A superstructure-based framework for simultaneous process synthesis,heat integration,and utility plant design

We propose a superstructure optimization framework for process synthesis with simultaneous heat integration and utility plant design. Processing units in the chemical plant can be modeled using rigorous unit models or surrogate models generated from experimental results or off-line calculations. The utility plant subsystem includes multiple steam types with variable temperature and pressure. For the heat integration subsystem, we consider variable heat loads of process streams as well as variable intervals for the utilities. To enhance the solution of the resulting mixed-integer nonlinear programming models, we develop (1) new methods for the calculation of steam properties, (2) algorithms for variable bound calculation, and (3) systematic methods for the generation of redundant constraints. The applicability of our framework is illustrated through a biofuel case study which includes a novel non-enzymatic hydrolysis technology and new separation technologies, both of which are modeled based on experimental results.     

Models for circular data from time series spectra

Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex-valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high-order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra-generated models is illustrated in an analysis of wind direction data.     

A novel approach to scheduling multipurpose batch plants using unit‐slots

Several models for scheduling multipurpose batch plants exist in the literature. The models using unit‐specific event points have shown better solution efficiency on various literature examples. This article presents a novel approach to scheduling multipurpose batch plants, which uses unit‐slots instead of process‐slots to manage shared resources such as material storage. We develop two slightly different models that are even more compact and simpler than that of Sundaramoorthy and Karimi, Chem Eng Sci. 2005;60:2679–2702. Although we focus on material as a shared resource, our multi‐grid approach rationalizes, generalizes, and improves the current multi‐grid approaches for scheduling with shared resources. Our models allow nonsimultaneous transfers of materials into and out of a batch. We show by an example that this flexibility can give better schedules than those from existing models in some cases. Furthermore, our approach uses fewer slots (event‐points) on some examples than even those required by the most recent unit‐specific event‐based model. Numerical evaluation using literature examples shows significant gains in solution efficiency from the use of unit‐slots except where the number of unit‐slots required for the optimal solution equals that of process slots. We also highlight the importance of constraint sequencing in GAMS implementation for evaluating mixed‐integer linear programming based scheduling models fairly. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Surrogate‐based superstructure optimization framework

In principle, optimization‐based “superstructure” methods for process synthesis can be more powerful than sequential‐conceptual methods as they account for all complex interactions between design decisions. However, these methods have not been widely adopted because they lead to mixed‐integer nonlinear programs that are hard to solve, especially when realistic unit operation models are used. To address this challenge, we develop a superstructure‐based strategy where complex unit models are replaced with surrogate models built from data generated via commercial process simulators. In developing this strategy, we study aspects such as the systematic design of process unit surrogate models, the generation of simulation data, the selection of the surrogate's structure, and the required model fitting. We also present how these models can be reformulated and incorporated into mathematical programming superstructure formulations. Finally, we discuss the application of the proposed strategy to a number of applications. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Symmetry breaking in MILP formulations for Unit Commitment problems

This paper addresses the study of symmetry in Unit Commitment (UC) problems solved by Mixed Integer Linear Programming (MILP) formulations, and using Linear Programming based Branch & Bound MILP solvers. We propose three sets of symmetry breaking constraints for UC MILP formulations exhibiting symmetry, and its impact on three UC MILP models are studied. The case studies involve the solution of 24 instances by three widely used models in the literature, with and without symmetry breaking constraints. The results show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed. The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.     

UNIT ROOTS IN PERIODIC AUTOREGRESSIONS

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model.     

Large scale optimization of a sour water stripping plant using surrogate models

In this work, we propose a new methodology for the large scale optimization and process integration of complex chemical processes that have been simulated using modular chemical process simulators. Units with significant numerical noise or large CPU times are substituted by surrogate models based on Kriging interpolation. Using a degree of freedom analysis, some of those units can be aggregated into a single unit to reduce the complexity of the resulting model. As a result, we solve a hybrid simulation-optimization model formed by units in the original flowsheet, Kriging models, and explicit equations.We present a case study of the optimization of a sour water stripping plant in which we simultaneously consider economics, heat integration and environmental impact using the ReCiPe indicator, which incorporates the recent advances made in Life Cycle Assessment (LCA).The optimization strategy guarantees the convergence to a local optimum inside the tolerance of the numerical noise.     

Toward improved aesthetics and data discrimination for treemaps via color schemes

In this article, we present a novel treemap coloring method which can help users to analyze visual data more easily. Our method overcomes two major limitations of existing treemaps in that they are either aesthetically unpleasing or unable to readily discriminate data blocks with close sizes. Our study indicates that the use of proper color schemes can surprisingly address these two seemingly uncorrelated limitations simultaneously. To improve the aesthetic value of a treemap, we apply the color aesthetic model to treemap generation. To better the degree of data discrimination of similar data, based on the principle of expansive and contractive colors, we propose a novel quantitative color‐visually perceived area (C‐VPA) model via experimental methods. Furthermore, we combine these two models to derive a genetic algorithm‐based treemap coloring method. Our experimental results confirm the superiority of our method in terms of improved data discrimination and aesthetics of the treemaps.     

UNIFIED INTERVAL ESTIMATION FOR RANDOM COEFFICIENT AUTOREGRESSIVE MODELS

The consistency of the quasi‐maximum likelihood estimator for random coefficient autoregressive models requires that the coefficient be a non‐degenerate random variable. In this article, we propose empirical likelihood methods based on weighted‐score equations to construct a confidence interval for the coefficient. We do not need to distinguish whether the coefficient is random or deterministic and whether the process is stationary or non‐stationary, and we present two classes of equations depending on whether a constant trend is included in the model. A simulation study confirms the good finite‐sample behaviour of our resulting empirical likelihood‐based confidence intervals. We also apply our methods to study US macroeconomic data.     

Multiple and nonuniform time grids in discrete-time MIP models for chemical production scheduling

The modeling of time plays a key role in the formulation of mixed-integer programming (MIP) models for scheduling, production planning, and operational supply chain planning problems. It affects the size of the model, the computational requirements, and the quality of the solution. While the development of smaller continuous-time scheduling models, based on multiple time grids, has received considerable attention, no truly different modeling methods are available for discrete-time models. In this paper, we challenge the long-standing belief that employing a discrete modeling of time requires a common uniform grid. First, we show that multiple grids can actually be employed in discrete-time models. Second, we show that not only unit-specific but also task-specific and material-specific grids can be generated. Third, we present methods to systematically formulate discrete-time multi-grid models that allow different tasks, units, or materials to have their own time grid. We present two different algorithms to find the grid. The first algorithm determines the largest grid spacing that will not eliminate the optimal solution. The second algorithm allows the user to adjust the level of approximation; more approximate grids may have worse solutions, but many fewer binary variables. Importantly, we show that the proposed models have exactly the same types of constraints as models relying on a single uniform grid, which means that the proposed models are tight and that known solution methods can be employed. The proposed methods lead to substantial reductions in the size of the formulations and thus the computational requirements. In addition, they can yield better solutions than formulations that use approximations. We show how to select the different time grids, state the formulation, and present computational results.     

Preprocessing and tightening methods for time-indexed MIP chemical production scheduling models

We propose a series of preprocessing algorithms for the generation of strong valid inequalities for time-indexed, discrete and continuous, mixed-integer programming scheduling models for problems in network production environments. Specifically, starting from time- and inventory-related instance data, the proposed algorithms use constraint propagation techniques to calculate parameters that are used to bound the number of times subsets of tasks can be executed in a feasible solution. We also extend some of the propagation ideas to generate three classes of new tightening constraints. The proposed methods result in tightening constraints expressed in terms of assignment binary variables (X_ijt = 1 if task i is assigned to start on unit j at time point t) which are present in all time-indexed MIP models, therefore they are applicable to all time-indexed models accounting for a wide range of processing features. Finally, the methods are shown to lead to up to two orders of magnitude reduction in computational time when optimal solutions are found and significantly improve optimality gap when a time limit is enforced.     

Analysis of the local well-posedness of optimization-constrained differential equations by local optimality conditions

Optimization-constrained differential equations (OCDE) are a class of mathematical problems where differential equations are constrained by an embedded algebraic optimization problem. We analyze the well-posedness of the local solutions of OCDE based on local optimality. By assuming linear independence constraint qualification and applying the Karush-Kuhn-Tucker optimality conditions, an OCDE is transformed into a complementarity system (CS). Under second-order sufficient condition we show that (a) if strict complementary condition (SCC) holds, the local solution of OCDE is well-posed, which corresponds to a mode of the derived CS; (b) at points where SCC is violated, a local solution of OCDE exists by sequentially connecting the local solutions of two selected modes of the derived CS. We propose an event-based algorithm to numerically solve OCDE. We illustrate the approach and algorithm for microbial cultivation, single flash unit and contrived numerical examples.     

Bootstrapping unit root tests for integrated processes

Abstract. In this paper, we consider two bootstrap algorithms for testing unit roots under the condition that the observed process is unit root integrated. The first method consists of generating the resampled data after fitting an autoregressive model to the first differences of the observations. The second method consists of applying the stationary bootstrap to the first differences. Both procedures are shown to give methods that approach the correct asymptotic distribution under the null hypothesis of a unit root. We also present a Monte-Carlo study comparing the two methods for some ARIMA models.     

Generalized initialization for the dynamic simulation and optimization of grade transition processes using two-dimensional collocation

Optimization modeling tools are essential to determine optimal design specifications and operation conditions of polymerization processes, especially when quality indices based on molecular weight distributions (MWDs) must be enforced. This study proposes a generalized MWD-based optimization strategy using orthogonal collocation in two dimensions, which can capture the dynamic features of MWDs accurately. To enable the strategy, this study considers generalized initialization methods for large-scale simulation and optimization. Here, a homotopy method based on intermediate solutions is adopted to generate initial values for general steady-state simulation models, starting from an arbitrary known solution for any steady-state simulation model. For dynamic simulation models, the response of a first-order linear system is adopted to initialize the state variables. Case studies show the effectiveness of this procedure to enable systematic, reliable, and efficient solution of the optimization problem.     

A robust mathematical formulation for multipurpose batch plants

Several scheduling techniques exist in literature based on continuous time representation. The models based on unit specific time points have shown better solution efficiency by reducing the number of time points and problem size. In this paper novel scheduling techniques based on unit specific time point continuous time representation are presented. The proposed models allow nonsimultaneous material transfer into a unit. Nonsimultaneous transfer refers to when a task requires more than one intermediate state it is possible for one state to be transferred and stored in a unit that is processing it for a while and wait for the other intermediates to come together to start the task. This approach gives a better schedule as compared to most published models. The developed MILP scheduling models are based on state sequence network representation that has proven to inherently result in smaller problems in terms of binary variables. The models require a smaller number of time points as compared to single-grid and multi-grid continuous time models. Consequently, they exhibit much better computational performance. Numerical evaluation using literature examples indicate in some of the complex examples that the proposed models give a better objective value as compared to other scheduling models. An added feature of the proposed models is their ability to exactly handle fixed intermediate storage operational philosophy, which has proven to be a subtle drawback in most published scheduling techniques.     

Towards joint disease mapping

This article discusses and extends statistical models to jointly analyse the spatial variation of rates of several diseases with common risk factors. We start with a review of methods for separate analyses of diseases, then move to ecological regression approaches, where the rates from one of the diseases enter as surrogate covariates for exposure. Finally, we propose a general framework for jointly modelling the variation of two or more diseases, some of which share latent spatial fields, but with possibly different risk gradients. In our application, we consider mortality data on oral, oesophagus, larynx and lung cancers for males in Germany, which all share smoking as a common risk factor. Furthermore, the first three cancers are also known to be related to excessive alcohol consumption. An empirical comparison of the different models based on a formal model criterion as well as on the posterior precision of the relative risk estimates strongly suggests that the joint modelling approach is a useful and valuable extension over individual analyses.     

Models for Interactions between Ionic Surfactants and Nonsurface-Active Ions in Foam Fractionation Processes

Abstract

Interactions are analyzed between an ionic surfactant and nonsurface-active ions (colligends) of opposite charge being separated in foam fractionations. Surfactant selectivity for competing colligends is determined in terms of models based on surfactant—colligend ion pair formation in the feed solution to a foam fractionation unit, based on colligend-surfactant counterion exchange at the gas-solution, bubble interfaces, and based on surface exchange coupled with ion pair formation in the bulk solution. Accurate, continuous-flow, single-equilibrium-stage foam fractionation data for NO^? ₃, BrO^? ₃, CIO^? ₃, and I^?, each versus Br^?, the counterion of the ethylhexadecyldimethylammonium cation, are used to discriminate among the models. Based on a detailed statistical analysis of the selectivity coefficients determined by two interaction models for each of the four colligends, the hypothesis of colligend-counterion exchange at the gas-solution interface is shown to be valid and that of solution ion pair formation is not substantiated. The surface exchange model provides selectivity coefficients which are quite constant over a tenfold concentration range and yet which are very sensitive to data inaccuracies.     

Flexible and Robust Mixed Poisson INGARCH Models

In this article, we propose a general class of INteger‐valued Generalized AutoRegressive Conditional Heteroskedastic (INGARCH) models based on a flexible family of mixed Poisson (MP) distributions. Our proposed class of count time series models contains the negative binomial (NB) INGARCH process as particular case and open the possibility to introduce new models such as the Poisson‐inverse Gaussian (PIG) and Poisson generalized hyperbolic secant processes. In particular, the PIG INGARCH model is an interesting and robust alternative to the NB model. We explore first‐order and second‐order stationary properties of our MPINGARCH models and provide expressions for the autocorrelation function and mean and variance marginals. Conditions to ensure strict stationarity and ergodicity properties for our class of INGARCH models are established. We propose an Expectation‐Maximization algorithm to estimate the parameters and obtain the associated information matrix. Further, we discuss two additional estimation methods. Monte Carlo simulation studies are considered to evaluate the finite‐sample performance of the proposed estimators. We illustrate the flexibility and robustness of the MPINGARCH models through two real‐data applications about number of cases of Escherichia coli and Campylobacter infections. This article contains a Supporting Information.     

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.     

RESIDUAL AUTOCOVARIANCES AND UNIT ROOT TESTS BASED ON INSTRUMENTAL VARIABLE ESTIMATORS FROM TIME SERIES REGRESSION MODELS

Abstract. Hall (Testing for a unit root in the presence of moving average errors. Biometrika 76 (1989), 49–56; Joint hypothesis tests for a random walk based on instrumental variable estimators. J. Time Ser. Anal. 13 (1992), 29–45), Pantula and Hall (Testing for unit roots in autoregressive moving average models:an instrumental variable approach. J. Econometrics 48 (1991), 325–53) and Lee and Schmidt (Unit root tests based on instrumental variable estimation. Int. Econ. Rev. 39 (1994), 449–62) proposed instrumental variable (IV) based tests for a unit root in an ARMA(p+ 1, q) time series. To perform the tests it is essentially necessary to know (p, q) but in many cases this information is unknown. In practice a natural solution to this problem is to estimate (p, q) from the data using a strategy based on the residual autocovariances from the IV regression. In this paper we examine the properties of these residual autocovariances under various assumptions about the true nature of the time series. This analysis allows us to propose a model selection procedure which has desirable asymptotic and finite sample properties whether the time series is stationary or possesses a unit root. A sideproduct of our analysis is that we extend Box and Pierce's (Distribution of residual autocorrelations in autoregressive integrated moving average time series models. J. Am. Statist. Assoc. 65 (1970), 1509–26) analysis of the least squares residual autocorrelations to the residual autocovariances from IV regressions.