不确定条件下的湿法炼锌除铜过程机会约束优化控制

除铜过程是湿法炼锌净化工艺中的重要步骤,受生产环境多变、矿源多样、机理复杂等因素的影响,除铜过程存在不确定性,影响生产的稳定性和可靠性。针对除铜过程中入口溶液流量、底流返回量和入口铜离子浓度的不确定性,造成出口铜离子浓度不稳定的问题,研究不确定条件下的除铜过程机会约束优化控制方法。首先分析了除铜过程的不确定性,利用统计学方法分析不确定参数的分布特性,引入了机会约束的思想,将不确定条件下的除铜过程优化问题建模为机会约束优化问题。然后采用可行域映射方法,将机会约束优化问题转化为非线性规划问题。最后,使用序列二次规划求解该非线性规划问题。Monte Carlo仿真验证了该方法的有效性,可以提高系统的鲁棒性。     

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.     

Optimization of grade transitions in polyethylene solution polymerization process under uncertainty

Model-based dynamic optimization is an effective tool for control and optimization of chemical processes, especially during transitions in operation. This study considers the dynamic optimization of grade transitions for a solution polymerization process. Here, a detailed dynamic model comprises the entire flowsheet and includes a method-of-moments reactor model to determine product properties, a simple yet accurate vapor–liquid equilibrium (VLE) model derived from rigorous calculations, and a variable time delay model for recycle streams. To solve the grade transition problem, both single stage and multistage optimization formulations have been developed to deal with specification bands of product properties.This dynamic optimization framework demonstrates significant performance improvements for grade transition problems. However, performance can deteriorate in the presence of uncertainties, disturbances and model mismatch. To deal with these uncertainties, this study applies robust optimization formulations through the incorporation of back-off constraints within the optimization problem. With back-off terms calculated from Monte Carlo simulations, the resulting robust optimization formulation can be solved with the same effort as the nominal dynamic optimization problem, and the resulting solution is shown to be robust under various uncertainty levels with minimal performance loss. Additional case studies show that our optimization approach extends naturally to different regularizations and multiple sources of uncertainty.     

Optimal robust optimization approximation for chance constrained optimization problem

Chance constraints are useful for modeling solution reliability in optimization under uncertainty. In general, solving chance constrained optimization problems is challenging and the existing methods for solving a chance constrained optimization problem largely rely on solving an approximation problem. Among the various approximation methods, robust optimization can provide safe and tractable analytical approximation. In this paper, we address the question of what is the optimal (least conservative) robust optimization approximation for the chance constrained optimization problems. A novel algorithm is proposed to find the smallest possible uncertainty set size that leads to the optimal robust optimization approximation. The proposed method first identifies the maximum set size that leads to feasible robust optimization problems and then identifies the best set size that leads to the desired probability of constraint satisfaction. Effectiveness of the proposed algorithm is demonstrated through a portfolio optimization problem, a production planning and a process scheduling problem.     

An improved decomposition algorithm for optimization under uncertainty

This paper proposes a modification to the decomposition algorithm of Ierapetritou and Pistikopoulos (1994) for process optimization under uncertainty. The key feature of our approach is to avoid imposing constraints on the uncertain parameters, thus allowing a more realistic modeling of uncertainty. A theoretical analysis of the earlier algorithm leads to the development of an improved algorithm which successfully avoids getting trapped in local minima while accounting more accurately for the trade-offs between cost and flexibility. In addition, the improved algorithm is 3–6 times faster, on the problems tested, than the original one. This is achieved by avoiding the solution of feasibility subproblems, the number of which is exponential in the number of uncertain parameters.     

Optimal control of final state constrained systems

In using penalty functions to handle final state equality constraints, we propose a systematic scheme for adjusting the penalty function factors, so that all the constraints are satisfied within a specified tolerance, and so that the performance index is minimized. Two typical engineering problems, which are used to test the procedure, show that the proposed method of adjusting the penalty function factors can be used for reasonably complex systems to yield reliable results.     

Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty

Optimization under uncertainty has been an active area of research for many years. However, its application in Process Systems Engineering has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust/chance constrained optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty of interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers for mostly linear models.     

Optimization of refinery hydrogen network based on chance constrained programming

Deterministic optimization approaches have been developed and used in the optimization of hydrogen network in refinery. However, uncertainties may have a large impact on the optimization of hydrogen network. Thus the consideration of uncertainties in optimization approaches is necessary for the optimization of hydrogen network. A novel chance constrained programming (CCP) approach for the optimization of hydrogen network in refinery under uncertainties is proposed. The stochastic properties of the uncertainties are explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. The problem is then transformed to an equivalent deterministic mixed-integer nonlinear programming (MINLP) problem so that it can be solved by a MINLP solver. The solution of the optimization problem provides comprehensive information on the economic benefit under different confidence levels by satisfying process constraints. Based on this approach, an optimal and reliable decision can be made, and a suitable compensation between the profit and the probability of constraints violation can be achieved. The approach proposed in this paper makes better use of resources and can provide significant environmental and economic benefits. Finally, a case study from a refinery in China is presented to illustrate the applicability and efficiency of the developed approach.     

Integrated design and control under uncertainty: Embedded control optimization for plantwide processes

High performance processes should operate close to design boundaries and specification limits, while still guaranteeing robust performance without design constraint violations. Since design chemical process is operating close to tighter boundaries safely; much attention has been devoted to integrating design and control, in which the design decisions, dynamics, and control performance are considered simultaneously in some optimal fashion. However, rigorous methods for solving design and control simultaneously lead to challenging mathematical formulations which easily become computationally intractable. In an earlier paper of our group, a new mathematical methodology to reduce the combinatorial complexity of integrating design and control was introduced (Malcolm et al., 2007). We showed that substantial problem size reduction can be achieved by embedding control for specific process designs. In this paper, we extend the embedded control methodologies to plantwide flowsheet. The case study for the reactor-column flowsheet will demonstrate the current capabilities of the methodology for integrating design and control under uncertainty.     

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%).     

Optimal procurement contract selection with price optimization under uncertainty for process networks

In this work, we propose extending the production planning decisions of a chemical process network to include optimal contract selection under uncertainty with suppliers and product selling price optimization. We use three quantity-based contract models: discount after a certain purchased amount, bulk discount, and fixed duration contracts. We propose the use of general regression models to describe the relationship between selling price, demand, and possibly other predictors, such as economic indicators. For illustration purposes, we consider three demand-response models (i.e., selling price as a function of demand) that are typically encountered in the literature: linear, constant-elasticity, and logit. We develop a mixed-integer nonlinear two-stage stochastic programming that accounts for uncertainty in both supply (e.g., raw material spot market price) and demand (random nature of the residuals of the regression models) for the planning of the process network. The proposed method is illustrated with two numerical examples of chemical process networks.     

Dynamic parameter estimation and optimization for batch distillation

This work reviews a well-known methodology for batch distillation modeling, estimation, and optimization but adds a new case study with experimental validation. Use of nonlinear statistics and a sensitivity analysis provides valuable insight for model validation and optimization verification for batch columns. The application is a simple, batch column with a binary methanol–ethanol mixture. Dynamic parameter estimation with an ℓ₁-norm error, nonlinear confidence intervals, ranking of observable parameters, and efficient sensitivity analysis are used to refine the model and find the best parameter estimates for dynamic optimization implementation. The statistical and sensitivity analyses indicated there are only a subset of parameters that are observable. For the batch column, the optimized production rate increases by 14% while maintaining product purity requirements.     

Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

Interest in chemical processes that perform well in dynamic environments has led to the development of design methodologies that account for operational aspects of processes, including flexibility, operability, and controllability. In this article, we address the problem of identifying process designs that optimize an economic objective function and are guaranteed to be stable under parametric uncertainties. The underlying mathematical problem is difficult to solve as it involves infinitely many constraints, nonconvexities and multiple local optima. We develop a methodology that embeds robust stability constraints to steady‐state process optimization formulations without any a priori bifurcation analysis. We propose a successive row and column generation algorithm to solve the resulting generalized semi‐infinite programming problem to global optimality. The proposed methodology allows modeling different levels of robustness, handles uncertainty regions without overestimating them, and works for both unique and multiple steady states. We apply the proposed approach to a number of steady‐state optimization problems and obtain the least conservative solutions that guarantee robust stability. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

A modeling strategy for integrated batch process development based on mixed-logic dynamic optimization

This paper introduces an optimization-based approach for the simultaneous solution of batch process synthesis and plant allocation, with decisions like the selection of chemicals, process stages, task-unit assignments, operating modes, and optimal control profiles, among others. The modeling strategy is based on the representation of structural alternatives in a state-equipment network (SEN) and its formulation as a mixed-logic dynamic optimization (MLDO) problem. Particularly, the disjunctive multistage modeling strategy by Oldenburg and Marquardt (2008) is extended to combine and organize single-stage and multistage models for representing the sequence of continuous and batch units in each structural alternative and for synchronizing dynamic profiles in input and output operations with material transference. Two numerical examples illustrate the application of the proposed methodology, showing the enhancement of the adaptability potential of batch plants and the improvement of global process performance thanks to the quantification of interactions between process synthesis and plant allocation decisions.     

Medium-term maintenance turnaround planning under uncertainty for integrated chemical sites

Plant maintenance poses extended disruptions to production. Maintenance effects are amplified when the plant is part of an integrated chemical site, as production levels of adjacent plants in the site are also significantly influenced. A challenge in dealing with turnarounds is the difficulty in predicting their duration, due to discovery work and delays. This uncertainty in duration affects two major planning decisions: production levels and maintenance manpower allocation. The latter must be decided several months before the turnarounds occur. We address the scheduling of a set of plant turnarounds over a medium-term of several months using integer programming formulations. Due to the nature of uncertainty, production decisions are treated through stochastic programming ideas, while the manpower aspect is handled through a robust optimization framework. We propose combined robust optimization and stochastic programming formulations to address the problem and demonstrate, through an industrial case study, the potential for significant savings.     

A two-level measurement-based dynamic optimization strategy for a bioreactor in penicillin fermentation process

One measurement-based dynamic optimization scheme can achieve optimality under uncertainties by tracking the necessary condition of optimality (NCO-tracking), with a basic assumption that the solution ...     

一种基于测量的双层动态优化策略及其在青霉素发酵过程中的应用(英文)

One measurement-based dynamic optimization scheme can achieve optimality under uncertainties by tracking the necessary condition of optimality (NCO-tracking), with a basic assumption that the solution model remains invariant in the presence of al kinds of uncertainties. This assumption is not satisfied in some cases and the stan-dard NCO-tracking scheme is infeasible. In this paper, a novel two-level NCO-tracking scheme is proposed to deal with this problem. A heuristic criterion is given for triggering outer level compensation procedure to update the solution model once any change is detected via online measurement and estimation. The standard NCO-tracking process is carried out at the inner level based on the updated solution model. The proposed approach is il ustrated via a bioreactor in penicil in fermentation process.     

Operational optimization of industrial steam systems under uncertainty using data-Driven adaptive robust optimization

This article addresses the operational optimization of industrial steam systems under device efficiency uncertainty using a data-driven adaptive robust optimization approach. A semiempirical model of steam turbine is first developed based on process mechanism and operational data. Uncertain parameters of the proposed steam turbine model are further derived from the historical process data. A robust kernel density estimation method is then used to construct the uncertainty sets for modeling these uncertain parameters. The data-driven uncertainty sets are incorporated into a two-stage adaptive robust mixed-integer linear programming (MILP) framework for operational optimization of steam systems to minimize the total operating cost. Integer variables are introduced to model the on/off decisions of the steam turbines and electrical motors, which are the major energy consumers of the steam system. By applying the affine decision rule, the proposed multilevel optimization model is transformed into its robust counterpart, which is a single-level MILP problem. The proposed framework is applied to the steam system of a real-world ethylene plant to demonstrate its applicability. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16500 2019     

A multiobjective optimization framework for design of integrated biorefineries under uncertainty

A systematic approach for development of a reliable optimization framework to address the optimal design of integrated biorefineries in the face of uncertainty is presented. In the current formulation, a distributed strategy which is composed of different layers including strategic optimization, risk management, detailed mechanistic modeling, and operational level optimization is applied. In the strategic model, a multiobjective stochastic optimization approach is utilized to incorporate the tradeoffs between the cost and the financial risk. Then, Aspen Plus models are built to provide detailed simulation of biorefineries. In the final layer, an evolutionary algorithm is employed to optimize the operating condition. To demonstrate the effectiveness of the framework, a hypothetical case study referring to a multiproduct lignocellulosic biorefinery is utilized. The numerical results reveal the efficacy of the proposed approach; it provides decision makers with a quantitative analysis to determine the optimum capacity plan and operating conditions of the biorefinery. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3208–3222, 2015     

化工过程设计的多目标不确定优化研究

In many circumstances, chemical process design can be formulated as a multi-objective optimization （MOO） problem. Examples include bi-objective optimization problems, where the economic objective is maximized and environmental impact is minimized simultaneously. Moreover, the random behavior in the process,property, market fluctuation, errors in model prediction and so on would affect the performance of a process. Therefore, it is essential to develop a MOO methodology under uncertainty. In this article, the authors propose a generic and systematic optimization methodology for chemical process design under uncertainty. It aims at identifying the optimal design from a number of candidates. The utility of this methodology is demonstrated by a case study based on the design of a condensate treatment unit in an ammonia plant.