Thermodynamic uncertainties in batch processing and optimal control

Ulas, Saadet; Diwekar, Urmila M.

doi:10.1016/j.compchemeng.2004.04.001

Cited by 26 publications

(14 citation statements)

References 12 publications

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“…This figure shows how the uncertainties in activity coefficients predicted by the UNIFAC method affect the time-dependent relative volatility profile in a batch distillation column (47). Despite this fact, a generalized method of treatment for dynamic uncertainties for chemical systems was presented recently (47,51,52). This method is based on Ito processes and real options theory from finance literature.…”

Section: Dynamic Uncertaintiesmentioning

confidence: 99%

“…Other examples of Ito processes are the geometric Brownian motion with drift given in equation 21 and the geometric mean reverting process given in equation 22. Also, it has been shown that the relative volatility profile in Figure 18b can be represented by a geometric mean reverting process (47):…”

Section: Dynamic Uncertaintiesmentioning

confidence: 99%

“…The dynamic uncertainties in chemical processes (batch processes) could be represented by these Ito processes, depending on the character of uncertainty. For example, the thermodynamic uncertainties in batch processes were modeled using Ito processes and system nonidealities were easily distinguished (47). The parameters of the Ito process are estimated based on a regression analysis technique.…”

Section: Dynamic Uncertaintiesmentioning

confidence: 99%

“…To control trajectories in the face of time-dependent uncertainties, a stochastic maximum principle formulation was developed based on real options theory and using a class of stochastic processes called Ito processes (51,138). By using this methodology, thermodynamic model uncertainties in batch distillation were characterized and stochastic optimal control profiles were computed (47,51,139). Sampling techniques and stochastic modeling approaches were used to characterize, quantify, and propagate uncertainties.…”

Section: Process Operationmentioning

confidence: 99%

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Sampling Techniques

Diwekar

Ulas

2007

Kirk-Othmer Encyclopedia of Chemical Technology

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Sampling is a statistical procedure that involves the selection of a finite number of individuals to represent and infer some knowledge about a population of concern. Sampling techniques are used in a wide range of science and engineering applications; they are of basic importance in computational statistics, in the implementation of probabilistic algorithms, and in related problems of statistical computing that have a stochastic ingredient (eg, financial modeling, artificial intelligence, computational chemistry, risk and uncertainty analysis, and design of experiments). This article is devoted to the role of sampling in process systems engineering.

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Section: Dynamic Uncertaintiesmentioning

confidence: 99%

Section: Dynamic Uncertaintiesmentioning

confidence: 99%

Section: Dynamic Uncertaintiesmentioning

confidence: 99%

Section: Process Operationmentioning

confidence: 99%

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Sampling Techniques

Diwekar

Ulas

2007

Kirk-Othmer Encyclopedia of Chemical Technology

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“…Such an approach has been successfully used in various fields. For instance, in engineering, Ulas and Diwekar [7] addressed thermodynamics uncertainties in the batch separation process. Diwekar's group members use this method to obtain optimal temperature profiles for both crystallization [8] and biodiesel production in batch reactors [9,10]; in the area of ecology, the approach was used to establish optimal guidelines and strategies for pH control in lakes [11] and ecosystem management [12]; whereas in medicine, the stochastic maximum principle was used for predicting optimal drug dosage in both insulin-dependent diabetic patients [13] and in the superovulation stage of in vitro fertilization [14].…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Solving Stochastic Optimal Control Problems

et al. 2019

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A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle.

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Sampling Techniques

Acikgoz

Diwekar

2017

Kirk-Othmer Encyclopedia of Chemical Technology

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Sampling is a statistical procedure used for uncertainty analysis and stochastic modeling in many applications related to process design, operation, control and optimization. The increased efforts for pollution prevention and sustainability necessitate a more contemporary approach for process design, in which objectives such as reducing environmental and health impacts, increasing reliability, safety and controllability, reducing risk and achieving better profitability are considered simultaneously. In this multifaceted approach to process design and operation, uncertainties need to be considered and included in process models and simulations. These uncertainties can be static or dynamic. A review of sampling techniques such as Monte Carlo sampling, importance sampling, Latin Hypercube Sampling (LHS) and Hammersley Sequence Sampling (HSS) are provided here. These sampling techniques have a wide range of use in chemical and process synthesis, process scheduling, supply chain management, process control and reliability as well as risk management. Apart from uncertainty analysis, sampling and sampling accuracy plays an important role in discrete, stochastic, and multi‐objective optimization algorithms. This review also describes the recent developments in this area. In addition, future trends in process design and sampling techniques are also presented.

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Thermodynamic uncertainties in batch processing and optimal control

Cited by 26 publications

References 12 publications

Sampling Techniques

Sampling Techniques

A New Approach to Solving Stochastic Optimal Control Problems

Sampling Techniques

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