A fuzzy multiobjective approach for minimization of injection molding defects

This paper describes a fuzzy multiobjective optimization approach for determining the set‐points of the injection molding processing parameters to minimize the defects formed on the molded parts. The severities of the defects are represented by membership functions using the fuzzy set theory. The minimization of these membership functions, which is a multiobjective optimization problem, is transformed into a substitute problem. The preference function in the substitute problem is original and is proposed specifically for characterizing the quality requirements of the injection molding defects. The formulated optimization problem is solved with design of experiments, in which the process behavior is approximated empirically by a set of quadratic polynomials that can be easily optimized. Experimental results are presented to emphasis the workability of the proposed methodology.     

炼焦生产过程质量产量能耗的集成优化控制

针对炼焦生产过程强非线性、大时滞等特点,基于过程参数的主元分析和灰色关联分析,建立了焦炭质量、产量及焦炉能耗的神经网络预测模型和以焦炭质量为约束条件,产量、能耗为目标函数的优化控制模型。提出一种融合模糊C均值聚类粗优化和差分进化细优化的集成优化控制方法,进行过程参数的优化并给出操作优化指导。系统仿真结果表明,该方法能有效地抑制工况的波动,达到高产、优质、低耗的生产目标,为复杂工业过程的建模和优化控制提供了一种新思路。     

模糊系统理论的工业应用：（Ⅲ）工业过程的模糊调优技术

本文是《模糊系统理论的工业应用》专题系列的最后一部分，介绍模糊逻辑应用于工业调优的理论进展和具体技术，并简单介绍对造纸制浆过程质量控制和操作优化的一个应用实例。     

Multiobjective optimization of an industrial grinding operation under uncertainty

Multiobjective optimization of an industrial grinding operation under various parameter uncertainties is carried out in this work. Two sources of uncertainties considered here are related to the (i) parameters that are used inside a model representing the process under consideration and subjected to experimental and regression errors and (ii) parameters that express operators’ choice for assigning bounds in the constraints and operators prefer them to be expressed around some value rather than certain crisp value. Uncertainty propagation of these parameters through nonlinear model equations is reflected in terms of system constraints and objectives that are treated here using chance constrained fuzzy simulation based approach. Such problems are treated in literature using the standard two stage stochastic programming methodology that has a drawback of leading to combinatorial explosion with an increase in the number of uncertain parameters. This problem is overcome here using a combination of fuzzy and chance constrained programming approach that tackles the problem by representing and treating the uncertain parameters in a different manner. Simultaneous maximization of grinding circuit throughput and percent passing mid size fraction are studied here with upper bound constraints for various performance metrics for the grinding circuit, e.g. percent passing of fine and coarse size classes, percent solids in the grinding circuit final outlet stream and circulation load of the grinding circuit. Uncertain parameters considered are grindability indices of rod mill and ball mill, sharpness indices of primary and secondary cyclones and the respective upper bounds for the constraints mentioned above. The deterministic multiobjective grinding optimization model of Mitra and Gopinath [2004. Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm. Chem. Eng. Sci. 59, 385-396.] forms the basis of this work on which various effects of uncertain parameters are shown and analyzed in a Pareto fashion. Nondominated sorting genetic algorithm, NSGA II, a popular elitist evolutionary multiobjective optimization approach, is used for this purpose.     

Hydrogen and CO2 Management in the Refinery with Fuzzy Multiobjective Nonlinear Programming

An innovative approach for optimization of the hydrogen network in a refinery is presented. The optimization problem was formulated as a fuzzy‐based multiobjective nonlinear programming (FMONLP), aiming at simultaneous minimization of the total annual cost and CO₂ emission. This is achieved by defining an objective function with a weighted sum of the annual cost and CO₂ emission. The weighting factors are considered as fuzzy parameters which are described based on the experts' experiences. The applicability of the proposed approach is illustrated by optimization of an Iranian refinery hydrogen network.     

质子交换膜燃料电池混合动力系统能量优化的仿真分析

分析了混合动力系统的控制目标及需要考虑的几个关键参数。以PEMFC混合动力系统为对象，分别针对给定负载模式和实时运行模式进行控制策略设计和能量优化仿真。对给定的负载模式，采用遗传算法对多约束组合优化问题进行求解，仿真结果证明了算法的可行性。对于实时运行模式，在原有模糊控制策略的基础上，引入燃料电池电压和电压变化量对模糊输出进行两级修正。仿真结果表明，改进后的模糊控制策略可以有效提高燃料电池运行效率，降低燃料电池功率波动。     

Optimal biocompatible solvent design for a two-stage extractive fermentation process with cell recycling

In this study, crisp and fuzzy multiple-goal optimization approaches are respectively introduced to design an optimal biocompatible solvent to a two-stage extractive fermentation with cell recycling for ethanol production. When designing a biocompatible solvent for the extractive fermentation process, many issues, such as extractive efficiency, conversion, amount of solvent utilized and so on, have to be considered. An interactive multiple-goal design procedure is introduced to determine a trade-off result in order to satisfy such contradicted goals. Both approaches could be iterated to solve the interactive multiple-goal design problem in order to yield a trade-off result. However, the crisp optimization design is a tedious task that requires the designer to provide various pairs of the upper bounds for the design problem to obtain the corresponding solution. The fuzzy optimization approach is able to be trade-off several goals simultaneously and to yield the overall satisfactory grade for the product/process design problem.     

漂白纸浆质量的模糊评判

介绍模糊评判的基本步骤并将其应用于纸浆漂白过程中,实现了对漂白纸浆质量的在线评判,方法简单可行。     

Factors affecting the optimal performance of a high-yield pulping operation

Process models based on data from close to one hundred pilot scale pulping runs are used to investigate strategies for operating a chemimechanical pulp mill. Optimal values for a total of 55 process and pulp quality variables have been calculated by applying a genetic algorithm search to a fuzzy model of the overall system. This model consists of over 90 distinct empirical relationships. Results indicate that pulp quality is maintained at minimal fibre and energy costs when the chemical pretreatment is conducted at moderately low temperature using a high SO₂ concentration producing both high sulphonation and high yield simultaneously. Subsequent refining should involve applying at least 65% of the total energy in the primary stage. The pulp quality obtained is comparable to that of a CTMP pulp but with the added benefit of higher freeness.     

Performance analysis and fuzzy optimization of a two-stage fermentation process with cell recycling including an extractor for lactic acid production

In this study, we consider a two-stage fermenter with cell recycling including an extractor to produce lactic acid. When the extractor was omitted, the proposed process was simplified to two special processes. Under the same operating conditions, we compared the overall lactic acid productivity and glucose conversion for the three processes. The proposed fermentation process was more efficient than the other processes. To simultaneously obtain the maximum productivity and conversion, the problem is formulated as a fuzzy multiobjective optimization problem. The fuzzy decision is introduced to convert the multiobjective fuzzy optimization problem into the fuzzy goal attainment problem. Hybrid differential evolution is applied to solve the fuzzy goal attainment problem to obtain a global Pareto solution.     

Stochastic pooling problem for natural gas production network design and operation under uncertainty

Product quality and uncertainty are two important issues in the design and operation of natural gas production networks. This paper presents a stochastic pooling problem optimization formulation to address these two issues, where the qualities of the flows in the system are described with a pooling model and the uncertainty in the system is handled with a multi‐scenario, two‐stage stochastic recourse approach. In addition, multi‐objective problems are handled via a hierarchical optimization approach. The advantages of the proposed formulation are demonstrated with case studies involving an example system based on Haverly's pooling problem and a real industrial system. The stochastic pooling problem is a potentially large‐scale nonconvex Mixed‐Integer Nonlinear Program (MINLP), and a rigorous decomposition method developed recently is used to solve this problem. A computational study demonstrates the advantage of the decomposition method over a state‐of‐the‐art branch‐and‐reduce global optimizer, BARON. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Chemical Composition Determination at the Bottom Region of a Recovery Boiler Furnace by Direct Minimization of Gibbs Free Energy

An optimization strategy has been applied to describe the chemical composition at the furnace bottom in the Kraft recovery boiler of a pulp production process. The concentrations of each involved chemical species were calculated through an optimization approach, minimizing the Gibbs free energy of the system. Various systems were proposed and tested, assuming different chemical species and phases number. Because serious initialization problems were found at this stage for some of the proposed systems, an optimization heuristic method (PSO) was used for the first approach to the problem. Once the appropriate phases number and chemical species in the system were determined, the initialization problems disappeared and the use of a deterministic optimization method (SQP) became viable. The proposed approach has shown to be satisfactory to reproduce industrial data and also data reported in the open scientific literature.     

Impact of Fuel Cell Power Plants on Multi‐objective Optimal Operation Management of Distribution Network

This paper presents an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and differential evolution (MHBMO‐DE) to solve the multi‐objective optimal operation management (MOOM) problem, which can be affected by fuel cell power plants (FCPPs). The objective functions are to minimize total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources, and deviation of bus voltages. A new interactive fuzzy satisfying method is presented to solve the multi‐objective problem by assuming that the decision‐maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods are used to solve this problem because of their independence from type of the objective function and constraints. Recently researchers have presented a new evolutionary method called honey bee mating optimization (HBMO) algorithm. Original HBMO often converges to local optima, in order to overcome this shortcoming, we propose a new method that improves the mating process and also, combines the modified HBMO with DE algorithm. Numerical results for a distribution test system have been presented to illustrate the performance and applicability of the proposed method.     

换热器多目标最佳化中模糊分析理论的应用

提出了较为完善的构造隶属函数的方法，扩充了可行域。同时应用结构模糊优化理论中的最大量小法，线性加权法及贴近度法解决多目标优化问题。并以板翅式换热器为例，进行说明。本文方法对一般机械工程设计中的多目标问题也具有实用价值。     

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.     

Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

To satisfy the diverse product quality specifications required by the broad range of polyolefin applications, polymerization plants are forced to operate under frequent grade transition policies. Commonly, the optimal solution to this problem is based on the minimization of a suitable objective function defined in terms of the changeover time, product quality specifications, process safety constraints and the amount of off-spec polymer, using dynamic optimization methods. However, considering the great impact that a given control structure configuration can have on the process operability and product quality optimization, the time optimal grade transition problem needs to be solved in parallel with the optimal selection of the closed-loop control pairings between the controlled and manipulated variables. In the present study, a mixed integer dynamic optimization approach is applied to a catalytic gas-phase ethylene-1-butene copolymerization fluidized bed reactor (FBR) to calculate both the “best” closed-loop control configuration and the time optimal grade transition policies. The gPROMS/gOPT computational tools for modelling and dynamic optimization, and the GAMS/CPLEX MILP solver are employed for the solution of the combined optimization problem. Simulation results are presented showing the significant quality and economic benefits that can be achieved through the application of the proposed integrated approach to the optimal grade transition problem for a gas-phase polyolefin FBR.     

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.     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

含分段线性隶属函数的模糊规划建模方法

针对具有分段线性隶属函数的模糊规划问题,提出了一种新的模糊规划建模方法。通过对二元变量的合理配置,准确地表达出了隶属函数的各分段之间的关系。这种方法可以有效地避免常规建模方法解决模糊规划时出现的系统失去约束的问题,使得优化问题能够获得满意的最优解。并且,在一些情况下可以使用比普通方法更少的二元项进行优化问题的建模,从而使得计算更为简便。详细地给出了两种相关的建模方法,并通过实例进行了验证。     

Optimal Temperature and pH Control for a Batch Simultaneous Saccharification and Co-Fermentation Process

Crisp and fuzzy optimization approaches were applied to design an optimal temperature and pH control policy for a batch process of simultaneous saccharification and co-fermentation (SSCF) for ethanol production from lignocellulose, using the enzyme and recombinant strain Zymomonas mobilis ZM (pZB5). To determine an optimal temperature and pH control policy, we applied the Arrhenius relationship to each rate constant to express the temperature and pH effects in the kinetic model for both saccharification and fermentation. The goal of the optimal design was to determine the optimal temperature, pH value, initial lignocellulosic concentration, and fermentation time for maximizing the ethanol productivity under the constraints of the follow-up separation specifications. The interactive crisp and fuzzy optimization methods were applied to solve the trade-off optimization problems for obtaining a compromised design. The fuzzy goal attainment approach obtained a compromised design more flexibly than did the crisp optimization. We also compared the performances for batch and fed-batch SSCF, and used various composition proportions for the batch SSCF to determine a series of optimal designs for the fuzzy goal attainment problem. Batch SSCF was slightly more effective than fed-batch fermentation, and spruce exhibited the maximum productivity because of its higher cellulose and lower hemicellulose contents compared with those of other sources.