1.华东理工大学国家盐湖资源综合利用工程技术研究中心,上海 200237
2.华东理工大学资源过程工程教育部 工程研究中心,上海 200237
闫艺航 (2002—),男,博士研究生,yanyihang1@163.com
刘程琳 (1986—),男,博士,副教授,liuchenglin@ecust.edu.cn
于建国 (1960—),男,博士,教授,jgyu@ecust.edu.cn
收稿:2025-11-22,
修回:2026-01-13,
纸质出版:2026-05-25
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闫艺航, 马渊, 刘程琳, 于建国. 机器学习在结晶过程建模与控制中的研究进展[J]. 化工学报, 2026, 77(5): 2307-2321
YAN Yihang, MA Yuan, LIU Chenglin, YU Jianguo. Recent advances in machine learning for modeling and control of crystallization processes[J]. CIESC Journal, 2026, 77(5): 2307-2321
闫艺航, 马渊, 刘程琳, 于建国. 机器学习在结晶过程建模与控制中的研究进展[J]. 化工学报, 2026, 77(5): 2307-2321 DOI: 10.11949/0438-1157.20251297.
YAN Yihang, MA Yuan, LIU Chenglin, YU Jianguo. Recent advances in machine learning for modeling and control of crystallization processes[J]. CIESC Journal, 2026, 77(5): 2307-2321 DOI: 10.11949/0438-1157.20251297.
结晶是化工、制药、食品和材料等领域最重要的固液分离操作单元,高质量结晶高度依赖于精准控制结晶温度、进料流率和溶剂组成等过程参数。传统基于机理和经验的建模与控制方法难以准确描述结晶体系的复杂非线性行为。近年来,机器学习凭借其强大的数据驱动特征提取与模式识别能力,为结晶过程的智能化研究提供了新的思路。通过系统梳理机器学习在结晶过程监测、预测建模与控制优化方面的主要进展,阐明了其在过程表征、模型精度提升及智能调控中的应用潜力,并对数据质量、模型泛化等问题及未来工业安全可靠应用进行了简要展望。
Crystallization is a fundamental solid-liquid separation operation in chemical
pharmaceutical
food and materials industries. Achieving high product quality requires precise control of critical process parameters such as temperature
feed rate and solvent composition. Conventional modeling and control strategies that rely on mechanistic formulations or empirical correlations often fail to represent the highly nonlinear and multiscale nature of crystallization systems. In recent years
machine learning
with its powerful data-driven feature extraction and pattern recognition capabilities
has provided new ideas for the intelligent research of crystallization processes. This review summarizes recent developments in machine learning enabled process monitoring
predictive modeling and control optimization for crystallization. The potential of these methods to enhance process characterization
improve model fidelity and support intelligent decision making is highlighted. Challenges related to data quality
model generalization and reliable industrial deployment are also discussed.
Lu J , Rohani S . Polymorphism and crystallization of active pharmaceutical ingredients (APIs) [J ] . Current Medicinal Chemistry , 2009 , 16 ( 7 ): 884 - 905 .
Chen J , Sarma B , Evans J M B , et al . Pharmaceutical crystallization [J ] . Crystal Growth & Design , 2011 , 11 ( 4 ): 887 - 895 .
Kandaswamy A , Schwaminger S P . Machine learning methods to improve crystallization through the prediction of solute-solvent interactions [J ] . Crystals , 2024 , 14 ( 6 ): 501 .
Ulrich J , Frohberg P . Problems, potentials and future of industrial crystallization [J ] . Frontiers of Chemical Science and Engineering , 2013 , 7 ( 1 ): 1 - 8 .
Xiouras C , Cameli F , Quilló G L , et al . Applications of artificial intelligence and machine learning algorithms to crystallization [J ] . Chemical Reviews , 2022 , 122 ( 15 ): 13006 - 13042 .
Lu M J , Rao S L , Yue H , et al . Recent advances in the application of machine learning to crystal behavior and crystallization process control [J ] . Crystal Growth & Design , 2024 , 24 ( 12 ): 5374 - 5396 .
Lima F A R D , de Moraes M G F , Barreto A G , et al . Applications of machine learning for modeling and advanced control of crystallization processes: developments and perspectives [J ] . Digital Chemical Engineering , 2025 , 14 : 100208 .
Gao Y , Zhang T , Ma Y M , et al . Application of PAT-based feedback control approaches in pharmaceutical crystallization [J ] . Crystals , 2021 , 11 ( 3 ): 221 .
Schweidtmann A M , Zhang D D , Von Stosch M . A review and perspective on hybrid modeling methodologies [J ] . Digital Chemical Engineering , 2024 , 10 : 100136 .
Esposito F , Di Caprio U , Buzzi S , et al . Hybrid modelling approaches in process intensification: a thorough review [J ] . Chemical Engineering and Processing: Process Intensification , 2025 , 217 : 110496 .
Torraca J R , Capron B D O , Secchi A R . A robust deep reinforcement learning approach for the control of crystallization processes [J ] . Computers & Chemical Engineering , 2025 , 199 : 109114 .
Su Q L , Ganesh S , Moreno M , et al . A perspective on quality-by-control (QbC) in pharmaceutical continuous manufacturing [J ] . Computers & Chemical Engineering , 2019 , 125 : 216 - 231 .
Zhang F K , Du K , Guo L Y , et al . Progress, problems, and potential of technology for measuring solution concentration in crystallization processes [J ] . Measurement , 2022 , 187 : 110328 .
Jong C Y , Tristan G , Felix L J J , et al . Systematic assessment of calibration strategies in spectroscopic analysis: a case study of paracetamol crystallization [J ] . Organic Process Research & Development , 2025 , 29 ( 2 ): 503 - 520 .
Griffin D J , Grover M A , Kawajiri Y , et al . Robust multicomponent IR-to-concentration model regression [J ] . Chemical Engineering Science , 2014 , 116 : 77 - 90 .
Saleemi A N , Rielly C D , Nagy Z K . Monitoring of the combined cooling and antisolvent crystallisation of mixtures of aminobenzoic acid isomers using ATR-UV/Vis spectroscopy and FBRM [J ] . Chemical Engineering Science , 2012 , 77 : 122 - 129 .
Agimelen O S , Hamilton P , Haley I , et al . Estimation of particle size distribution and aspect ratio of non-spherical particles from chord length distribution [J ] . Chemical Engineering Science , 2015 , 123 : 629 - 640 .
Li M Z , Wilkinson D . Determination of non-spherical particle size distribution from chord length measurements (Part 1): Theoretical analysis [J ] . Chemical Engineering Science , 2005 , 60 ( 12 ): 3251 - 3265 .
Szilágyi B , Nagy Z K . Aspect ratio distribution and chord length distribution driven modeling of crystallization of two-dimensional crystals for real-time model-based applications [J ] . Crystal Growth & Design , 2018 , 18 ( 9 ): 5311 - 5321 .
Irizarry R , Chen A T , Crawford R , et al . Data-driven model and model paradigm to predict 1D and 2D particle size distribution from measured chord-length distribution [J ] . Chemical Engineering Science , 2017 , 164 : 202 - 218 .
Neuendorf L , Höving S , Bennemann L , et al . Detecting crystals in suspensions: convolutional neural networks vs . gravity-based approach for size distribution detection [J ] . Chemie Ingenieur Technik , 2023 , 95 ( 7 ): 1146 - 1153 .
He K M , Gkioxari G , Dollar P , et al . Mask R-CNN [J ] . IEEE Transactions on Pattern Analysis and Machine Intelligence , 2020 , 42 ( 2 ): 386 - 397 .
Zong S L , Zhou G Z , Li M , et al . Deep learning-based on-line image analysis for continuous industrial crystallization processes [J ] . Particuology , 2023 , 74 : 173 - 183 .
Gao Z G , Wu Y Y , Bao Y , et al . Image analysis for in-line measurement of multidimensional size, shape, and polymorphic transformation of l-glutamic acid using deep learning-based image segmentation and classification [J ] . Crystal Growth & Design , 2018 , 18 ( 8 ): 4275 - 4281 .
Mangin D , Puel F , Veesler S . Polymorphism in processes of crystallization in solution: a practical review [J ] . Organic Process Research & Development , 2009 , 13 ( 6 ): 1241 - 1253 .
Pindelska E , Sokal A , Kolodziejski W . Pharmaceutical cocrystals, salts and polymorphs: advanced characterization techniques [J ] . Advanced Drug Delivery Reviews , 2017 , 117 : 111 - 146 .
Févotte G . In situ Raman spectroscopy for in-line control of pharmaceutical crystallization and solids elaboration processes: a review [J ] . Chemical Engineering Research and Design , 2007 , 85 ( 7 ): 906 - 920 .
Braun D E , Maas S G , Zencirci N , et al . Simultaneous quantitative analysis of ternary mixtures of d-mannitol polymorphs by FT-Raman spectroscopy and multivariate calibration models [J ] . International Journal of Pharmaceutics , 2010 , 385 ( 1/2 ): 29 - 36 .
Barmpalexis P , Karagianni A , Nikolakakis I , et al . Artificial neural networks (ANNs) and partial least squares (PLS) regression in the quantitative analysis of cocrystal formulations by Raman and ATR-FTIR spectroscopy [J ] . Journal of Pharmaceutical and Biomedical Analysis , 2018 , 158 : 214 - 224 .
Salami H , McDonald M A , Bommarius A S , et al . In situ imaging combined with deep learning for crystallization process monitoring: application to cephalexin production [J ] . Organic Process Research & Development , 2021 , 25 ( 7 ): 1670 - 1679 .
Yao T , Liu J , Wan X X , et al . Deep-learning based in situ image monitoring crystal polymorph and size distribution: modeling and validation [J ] . AIChE Journal , 2024 , 70 ( 2 ): e18279 .
Jiao T Z , Guo C P , Feng X Y , et al . A comprehensive survey on deep learning multi-modal fusion: methods, technologies and applications [J ] . Computers , Materials & Continua, 2024 , 80 ( 1 ).
Tang Q , Liang J , Zhu F Q . A comparative review on multi-modal sensors fusion based on deep learning [J ] . Signal Processing , 2023 , 213 : 109165 .
Strelet E , Castillo I , Peng Y , et al . Data fusion: integrating heterogeneous information sources in the chemical processing industry [J ] . Journal of Chemometrics , 2025 , 39 ( 11 ): e70075 .
Ali H , Safdar R , Liu J F , et al . Hybrid fusion paradigm in advanced process monitoring: a panoramic review and future perspectives [J ] . Industrial & Engineering Chemistry Research , 2025 , 64 ( 47 ): 22465 - 22514 .
Woinaroschy A , Isopescu R , Filipescu L . Crystallization process optimization using artificial neural networks [J ] . Chemical Engineering & Technology , 1994 , 17 ( 4 ): 269 - 272 .
Vasanth Kumar K , Martins P , Rocha F . Modelling of the batch sucrose crystallization kinetics using artificial neural networks: comparison with conventional regression analysis [J ] . Industrial & Engineering Chemistry Research , 2008 , 47 ( 14 ): 4917 - 4923 .
Ma S Y , Li C , Gao J , et al . Artificial neural network prediction of metastable zone widths in reactive crystallization of lithium carbonate [J ] . Industrial & Engineering Chemistry Research , 2020 , 59 ( 16 ): 7765 - 7776 .
Ma Y M , Li W , Yang H Y , et al . Digital design of cooling crystallization processes using a machine learning-based strategy [J ] . Industrial & Engineering Chemistry Research , 2024 , 63 ( 46 ): 20236 - 20251 .
Zheng Y Z , Wang X N , Wu Z . Machine learning modeling and predictive control of the batch crystallization process [J ] . Industrial & Engineering Chemistry Research , 2022 , 61 ( 16 ): 5578 - 5592 .
Zheng Y Z , Zhao T Y , Wang X N , et al . Online learning-based predictive control of crystallization processes under batch-to-batch parametric drift [J ] . AIChE Journal , 2022 , 68 ( 11 ): e17815 .
郝建华 . 基于深度学习的时间序列预测算法研究 [D ] . 济南 : 山东师范大学 , 2024 .
Hao J H . Research on time series forecasting algorithms based on deep learning [D ] . Jinan : Shandong Normal University , 2024 .
Wu Z , Christofides P D , Wu W L , et al . A tutorial review of machine learning-based model predictive control methods [J ] . Reviews in Chemical Engineering , 2025 , 41 ( 4 ): 359 - 400 .
Zhu Y Q , Zhang C , Zhang R D , et al . Design of model fusion learning method based on deep bidirectional GRU neural network in fault diagnosis of industrial processes [J ] . Chemical Engineering Science , 2025 , 302 : 120884 .
Boskabadi M R , Murugaiah M , Nielsen T R , et al . Virtual sensor for sustainable large-scale process monitoring [J ] . Industrial & Engineering Chemistry Research , 2025 , 64 ( 7 ): 3902 - 3917 .
Lima F A R D , de Miranda G F M , de Moraes M G F , et al . A recurrent neural networks-based approach for modeling and control of a crystallization process [J ] . Computer Aided Chemical Engineering , 2022 , 51 : 1423 - 1428 .
Lima F A R D , de Moraes M G F , Secchi A R , et al . Development of a recurrent neural networks-based NMPC for controlling the concentration of a crystallization process [J ] . Digital Chemical Engineering , 2022 , 5 : 100052 .
An N , Kwon H , Cho H , et al . Data-driven modeling for magma density in the continuous crystallization process [J ] . Computer Aided Chemical Engineering , 2022 , 49 : 1813 - 1818 .
Lim B , Zohren S . Time-series forecasting with deep learning: a survey [J ] . Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , 2021 , 379 ( 2194 ): 20200209 .
Sitapure N , Kwon J S I . Exploring the potential of time-series transformers for process modeling and control in chemical systems: an inevitable paradigm shift [J ] . Chemical Engineering Research and Design , 2023 , 194 : 461 - 477 .
Sitapure N , Kwon J S I . CrystalGPT: enhancing system-to-system transferability in crystallization prediction and control using time-series-transformers [J ] . Computers & Chemical Engineering , 2023 , 177 : 108339 .
Cabral T O , Bagheri A , Pourkargar D B . Learning-based model reduction and predictive control of an ammonia synthesis process [J ] . Industrial & Engineering Chemistry Research , 2024 , 63 ( 23 ): 10325 - 10342 .
Lin T Y , Wang Y X , Liu X Y , et al . A survey of transformers [J ] . AI Open , 2022 , 3 : 111 - 132 .
Flanagan A R , Dalal D , Glavin F G . Exploring generative artificial intelligence and data augmentation techniques for spectroscopy analysis [J ] . Chemical Reviews , 2025 , 125 ( 13 ): 6130 - 6155 .
Li M Y , Yao T , Liu J , et al . Deep learning-based in situ micrograph synthesis and augmentation for crystallization process image analysis [J ] . Mathematics , 2024 , 12 ( 22 ): 3448 .
Zeng W . Image data augmentation techniques based on deep learning: a survey [J ] . Mathematical Biosciences and Engineering , 2024 , 21 ( 6 ): 6190 - 6224 .
Arce Munoz S , Pershing J , Hedengren J D . Physics-informed transfer learning for process control applications [J ] . Industrial & Engineering Chemistry Research , 2024 , 63 ( 49 ): 21432 - 21443 .
Zhao S Y , Yang H Y , Kareck T L , et al . Data-driven fault detection and diagnosis in industrial process systems: a systematic review and perspective [J ] . Reliability Engineering & System Safety , 2025 : 112159 .
Gan C Y , Wang L Y , Xiao S K , et al . Feedback control of crystal size distribution for cooling batch crystallization using deep learning-based image analysis [J ] . Crystals , 2022 , 12 ( 5 ): 570 .
Wang L Y , Zhu Y L , Gan C Y . Predictive control of particle size distribution of crystallization process using deep learning based image analysis [J ] . AIChE Journal , 2022 , 68 ( 11 ): e17817 .
Wang L Y , Zhu Y L . Neural-network-based nonlinear model predictive control of multiscale crystallization process [J ] . Processes , 2022 , 10 ( 11 ): 2374 .
de Moraes M G F , Lima F A R D , Lage P L D C , et al . Modeling and predictive control of cooling crystallization of potassium sulfate by dynamic image analysis: exploring phenomenological and machine learning approaches [J ] . Industrial & Engineering Chemistry Research , 2023 , 62 ( 24 ): 9515 - 9532 .
Vrban I , Bolf N , Sacher J B . Data-driven prediction of crystal size metrics using LSTM networks and in situ microscopy in seeded cooling crystallization [J ] . Processes , 2025 , 13 ( 6 ): 1860 .
吴毓强 . 数据驱动的物理学动力方程辨识方法与应用研究 [D ] . 武汉 : 华中科技大学 , 2025 .
Wu Y Q . Research on Data-driven identification of dynamical equations in physics: methods and applications [D ] . Wuhan : Huazhong University of Science and Technology , 2025 .
Schmidt M , Lipson H . Distilling free-form natural laws from experimental data [J ] . Science , 2009 , 324 ( 5923 ): 81 - 85 .
Brunton S L , Proctor J L , Kutz J N . Discovering governing equations from data by sparse identification of nonlinear dynamical systems [J ] . Proceedings of the National Academy of Sciences , 2016 , 113 ( 15 ): 3932 - 3937 .
Lima F A R D , de Moraes M G F , Rebello C M , et al . Interpretable and uncertainty-aware machine learning for trustworthy prediction in batch crystallization [J ] . Chemical Engineering and Processing: Process Intensification , 2025 , 215 : 110350 .
Nyande B W , Nagy Z K , Lakerveld R . Data‐driven identification of crystallization kinetics [J ] . AIChE Journal , 2024 , 70 ( 5 ): e18333 .
Georgieva P , Meireles M J , de Azevedo S F . Knowledge-based hybrid modelling of a batch crystallisation when accounting for nucleation, growth and agglomeration phenomena [J ] . Chemical Engineering Science , 2003 , 58 ( 16 ): 3699 - 3713 .
Sitapure N , Kwon J S I . Introducing hybrid modeling with time-series-transformers: a comparative study of series and parallel approach in batch crystallization [J ] . Industrial & Engineering Chemistry Research , 2023 , 62 ( 49 ): 21278 - 21291 .
Raissi M , Perdikaris P , Karniadakis G E . Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations [J ] . Journal of Computational Physics , 2019 , 378 : 686 - 707 .
Wu G Q , Yion W T G , Dang K L N Q , et al . Physics-informed machine learning for MPC: application to a batch crystallization process [J ] . Chemical Engineering Research and Design , 2023 , 192 : 556 - 569 .
Wu G Q , Wu Z . Machine learning-based MPC of batch crystallization process using physics-informed RNNs [J ] . IFAC-PapersOnLine , 2023 , 56 ( 2 ): 2846 - 2851 .
Wang S F , Teng Y J , Perdikaris P . Understanding and mitigating gradient pathologies in physics-informed neural networks [J ] . SIAM Journal on Scientific Computing , 2021 , 43 ( 5 ): A3055 - A3081 .
Rackauckas C , Ma Y B , Martensen J , et al . Universal differential equations for scientific machine learning [J ] . arXiv preprint arXiv: 2001.04385 , 2020 .
Lima F A R D , Rebello C M , Costa E A , et al . Improved modeling of crystallization processes by universal differential equations [J ] . Chemical Engineering Research and Design , 2023 , 200 : 538 - 549 .
Ma Y M , Wu S G , Macaringue E G J , et al . Recent progress in continuous crystallization of pharmaceutical products: precise preparation and control [J ] . Organic Process Research & Development , 2020 , 24 ( 10 ): 1785 - 1801 .
Budimir Sacher J , Bolf N , Sejdić M . Batch cooling crystallization of a model system using direct nucleation control and high-performance in situ microscopy [J ] . Crystals , 2024 , 14 ( 12 ): 1079 .
Nagy Z K , Braatz R D . Advances and new directions in crystallization control [J ] . Annual Review of Chemical and Biomolecular Engineering , 2012 , 3 ( 1 ): 55 - 75 .
Chowdhury I J , Yusoff S H , Gunawan T S , et al . Analysis of model predictive control-based energy management system performance to enhance energy transmission [J ] . Energies , 2024 , 17 ( 11 ): 2595 .
Orehek J , Teslić D , Likozar B . Continuous crystallization processes in pharmaceutical manufacturing: a review [J ] . Organic Process Research & Development , 2021 , 25 ( 1 ): 16 - 42 .
Zheng Y Z , Wu Z . Predictive control of batch crystallization process using machine learning [J ] . IFAC-PapersOnLine , 2022 , 55 ( 7 ): 798 - 803 .
Lima F A R D , de Moraes M G F , Grover M A , et al . Neural network inverse model controllers for paracetamol unseeded batch cooling crystallization [J ] . Industrial & Engineering Chemistry Research , 2024 , 63 ( 45 ): 19613 - 19627 .
Wang L Y , Zhu Y L , Gan C Y . Nonlinear model predictive control of crystal size in batch cooling crystallization processes [J ] . Journal of Process Control , 2023 , 128 : 103020 .
Öner M , Montes F C C , Ståhlberg T , et al . Comprehensive evaluation of a data driven control strategy: experimental application to a pharmaceutical crystallization process [J ] . Chemical Engineering Research and Design , 2020 , 163 : 248 - 261 .
Sitapure N , Kwon J S I . Machine learning meets process control: unveiling the potential of LSTMc [J ] . AIChE Journal , 2024 , 70 ( 7 ): e18356 .
Lima F A R D , de Moraes M G F , Grover M A , et al . Controlling paracetamol unseeded batch crystallization with NMPC and inverse model [J ] . IFAC-PapersOnLine , 2024 , 58 ( 14 ): 31 - 36 .
Faria R R , Capron B D O , Secchi A R , et al . A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems [J ] . Engineering Applications of Artificial Intelligence , 2024 , 127 : 107256 .
Manee V , Baratti R , Romagnoli J A . Optimal strategies to control particle size and variance in antisolvent crystallization operations using deep RL [J ] . Chemical Engineering Transactions , 2021 , 86 : 943 - 948 .
Benyahia B , Anandan P D , Rielly C . Control of batch and continuous crystallization processes using reinforcement learning [M ] // Computer Aided Chemical Engineering . Amsterdam : Elsevier , 2021 , 50 : 1371 - 1376 .
Benyahia B , Anandan P D , Rielly C . Robust model-based reinforcement learning control of a batch crystallization process [C ] // 2021 9th International Conference on Systems and Control (ICSC) . IEEE , 2021 : 89 - 94 .
Manee V , Baratti R , Romagnoli J A . Learning to navigate a crystallization model with deep reinforcement learning [J ] . Chemical Engineering Research and Design , 2022 , 178 : 111 - 123 .
Anandan P D , Rielly C D , Benyahia B . Optimal control policies of a crystallization process using inverse reinforcement learning [M ] // Computer Aided Chemical Engineering . Amsterdam : Elsevier , 2022 , 51 : 1093 - 1098 .
Meng Q B , Anandan P D , Rielly C D , et al . Multi-agent reinforcement learning and RL-based adaptive PID control of crystallization processes [M ] ∥ Computer Aided Chemical Engineering . Amsterdam : Elsevier , 2023 , 52 : 1667 - 1672 .
Nievas N , Pages-Bernaus A , Bonada F , et al . Reinforcement learning for autonomous process control in industry 4.0: advantages and challenges [J ] . Applied Artificial Intelligence , 2024 , 38 ( 1 ): 2383101 .
Dogru O , Xie J Y , Prakash O , et al . Reinforcement learning in process industries: review and perspective [J ] . IEEE/CAA Journal of Automatica Sinica , 2024 , 11 ( 2 ): 283 - 300 .
Alginahi Y M , Sabri O , Said W . Reinforcement learning for industrial automation: a comprehensive review of adaptive control and decision-making in smart factories [J ] . Machines , 2025 , 13 ( 12 ): 1140 .
Devarakonda V S , Sun W , Tang X , et al . Recent advances in reinforcement learning for chemical process control [J ] . Processes , 2025 , 13 ( 6 ): 1791 .
Park J , Jung H , Kim J W , et al . Reinforcement learning for process control: review and benchmark problems [J ] . International Journal of Control, Automation and Systems , 2025 , 23 ( 1 ): 1 - 40 .
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