Flexibility analysis for continuous ibuprofen manufacturing processes

Continuous ibuprofen (a widespread used analgesic drug) manufacturing is full of superiorities and is a fertile field both in industry and academia since it can not only effectively treat rheumatic and other chronic and painful diseases, but also shows great potential in dental diseases. As one of central elements of operability analysis, flexibility analysis is in charge of the quantitative assessment of the capability to guarantee the feasible operation in face of variations on uncertain parameters. In this paper, we focus on the flexibility index calculation for the continuous ibuprofen manufacturing process. We update existing state-of-the-art formulations, which traditionally lead to the max-max-max optimization problem, to approach the calculation of the flexibility index with a favorable manner. Advantages regarding the size of the mathematical model and the computational CPU time of the modified method are examined by four cases. In addition to identifying the flexibility index without any consideration of control variables, we also investigate the effects of different combinations of control variables on the flexibility property to reveal the benefits from taking recourse actions into account. Results from systematic investigations are expected to provide a solid basis for the further control system design and optimal operation of continuous ibuprofen manufacturing.     

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.     

An approach to multicriteria optimization under uncertainty

Inherent in chemical process models are parameters that have uncertainty associated with them. This paper addresses multicriteria optimization that accounts for model and process uncertainty at the design stage. Specifically the authors have developed extensions of the average criterion method, the worst-case strategy and the ε-constraint method under the following conditions: (a) at the design stage the only information available about the uncertain parameters is that they are bounded by a known uncertainty region T, and (b) at the operation stage, process data is rich enough to allow the determination of exact values of all the uncertain parameters. The suggested formulation assumes that at the operation stage, certain process variables (called control variables) can be tuned or manipulated in order to offset the effects of uncertainty. Three illustrative examples (two benchmark and one direct methanol fuel cell) have been employed.     

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。     

A UNIQUE APPROACH FOR SOLVING SUB-PROBLEMS IN FLEXIBILITY ANALYSIS

In the design of a chemical process (CP), certain design specifications (for example those related to process economics, process performance, safety, and the environment) must be satisfied. During the operation of the plant, since design models have uncertainties associated with them, we need to ensure the flexibility of the CP. This means that within the region of uncertainty, all design specifications must be satisfied. In recent years, research has focused on the development of methods for flexibility analysis of the CP. There are three main sub-problems associated with flexibility analysis, namely evaluation of CP flexibility, evaluation of CP structural flexibility anddetermination of the optimal regime over which the flexibility of the CP is guaranteed. We have developed a general approach to solving the sub-problems based on the split and bound strategy.     

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     

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.     

操作时间不确定的间歇过程最优化设计(Ⅰ)不限制等待时间过程

对操作时间不确定的不限制等待时间的间歇过程的优化设计问题 ,提出一种在操作时间不确定条件下确定过程的限定循环时间的方法。该方法使模型的限定循环时间变为相互独立的 ,从而可将原过程转化为更新过程 ,并根据更新过程原理建立了优化该过程的期望值模型。算例表明考虑操作时间不确定性的优化结果要好于不考虑操作时间不确定性的优化结果。通过Monte-Carlo模拟表明采用新模型优化的结果在实际生产时是可行的     

On the relation between flexibility analysis and robust optimization for linear systems

Flexibility analysis and robust optimization are two approaches to solving optimization problems under uncertainty that share some fundamental concepts, such as the use of polyhedral uncertainty sets and the worst‐case approach to guarantee feasibility. The connection between these two approaches has not been sufficiently acknowledged and examined in the literature. In this context, the contributions of this work are fourfold: (1) a comparison between flexibility analysis and robust optimization from a historical perspective is presented; (2) for linear systems, new formulations for the three classical flexibility analysis problems—flexibility test, flexibility index, and design under uncertainty—based on duality theory and the affinely adjustable robust optimization (AARO) approach are proposed; (3) the AARO approach is shown to be generally more restrictive such that it may lead to overly conservative solutions; (4) numerical examples show the improved computational performance from the proposed formulations compared to the traditional flexibility analysis models. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3109–3123, 2016     

One-stage optimization problem with chance constraints

Generally, the design of chemical processes (CP) is performed with the use of inaccurate mathematical models. Therefore, it is essential to create chemical processes that can satisfy all the design specifications at the operation stage in spite of the changes in internal and external factors. Consequently, the problem of chemical process optimization under uncertainty is of prime importance in chemical engineering. The paper considers one-stage optimization problems with chance constraints. The main issue in solving one-stage optimization problems is calculation of multiple integrals (calculating the expected value of the objective function and probabilities of constraints satisfaction). Here we consider a new approach to solving a one-stage optimization problem which is based on transformation of chance constraints into deterministic ones. A computational experiment has shown the efficiency of this approach.     

Robust Optimal Operation of Two‐Chamber Microbial Fuel Cell System Under Uncertainty: A Stochastic Simulation Based Multi‐Objective Genetic Algorithm Approach

This investigation is performed to study the optimal operation decision of two‐chamber microbial fuel cell (MFC) system under uncertainty. To gain insight into the mechanism of uncertainty propagation, a Quasi‐Monte Carlo method‐based stochastic analysis is conducted not only to elucidate the effect of each uncertain parameter on the variability of power density output, but also to illustrate the interactive effects of the all uncertain parameters on the performance of MFC. Moreover, a systematic stochastic simulation‐based multi‐objective genetic algorithm framework is proposed to identify a set of Pareto‐optimal robust operation strategies, which is helpful to provide an imperative insight into the relationship between the mean and standard deviation of output power density. The results indicate that (1) the coefficient of variance (COV) value of output power density has a linear relationship with the COV value of each uncertainty parameter as well as all interactive parameters; and (2) a significant performance improvement with respect to both mean and standard deviation of power density is observed by implementing the multi‐objective robust optimization. These results thus validate that the proposed uncertainty analysis and robust optimization framework provide a promising tool for robust optimal design and operation of fuel cell systems under uncertainty.     

Design of robust,reliable sensor networks using constraint programming

Various criteria have been considered in the literature for selection of optimal sensor networks. Amongst these, maximization of network reliability is an important criterion. While there are several approaches for designing maximum reliability networks, uncertainty in the available sensor reliability data has not been considered in these designs. In this article we present two novel formulations that incorporate robustness to uncertainties in the reliability data. Towards this end the sensor network design problem for maximizing reliability is formulated as explicit-optimization (MINLP) problem using failure rates of sensors which have better scaling properties instead of sensor reliabilities. Constraint programming (CP) has been used for solving the resulting optimization problems. Use of CP also enables easy generation of pareto front characterizing trade-offs between performance, cost and robustness for various uncertainty scenarios. The utility of the proposed approach is demonstrated on a case study taken from the literature.     

A Modified Model for Flexibility Analysis in Chemical Engineering Processes

This paper discussed an extended model for flexibility analysis of chemical process. Under uncertainty, probability density function is used to describe uncertain parameters instead of hyper-rectangle, and chance-constrained programming is a feasible way to deal with the violation of constraints. Because the feasible region of control variables would change along with uncertain parameters, its smallest acceptable size threshold is presented to ensure the controllability condition. By synthesizing the considerations mentioned above, a modified model can describe the flexibility analysis problem more exactly. Then a hybrid algorithm, which integrates: stochastic simulation and genetic algorithm, is applied to solve this model and maximize the flexibility region. Both numerical and chemical process examples are presented to demonstrate the effectiveness of the method.     

化工过程中柔性分析的改进模型

This paper discussed an extended model for flexibility analysis of chemical process. Under uncertainty, probability density function is used to describe uncertain parameters instead of hyper-rectangle, and chanceconstrained programming is a feasible way to deal with the violation of constraints. Because the feasible region of control variables would change along with uncertain parameters, its smallest acceptable size threshold is presented to ensure the controllability condition. By synthesizing the considerations mentioned above, a modified model can describe the flexibility analysis problem more exactly. Then a hybrid algorithm, which integrates stochastic simulation and genetic algorithm, is applied to solve this model and maximize the flexibility region. Both numerical and chemical process examples are presented to demonstrate the effectiveness of the method.     

基于高斯模型的聚乙烯过程设计与控制集成优化

聚乙烯反应过程中物流-能流剧烈交叠、反应-传递相互耦合,使得过程具有强非线性以及多重稳态。传统的顺序设计方法不能保证系统有足够的控制自由度,当存在扰动和过程参数不确定性时,仅依靠设计控制器很难提高产品质量。提出一种聚乙烯工艺稳态设计与运行控制的集成优化方案,创造性地引入Kriging高斯模型同时预测模型动态和模型不确定性。另一个重要的贡献是在聚乙烯工艺设计阶段,设计性能指标,定量描述过程稳态设计对闭环动态的影响。所提出的方法已经通过对气相聚乙烯工艺设计和运行控制的集成优化进行了验证,并在参数不确定性和扰动存在情况下仿真证实了集成优化设计方案的高效性。     

Proactive approach to address the uncertainty in short-term scheduling

The identification of reliable schedules serves a valuable function as a basis for coordinating outside activities within the highly dynamic and uncertain supply chain (SC) environment. A contribution is made in the area of proactive scheduling with the development of a stochastic modeling framework to support the short-term scheduling problem with uncertain operation times and equipment breakdowns. A set of scenarios for the uncertain parameters is anticipated in the decision stage, along with information concerning the reactive scheduling approach to be taken during schedule execution. A robust predictive schedule is pursued, with the flexibility to absorb disruptive events without major changes when rescheduling is required. Either rigorous or heuristic techniques can be used to optimize a robustness measure that explicitly accounts for the eventual wait times and idle times that may arise during execution. The application of the framework to different case studies shows the flexibility of the predictive schedule, the different decisions that can be drawn based on the rescheduling strategy considered, and the importance of exploiting the information of the uncertainty as well as the incorporation of the rescheduling policy proactively.     

Flexibility assessment and risk management in supply chains

Increased uncertainty in recent years has led the supply chains to incorporate measures to be more flexible in order to perform well in the face of the uncertain events. It has been shown that these measures improve the performance of supply chains by mitigating the risks associated with uncertainties. However, it is also important to assess the uncertainty under which a supply chain network can perform well and manage risk. Flexibility is defined in terms of the bounds of uncertain parameters within which supply chain operation is feasible. A hybrid simulation‐based optimization framework that uses two‐stage stochastic programming in a rolling horizon framework is proposed. The framework enables taking optimum planning decisions considering demand uncertainty while managing risk. The framework is used to study the trade‐offs between flexibility, economic performance, and risk associated with supply chain operation. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4166–4178, 2015     

Multiobjective batch process design aiming at robust performances

The most common batch design approach in practice and literature is a deterministic one. However, given the uncertainties prevailing in early stages of process design, a deterministically calculated productivity is not sufficient to select one of the large number of optional designs. Therefore, we propose a Tabu Search multiobjective optimization framework, which allows to approximate the Pareto-optimal set of designs while considering uncertain variables in the initial recipe. As a novel technique, we include performance robustness as a separate objective function within the multiobjective optimization alongside with productivity of a design, thus obtaining not only designs with high productivity or solely robust designs, but both high productivity and robust designs in one set of solutions. We examined several robustness criteria as a possible quantification of performance deviations under uncertain recipe variables. The implementation of a Tabu Search framework in combination with Monte-Carlo simulation and Latin Hypercube sampling provides a huge flexibility in the problem specification, in particular in the definition of parameter uncertainties. As a result we successfully demonstrate that metaheuristic optimization techniques are capable to approximate the Pareto-optimal set under uncertainty and are able to capture potentially antagonistic solution qualities such as high productivity and robustness by multiobjective optimization. With the help of this approach, parameters can be identified that have to be put into the focus of process research and development efforts in order to obtain high performance batch process designs.     

Synthesis of flexible heat exchanger networks with uncertain flowrates and temperatures

A systematic procedure is presented for the synthesis of flexible heat exchanger networks that involve specified uncertainties in the flowrates and inlet temperatures of the process streams. The problem is decomposed into two stages: (i) prediction of matches (ii) derivation of the network configuration. At each stage, synthesis techniques are combined with a flexibility analysis to test the feasibility of operation of the design over the specified range of the uncertain parameters. It is shown that special properties can be exploited to efficiently perform the flexibility analysis. Two examples are given to illustrate the application of the proposed strategy.