solution and nadir ideal solution represent the best and worst of each objective, respectively. Both explicit and implicit approaches are thoroughly evaluated and compared through experimental pulse current discharge test and hybrid pulse power characterization test of a commercial LIB. The fitting and prediction results illustrate that the proposed methods can effectively construct an optimal ECM with minimum complexity and prescribed precision requirement. It is thus indicated that the proposed MINLP‐based solution framework, which could automatically guide the optimal ECM construction procedure, can be greatly helpful to both SOC estimation and SOH monitoring for LIBs. © 2015 American Institute of Chemical Engineers AIChE J, 62: 78–89, 2016     

Half order plus time delay (HOPTD) models to tune PI controllers

Methods based on the first‐order plus time delay (FOPTD) model are very popular for tuning proportional‐integral (PI) controllers. The FOPTD model‐based methods are simple and their utility has been proved with many successful applications to a wide range of processes in practice. However, even for some overdamped processes where the FOPTD model seems to be applied successfully, these empirical FOPTD model‐based methods can fail to provide stable tuning results. To remove these drawbacks, a PI controller tuning method based on half‐order plus time delay (HOPTD) model is proposed. Because FOPTD model‐based methods can be applied to higher order processes, the proposed HOPTD model‐based method can be applied to higher order processes as well. It does not require any additional process information compared to the FOPTD model‐based method and hence can be used for overdamped processes in practice, complementing the traditional FOPTD model‐based methods. © 2016 American Institute of Chemical Engineers AIChE J, 63: 601–609, 2017     

Robust batch‐to‐batch optimization in the presence of model‐plant mismatch and input uncertainty

In model‐based optimization in the presence of model‐plant mismatch, the set of model parameter estimates which satisfy an identification objective may not result in an accurate prediction of the gradients of the cost‐function and constraints. To ensure convergence to the optimum, the predicted gradients can be forced to match the measured gradients by adapting the model parameters. Since updating all available parameters is impractical due to estimability problems and overfitting, there is a motivation for adapting a subset of parameters for updating the predicted outputs and gradients. This article presents an approach to select a subset of parameters based on the sensitivities of the model outputs and of the cost function and constraint gradients. Furthermore, robustness to uncertainties in initial batch conditions is introduced using a robust formulation based on polynomial chaos expansions. The improvements in convergence to the process optimum and robustness are illustrated using a fed‐batch bioprocess. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2660–2670, 2017     

A cognitive approach to develop dynamic models: Application to polymerization systems

An alternative procedure based on cognitive approach is applied to develop dynamic models. The solution copolymerization of methyl methacrylate and vinyl acetate in a continuous stirred tank reactor is analyzed to illustrate the cognitive model development. Factorial planning was used to discriminate the process variables with higher impact on the process performance (effects) and they are used to built‐up a dynamic model based on the functional fuzzy relationship of Takagi–Sugeno type. Gaussian membership functions are considered for the cognitive sets and subtractive clustering method supplied the parameters of the premises of the model. Consequence functions are obtained through an optimization problem solved by a least square based algorithm. The kinetic parameters and reactor operating conditions are obtained from the literature and a mathematical model is considered as plant for identification data generation. Dynamic cognitive models showed satisfactory predictive capabilities and may be an interesting alternative to attack problems of modeling in chemical processes. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Nonlinear robust optimization for process design

A novel robust optimization framework is proposed to address general nonlinear problems in process design. Local linearization is taken with respect to the uncertain parameters around multiple realizations of the uncertainty, and an iterative algorithm is implemented to solve the problem. Furthermore, the proposed methodology can handle different categories of problems according to the complexity of the problems. First, inequality‐only constrained optimization problem as studied in most existing robust optimization methods can be addressed. Second, the proposed framework can deal with problems with equality constraint associated with uncertain parameters. In the final case, we investigate problems with operation variables which can be adjusted according to the realizations of uncertainty. A local affinely adjustable decision rule is adopted for the operation variables (i.e., an affine function of the uncertain parameter). Different applications corresponding to different classes of problems are used to demonstrate the effectiveness of the proposed nonlinear robust optimization framework. © 2017 American Institute of Chemical Engineers AIChE J, 64: 481–494, 2018     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

Trade-off optimal design of a biocompatible solvent for an extractive fermentation process

In this study, crisp and flexible optimization approaches are, respectively, introduced to design an optimal biocompatible solvent for an extractive fermentation process. The optimal design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objective and the constraints. In general, the requirements for the objective and constraints are not rigid; consequently, the flexible or fuzzy optimization approach is applied to soften the rigid requirement for maximization of the extraction efficiency and to consider the mass flow rate and biocompatibility of solvent as the softened inequality constraints to the solvent design problem. Having elicited the membership function for the objective function and the constraint, the optimal solvent design problem can be formulated as a flexible goal attainment problem. Mixed-integer hybrid differential evolution is applied to solve the problem in order to find a satisfactory design.     

树脂基热防护材料烧蚀传热的关键参数影响性分析

针对树脂基热防护材料烧蚀传热的关键参数分析问题,采用碳化层-热解层-原始材料层一维模型,分析了热防护材料烧蚀热解响应过程的传热特性,得出了不确定参数影响传热过程的敏感性大小,结果表明：材料的热导率对树脂基热防护材料烧蚀传热特性影响最大,密度、比热容和材料厚度影响程度较大,其他参数的影响性可以忽略。同时建立了温度和不确定参数之间的量纲1准则关系式,为热防护材料的选取设计以及模型参数修正提供了参考依据。     

An aesthetic measurement method for matching colours in product design

Since it is important to know how to evaluate human emotions reflected in the image of a product during the process of product design precisely, a means of evaluating the aesthetic measurement of the image of a product with colour matching is proposed in this article. This method entails a solid visual angle of the subject, the distribution of colour‐area ratios, and colour images as experimental samples for colour matching. The evaluation was conducted based on a formula of the aesthetic measurement of the coloured area. To ensure that the entire practical colour co‐ordinate system was covered, 111 coloured chips were distributed throughout the implementation procedure. The aesthetic measure of colour harmony in this study was calculated based on aesthetic measure theory; moreover, each of the three given images received three symbolic colour combinations before using the fuzzy theory to determine the relationship between the image and the colour combinations of the products. Observers' evaluations of the fuzzy theory and the aesthetic measurement model were then compared, and the results showed that the proposed method succeeded in obtaining a high degree of satisfaction for the top 2 ranked samples in the aesthetic measurement model evaluation and human evaluation. Although only 2 product designs were used as examples for performing the evaluation procedure, the procedure can also be applied to other products.     

Modelling and control of a continuous distillation tower through fuzzy techniques

This paper presents a methodology for the design of a fuzzy controller applicable to continuous processes based on local fuzzy models and velocity linearizations. It has been applied to the implementation of a fuzzy controller for a continuous distillation tower. Continuous distillation towers can be subjected to variations in feed characteristics that cause loss of product quality or excessive energy consumption. Therefore, the use of a fuzzy controller is interesting to control process performance.A dynamic model for continuous distillation was implemented and used to obtain data to develop the fuzzy controller at different operating points. The fuzzy controller was built by integration of linear controllers obtained for each linearization of the system. Simulation of the model with controller was used to validate the controller effectiveness under different scenarios, including a study of the sensibility of some parameters to the control.The results showed that the fuzzy controller was able to keep the target output in the desired range for different inputs disturbances, changing smoothly from a predefined target output to another. The developed techniques are applicable to more complex distillation systems including more operating variables.     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Expected energy analysis for industrial process planning problem with fuzzy time parameters

Industrial process planning is to make an optimal decision in terms of resource allocation. The planning objective can be to minimize the time required to complete a task, maximize customer satisfaction by completing orders in a timely fashion and minimize the cost required to complete a task. Based on time and energy consumption in an industrial process planning problem, a novel energy analysis method is proposed to solve it. According to different constraints and credibility theory, typical expected value models of energy for it are presented. In addition, a hybrid intelligent optimization algorithm integrating fuzzy simulation, neural network and genetic algorithm is provided for solving the proposed expected value models. Some numerical examples are also given to illustrate the proposed concepts and the effectiveness of the used algorithm.     

Optimal design of chemical processes with chance constraints

Generally, chemical processes (CP) are designed with the use of inaccurate mathematical models. Therefore, it is important to create a chemical process that guarantees satisfaction of all design specifications either exactly or with some probability. The paper considers the issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed. We have developed a common approach for solving the broad class of optimization problems with normally distributed uncertain parameters. This class includes the one-stage and two-stage optimization problems with chance constraints. This approach is based on approximate transformation of chance constraints into deterministic ones.     

流程模拟中不精确模块的模糊建模

将模糊集合理论与常规建模方法相结合,提出了采用经验规则对不精确单元建模的方法,研究了模糊关系模型的输入输出信息的界面问题,将模糊关系模型运用于工厂过程模拟。结果表明,充分利用专家知识和操作经验,采用人工智能的方法可以处理那结机理比较复杂而难以用常规方法模拟分析的过程系统单元,扩展了过程系统模拟的功能和范围。     

模糊系统的模型化和优化

过程工业中的生产过程变量关系比较复杂，难于获得精确的模型，常使得过程系统的模拟和优化有较大误差。本文提出基于模糊逻辑表述和处理系统变量间的不精确近似关系，使模型方程间的冲突和不协调性趋于最小，模糊目标函数趋于最大。从而实现对模糊系统的模拟和优化。