Stochastic Back-Off Approach for Integration of Design and Control Under Uncertainty

Rafiei, Mina; Ricardez‐Sandoval, Luis A.

doi:10.1021/acs.iecr.7b03935

Cited by 45 publications

(34 citation statements)

References 49 publications

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“…The back‐off approach featured with PSEs was introduced earlier by our group . The approach is a sequential approximate optimization method in which the system is evaluated around the worst‐case variability expected in process outputs.…”

Section: Methodsmentioning

confidence: 99%

“…The method mostly traces the closest feasible and near‐optimal solution to the initial steady‐state condition considering the worst‐case scenario. In our previous works, we have defined a priori an adequate (trust) region and thus a fixed search space for the PSE‐based optimization problem at each iteration . In the current approach, a surrogate model (PSE) has been used to approximate the actual model behavior of the process and alleviate the intense computational demands.…”

Section: Methodsmentioning

confidence: 99%

“…Function evaluations for the forward ( η + ) and backward ( η − ) points around the nominal condition ( η nom ) are used to calculate gradients as follows:

{\frac{\partial g_{s}}{\partial η_{p}} |}_{t_{w c}, ζ_{j}} = true(g_{s} true(η_{p}^{+} true) {| t_{w c}, ζ_{j} - g_{s} (η_{p}^{-}) |}_{t_{w c}, ζ_{j}} true) / 2 Δ η_{p}

{\frac{\partial^{2} g_{s}}{\partial η_{p} \partial η_{p}} |}_{t_{w c}, ζ_{j}} = true({g_{s} true(η_{p}^{+} true) |}_{t_{w c}, ζ_{j}} - 2 g_{s} true(η_{p_{n o m}} true) {| t_{w c}, ζ_{j} + g_{s} (η_{p}^{-} true) |}_{t_{w c}, ζ_{j}} true) / Δ η_{p}^{2}

where Δ η p is the finite difference step used to calculate forward and backward points of p th decision variable, that is,

normalΔ η_{p} bold-italic= η_{p_{italicnom}} ((), normalΔ η)

. Further details of the numerical and also analytical sensitivity calculations can be found in our previous works . Once the numerical sensitivities of cost function and constraints with regard to all decision variables have been identified, we examine the quality of the constructed PSE as a primary PSE check.…”

Section: Methodsmentioning

confidence: 99%

“…Table B1 in Appendix B provides the model equations as well as the cost function and the process constraints that determine the feasible operating region for this process. The model parameters and their corresponding nominal values can be found elsewhere . The disturbance profile comprises step changes in the inlet flow rate ( q i ) that happen at multiple time intervals (i.e., every 10 hr).…”

Section: Illustrative Case Study: Wastewater Treatment Plantmentioning

confidence: 99%

“…Kookos et al imposed back‐off terms on constraints to generate tighter upper and lower bounds for simultaneous consideration of design and control. Recently, we have developed a back‐off formulation using PSEs . The proposed back‐off method focuses on searching for the optimal design and control parameters by solving a set of optimization problems using PSE functions.…”

Section: Introductionmentioning

confidence: 99%

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A trust‐region framework for integration of design and control

Rafiei

Ricardez‐Sandoval

2020

AIChE Journal

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A trust‐region approach is presented to address the simultaneous design and control of large‐scale systems under uncertainty. The key idea is to represent the system using power series expansions (PSEs) as piecewise models in an iterative manner while the validity of those expansions is certified in a trusted region. The mean of squared errors is used as a metric to quantify the accuracy of the PSE approximations. Identified search regions specify the boundaries of the decision variables for the PSE‐based optimization problems. The proposed algorithm shows a significant accomplishment in locating dynamically feasible and near‐optimal design and operating conditions. The proposed approach was tested in a wastewater treatment plant and the Tennessee Eastman process. The results indicate that the proposed methodology leads to more economically attractive and reliable designs while maintaining the dynamic operability of the system in the presence of disturbances and uncertainty.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Function evaluations for the forward ( η + ) and backward ( η − ) points around the nominal condition ( η nom ) are used to calculate gradients as follows:

{\frac{\partial g_{s}}{\partial η_{p}} |}_{t_{w c}, ζ_{j}} = true(g_{s} true(η_{p}^{+} true) {| t_{w c}, ζ_{j} - g_{s} (η_{p}^{-}) |}_{t_{w c}, ζ_{j}} true) / 2 Δ η_{p}

{\frac{\partial^{2} g_{s}}{\partial η_{p} \partial η_{p}} |}_{t_{w c}, ζ_{j}} = true({g_{s} true(η_{p}^{+} true) |}_{t_{w c}, ζ_{j}} - 2 g_{s} true(η_{p_{n o m}} true) {| t_{w c}, ζ_{j} + g_{s} (η_{p}^{-} true) |}_{t_{w c}, ζ_{j}} true) / Δ η_{p}^{2}

where Δ η p is the finite difference step used to calculate forward and backward points of p th decision variable, that is,

normalΔ η_{p} bold-italic= η_{p_{italicnom}} ((), normalΔ η)

Section: Methodsmentioning

confidence: 99%

Section: Illustrative Case Study: Wastewater Treatment Plantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A trust‐region framework for integration of design and control

Rafiei

Ricardez‐Sandoval

2020

AIChE Journal

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Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

2022

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In the mid‐1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open‐loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

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A two‐step coordinated optimization model for a dewatering process

Zhang

Wang

et al. 2020

Can J Chem Eng

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In actual production processes, the feed mass of a dewatering process is uncertain and a future production state cannot be predicted. This results in improper operation, a substandard production index, and a high energy economic index (EEI). To solve these problems, the authors propose a two-step coordinated optimization model for the dewatering process based on production data. The prediction model of the dewatering process is first established using the data accumulated during production. A two-step optimization model is then established to solve the problems existing in the dewatering process. The objective of the optimization is to minimize the EEI in the dewatering process, and the constraints are the ladder electricity price, operation safety, and production index. The genetic algorithm (GA) and gravitational search algorithm-genetic algorithm (GSA-GA) are used to solve the two-step coordinated optimization model, and the computational time can meet the application demand. An offline simulation and a field application showed that the optimization model can be used to improve the production index and reduce the EEI, loss due to the filter cloth, and the frequency of abnormal production.

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Stochastic Back-Off Approach for Integration of Design and Control Under Uncertainty

Cited by 45 publications

References 49 publications

A trust‐region framework for integration of design and control

A trust‐region framework for integration of design and control

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

A two‐step coordinated optimization model for a dewatering process

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