Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

doi:10.1016/j.cjche.2020.03.007

中国化学工程学报 ›› 2020, Vol. 28 ›› Issue (6): 1637-1651.DOI: 10.1016/j.cjche.2020.03.007

• Process Systems Engineering and Process Safety • 上一篇下一篇

Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

Feiran Sun^1,2, Tao Liu^1,2, Yi Cao³, Xiongwei Ni⁴, Zoltan Kalman Nagy⁵

1 Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China;
2 School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China;
3 College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China;
4 School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, UK;
5 Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States

收稿日期:2019-11-10 修回日期:2020-02-12 出版日期:2020-06-28 发布日期:2020-07-29
通讯作者: Tao Liu

Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

Feiran Sun^1,2, Tao Liu^1,2, Yi Cao³, Xiongwei Ni⁴, Zoltan Kalman Nagy⁵

1 Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China;
2 School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China;
3 College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China;
4 School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, UK;
5 Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States

Received:2019-11-10 Revised:2020-02-12 Online:2020-06-28 Published:2020-07-29
Contact: Tao Liu

摘要/Abstract

摘要： In this paper, a cell average technique (CAT) based parameter estimation method is proposed for cooling crystallization involved with particle growth, aggregation and breakage, by establishing a more efficient and accurate solution in terms of the automatic differentiation (AD) algorithm. To overcome the deficiency of CAT that demands high computation cost for implementation, a set of ordinary differential equations (ODEs) entailed from CAT based discretized population balance equation (PBE) are solved by using the AD based high-order Taylor expansion. Moreover, an AD based trust-region reflective (TRR) algorithm and another interior-point (IP) algorithm are established for estimating the kinetic parameters associated with particle growth, aggregation and breakage. As a result, the estimation accuracy can be further improved while the computation cost can be significantly reduced, compared to the existing algorithms. Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT, TRR and IP algorithms in comparison with the existing algorithms. Moreover, seeded batch cooling crystallization experiments of β form L-glutamic acid are performed to validate the proposed method.

关键词: Cooling crystallization, Population balance model, Cell average technique, Parameter estimation, Automatic differentiation

Abstract: In this paper, a cell average technique (CAT) based parameter estimation method is proposed for cooling crystallization involved with particle growth, aggregation and breakage, by establishing a more efficient and accurate solution in terms of the automatic differentiation (AD) algorithm. To overcome the deficiency of CAT that demands high computation cost for implementation, a set of ordinary differential equations (ODEs) entailed from CAT based discretized population balance equation (PBE) are solved by using the AD based high-order Taylor expansion. Moreover, an AD based trust-region reflective (TRR) algorithm and another interior-point (IP) algorithm are established for estimating the kinetic parameters associated with particle growth, aggregation and breakage. As a result, the estimation accuracy can be further improved while the computation cost can be significantly reduced, compared to the existing algorithms. Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT, TRR and IP algorithms in comparison with the existing algorithms. Moreover, seeded batch cooling crystallization experiments of β form L-glutamic acid are performed to validate the proposed method.

Key words: Cooling crystallization, Population balance model, Cell average technique, Parameter estimation, Automatic differentiation

Feiran Sun, Tao Liu, Yi Cao, Xiongwei Ni, Zoltan Kalman Nagy. Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation[J]. 中国化学工程学报, 2020, 28(6): 1637-1651.

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Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

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