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Flexibility Index of Black-Box Models with Parameter Uncertainty through Derivative-Free Optimization
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  • Fei Zhao,
  • Ignacio Grossmann,
  • Salvador García Muñoz,
  • Stephen Stamatis
Fei Zhao
Carnegie Mellon University

Corresponding Author:[email protected]

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Ignacio Grossmann
Carnegie Mellon University
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Salvador García Muñoz
Eli Lilly and Company
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Stephen Stamatis
Eli Lilly and Company
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The existing methods of flexibility index are mainly based on mixed-integer linear or nonlinear programming methods, making it difficult to readily deal with complex mathematical models. In this article, a novel solution strategy is proposed for finding a reliable upper bound of the flexibility index where the process model is implemented in a black box that can be directly executed by a commercial simulator, and also avoiding the need for calculating derivatives. Then, the flexibility index problem is formulated as a sequence of univariate derivative-free optimization (DFO) models. An external DFO solver based on trust-region methods can be called to solve this model. Finally, after calculating the critical point of the model parameters, the vertex enumeration method and two gradient approximation methods are proposed to evaluate the impact of process parameters and to evaluate the flexibility index. A reaction model is studied to show the efficiency of the proposed algorithm.
10 Oct 2020Submitted to AIChE Journal
11 Oct 2020Submission Checks Completed
11 Oct 2020Assigned to Editor
19 Oct 2020Reviewer(s) Assigned
16 Nov 2020Editorial Decision: Revise Major
15 Dec 20201st Revision Received
17 Dec 2020Submission Checks Completed
17 Dec 2020Assigned to Editor
20 Dec 2020Reviewer(s) Assigned
31 Dec 2020Editorial Decision: Accept
18 Jan 2021Published in AIChE Journal. 10.1002/aic.17189