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     

Process design and control optimization: A simultaneous approach by multi‐parametric programming

We present a framework for the application of design and control optimization via multi‐parametric programming through four case studies. We develop design dependent multi‐parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115–138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

需求不确定下炼油企业生产计划优化混合规划模型

Abstract Production planning under uncertainty is considered as one of the most important problems in plant-wide optimization. In this article, first, a stochastic programming model with uniform distribution assumption is developed for refinery production planning under demand uncertainty, and then a hybrid programming model incorporating the linear programming model with the stochastic programming one by a weight factor is proposed. Subsequently, piecewise linear approximation functions are derived and applied to solve the hybrid programming model-under uniform distribution assumption. Case studies show that the linear approximation algorithm is effective to solve.the hybrid programming model, along with an error≤0.5% when the deviatiorgmean≤20%. The simulation results indicate that the hybrid programming model with an appropriate weight factor （0.1-0.2） can effectively improve the optimal operational strategies under demand uncertainty, achieving higher profit than the linear programming model and the stochastic programming one with about 1.3% and 0.4% enhancement, respectavely.     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

A backoff strategy for model‐based experiment design under parametric uncertainty

Model‐based experiment design techniques are an effective tool for the rapid development and assessment of dynamic deterministic models, yielding the most informative process data to be used for the estimation of the process model parameters. A particular advantage of the model‐based approach is that it permits the definition of a set of constraints on the experiment design variables and on the predicted responses. However, uncertainty in the model parameters can lead the constrained design procedure to predict experiments that turn out to be, in practice, suboptimal, thus decreasing the effectiveness of the experiment design session. Additionally, in the presence of parametric mismatch, the feasibility constraints may well turn out to be violated when that optimally designed experiment is performed, leading in the best case to less informative data sets or, in the worst case, to an infeasible or unsafe experiment. In this article, a general methodology is proposed to formulate and solve the experiment design problem by explicitly taking into account the presence of parametric uncertainty, so as to ensure both feasibility and optimality of the planned experiment. A prediction of the system responses for the given parameter distribution is used to evaluate and update suitable backoffs from the nominal constraints, which are used in the design session to keep the system within a feasible region with specified probability. This approach is particularly useful when designing optimal experiments starting from limited preliminary knowledge of the parameter set, with great improvement in terms of design efficiency and flexibility of the overall iterative model development scheme. The effectiveness of the proposed methodology is demonstrated and discussed by simulation through two illustrative case studies concerning the parameter identification of physiological models related to diabetes and cancer care. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Global optimization of large‐scale mixed‐integer linear fractional programming problems: A reformulation‐linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

Optimal processing network design under uncertainty for producing fuels and value‐added bioproducts from microalgae: Two‐stage adaptive robust mixed integer fractional programming model and computationally efficient solution algorithm

Fractional metrics, such as return on investment (ROI), are widely used for performance evaluation, but uncertainty in the real market may unfortunately diminish the results that are based on nominal parameters. This article addresses the optimal design of a large‐scale processing network for producing a variety of algae‐based fuels and value‐added bioproducts under uncertainty. We develop by far the most comprehensive processing network with 46,704 alternative processing pathways. Based on the superstructure, a two‐stage adaptive robust mixed integer fractional programming model is proposed to tackle the uncertainty and select the robust optimal processing pathway with the highest ROI. Since the proposed problem cannot be solved directly by any off‐the‐shelf solver, we develop an efficient tailored solution method that integrates a parametric algorithm with a column‐and‐constraint generation algorithm. The resulting robust optimal processing pathway selects biodiesel and poly‐3‐hydroxybutyrate as the final fuel and bioproduct, respectively. © 2016 American Institute of Chemical Engineers AIChE J, 63: 582–600, 2017     

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.     

The Multi‐Substrate Screening of Asymmetric Catalysts

The principle of the one‐pot multi‐substrate screening is presented. This methodology has been successfully applied to various types of catalyzed enantioselective reactions: borane reduction of ketones, addition of organozinc on aldehydes, conjugate addition of diethylzinc on cycloalkenones or nitroalkenes, hydroformylation of olefins, hetero‐Diels–Alder reaction on α‐keto esters, enzymatic hydrolysis of glycerol‐type monoesters as well as hydrogenation of 2‐aryl‐substituted terminal alkenes and enamides. The one‐pot multi‐catalyst screening methodology is also briefly discussed.     

Multistage stochastic programming for the closed-loop supply chain planning with mobile modules under uncertainty

Traditional supply chains usually follow fixed facility designs which coincide with the strategic nature of supply chain management (SCM). However, as the global market turns more volatile, the concept of mobile modularization has been adopted by increasingly more industrial practitioners. In mobile modular networks, modular units can be installed or removed at a particular site to expand or reduce the capacity of a facility, or relocated to other sites to tackle market volatility. In this work, we formulate a mixed-integer linear programming (MILP) model for the closed-loop supply chain network planning with modular distribution and collection facilities. To further deal with uncertain customer demands and recovery rates, we extend our model to a multistage stochastic programming model and efficiently solve it using a tailored stochastic dynamic dual integer programming (SDDiP) with Magnanti-Wong enhanced cuts. Computational experiments show that the added Magnanti-Wong cuts in the proposed algorithm can effectively close the gap between upper and lower bounds, and the benefit of mobile modules is evident when the temporal and spatial variability of customer demand is high.     

Worst‐case design of subsea production facilities using semi‐infinite programming

The problem of designing novel process systems for deployment in extreme and hostile environments is addressed. Specifically, the process system of interest is a subsea production facility for ultra deepwater oil and gas production. The costs associated with operational failures in deepwater environments are prohibitively high and, therefore, warrant the application of worst‐case design strategies. That is, prior to the construction and deployment of a process, a certificate of robust feasibility is obtained for the proposed design. The concept of worst‐case design is addressed by formulating the design feasibility problem as a semi‐infinite optimization problem with implicit functions embedded. A basic model of a subsea production facility is presented for a case study of rigorous performance and safety verification. Relying on recent advances in global optimization of implicit functions and semi‐infinite programming, the design feasibility problem is solved, demonstrating that this approach is effective in addressing the problem of worst‐case design of novel process systems. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2513–2524, 2014     

Multi‐scale and multi‐fractal characteristics of instantaneous velocity signals in impinging stream mixer

The axial and radial instantaneous velocity signals in impinging stream mixer (ISM) were decomposed to multi‐scale and studied by R/S analysis method. It showed that different fractal structure at different scales can be explained easily by Hurst analysis and there were different trends of Hs with the different positions. Besides, there were some non‐periodic components in the system, and in the process of particles impinged reciprocally, the vortex with different scale emerges.     

Preferential crystallization: Multi‐objective optimization framework

A four objective optimization framework for preferential crystallization of D‐L threonine solution is presented. The objectives are maximization of average crystal size and productivity, and minimization of batch time and the coefficient of variation at the desired purity while respecting design and operating constraints. The cooling rate, enantiomeric excess of the preferred enantiomer, and the mass of seeds are used as the decision variables. The optimization problem is solved by using adaptation of the nondominated sorting genetic algorithm. The results obtained clearly distinguish different regimes of interest during preferential crystallization. The multi‐objective analysis presented in this study is generic and gives a simplified picture in terms of three zones of operations obtained because of relative importance of nucleation and growth. Such analysis is of great importance in providing better insight for design and decision making, and improving the performance of the preferential crystallization that is considered as a promising future alternative to chromatographic separation of enantiomers. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Multi‐wavelength excitation method for measuring FWA‐treated paper

Colorimetric properties of fluorescent materials depend on the SPD of the illumination. That is why most standards for evaluating them specify the illuminations, which are often hard‐to‐realize daylight illuminants. The presented method using commercially available LEDs enables accurate enough colorimetric measurements of FWA‐treated papers or prints on them illuminated by the specified illuminant. The total spectral radiance factor of a fluorescent specimen, from which most colorimetric values are derived, consists of the luminescent spectral radiance factor and the spectral reflectance factor. This method separately estimates those of FWA‐treated paper to add up to the total spectral radiance factor. The luminescent spectral radiance factor is obtained by estimating the SPD of luminescence excited by the specified illuminant as the weighted sum of the multiple SPDs of luminescence excited by the respective narrow band LED emissions at different wavelengths. The LEDs and their weights are determined optimally for generally used papers. The spectral reflectance factor is derived from the estimated SPD of the radiation with fluorescence excluded from the paper illuminated by visible illumination. The method was applied with five different illumination systems each using two or three narrow band LEDs in the excitation range. They were evaluated by measuring the total spectral radiance factors by D50 of seven FWA‐treated papers and CMYK prints on four papers. The derived colorimetric values were compared to the respective references by the ideal D50.     

Data-driven distributionally robust optimization of shale gas supply chains under uncertainty

This article aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two-stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first-stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second-stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data-driven approach is applied to construct the ambiguity set based on principal component analysis and first-order deviation functions. By taking advantage of affine decision rules, a tractable mixed-integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a small-scale illustrative example and a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models, including the deterministic and stochastic programming counterparts, are investigated as well. © 2018 American Institute of Chemical Engineers AIChE J, 65: 947–963, 2019     

Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection

Abstract. In this article, under a semi‐parametric partly linear autoregression model, a family of robust estimators for the autoregression parameter and the autoregression function is studied. The proposed estimators are based on a three‐step procedure, in which robust regression estimators and robust smoothing techniques are combined. Asymptotic results on the autoregression estimators are derived. Besides combining robust procedures with M‐smoothers, predicted values for the series and detection residuals, which allow to detect anomalous data, are introduced. Robust cross‐validation methods to select the smoothing parameter are presented as an alternative to the classical ones, which are sensitive to outlying observations. A Monte Carlo study is conducted to compare the performance of the proposed criteria. Finally, the asymptotic distribution of the autoregression parameter estimator is stated uniformly over the smoothing parameter.