A journey from mechanistic to data-driven models in process engineering: dimensionality reduction, surrogate and hybrid approaches, and digital twins

Bizon, Katarzyna

doi:10.24425/cpe.2023.146726

Artykuł - szczegóły

Tytuł artykułu

A journey from mechanistic to data-driven models in process engineering: dimensionality reduction, surrogate and hybrid approaches, and digital twins

Autorzy

Bizon Katarzyna

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

DOI

10.24425/cpe.2023.146726

Warianty tytułu

Konferencja

24th Polish Conference of Chemical and Process Engineering, 13-16 June 2023, Szczecin, Poland. Guest editor: Prof. Rafał Rakoczy and 8th European Process Intensification Conference, 31.05–2.06.2023, Warsaw, Poland

Języki publikacji

Abstrakty

The study examines various approaches oriented towards conceptual and numerical reduction of firstprinciple models, data-driven methodologies for surrogate (black box) and hybrid (gray box) modeling, and addresses the prospect of using digital twins in chemical and process engineering. In the case of numerical reduction of mechanistic models, special attention is paid to methodologies in which simulation data are used to construct light but robust numerical models while preserving all the physics of the problem, yielding reduced-order data-driven but still white-box models. In addition to reviewing various methodologies and identifying their applications in chemical engineering, including industrial process engineering, as well as fundamental research, the study outlines associated problems and challenges, as well as the risks posed by the era of big data.

Słowa kluczowe

reduced-order model data-driven model surrogate model hybrid model digital twin

model o zmniejszonym rzędzie model oparty na danych model zastępczy model hybrydowy bliźniak cyfrowy

Wydawca

Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk

Czasopismo

Chemical and Process Engineering : New Frontiers

Rocznik

2023

Tom

Vol. 44, nr 3

Strony

art. no. e24

Opis fizyczny

Bibliogr. 109 poz., tab., wykr.

Twórcy

autor

Bizon Katarzyna

katarzyna.bizon@pk.edu.pl

Cracow University of Technology, Faculty of Chemical Engineering and Technology, Warszawska 24, 31-155 Kraków, Poland

Bibliografia

1. Ali W., Khan M.S., Qyyum M.A., Lee M., 2018. Surrogateassisted modeling and optimization of a natural-gas liquefaction plant. Comput. Chem. Eng., 118, 132–142. DOI: 10.1016/j.compchemeng.2018.08.003.
2. Angrisani G., Bizon K., Chirone R., Continillo G., Fusco G., Lombardi S., Marra F.S., Miccio F., Roselli C., Sasso M., Solimene R., Tariello F., Urciolo M., 2013. Development of a new concept solar-biomass cogeneration system. Energy Convers. Manage., 75, 552–560. DOI: 10.1016/j.enconman. 2013.06.042.
3. Appl C., Moser A., Baganz F., Hass V.C., 2020. Digital twins for bioprocess control strategy development and realization, In: Herwig C., Pörtner R., Möller J. (Eds.), Digital Twins. Advances in Biochemical Engineering/Biotechnology, 177, 63–94. Springer, Cham. DOI: 10.1007/10_2020_151. Aris R., 1976. How to get the most out of an equation without really trying. Educ. Chem. Eng., 10, 114–124.
4. Aris R., 1993. Ends and beginnings in the mathematical modelling of chemical engineering systems. Chem. Eng. Sci., 48, 2507–2517. DOI: 10.1016/0009-2509(93)80263-P.
5. Babanezhad M., Behroyan I., Nakhjiri A.T., Marjani A., Rezakazemi M., Shirazian S. 2020. High-performance hybrid modeling chemical reactors using differential evolution based fuzzy inference system. Sci. Rep., 10, 21304. DOI: 10.1038/s41598-020-78277-3.
6. Bárkányi Á, Chován T., Németh S., Abonyi J., 2021. Modelling for digital twins – potential role of surrogate models. Processes, 9, 476. DOI: 10.3390/pr9030476.
7. Bermejo-López A., Pereda-Ayo B., González-Marcos J.A., González-Velasco J.R., 2022. Simulation-based optimization of cycle timing for CO2 capture and hydrogenation with dual function catalyst. Catal. Today, 394–396, 314–324. DOI: 10.1016/j.cattod.2021.08.023.
8. Bhosekar A., Ierapetritou M., 2018. Advances in surrogate based modeling, feasibility analysis, and optimization: A review. Comput. Chem. Eng., 108, 250–267. DOI: 10.1016/j.compchemeng.2017.09.017.
9. Biegler L.R., Lang Y.-D., Lin W., 2014. Multi-scale optimization for process systems engineering. Comput. Chem. Eng., 60, 17–30. DOI: 10.1016/j.compchemeng.2013.07.009.
10. Bizon K., 2016. Autothermicity, multiplicity, yield and selectivity of catalytic processes in a polytropic fluidized bed reactor. Chem. Eng. J., 288, 834–844. DOI: 10.1016/j.cej.2015.12.061.
11. Bizon K., 2017. Assessment of a POD method for the dynamical analysis of a catalyst pellet with simultaneous chemical reaction, adsorption and diffusion: Uniform temperature case. Comput. Chem. Eng., 97, 259–270. DOI: 10.1016/j.compchemeng.2016.11.009.
12. Bizon K., 2021. Application of pseudohomogeneous and heterogeneous models in assessing the behavior of a fluidized-bed catalytic reactor. Energies, 14, 208. DOI: 10.3390/en14010208.
13. Bizon K., Continillo G., 2012. Reduced order modelling of chemical reactors with recycle by means of POD-penalty method. Comput. Chem. Eng., 39, 22–32. DOI: 10.1016/j.compchemeng.2011.10.001.
14. Bizon K., Continillo G., 2021. Efficient optimization of a multifunctional catalytic fixed-bed reactor via reduced-order modeling approach. Chem. Eng. Res. Des., 165, 214–229. DOI: 10.1016/j.cherd.2020.11.007.
15. Bizon K., Continillo G., Berezowski M., Smuła-Ostaszewska J., 2012. Optimal model reduction by empirical spectral methods via sampling of chaotic orbits. Physica D: Nonlinear Phenom., 241, 1441–1449. DOI: 10.1016/j.physd.2012.05.004.
16. Bizon K., Continillo G., Lombardi S., Mancaruso E., Vaglieco B.M, 2014. ANN-based virtual sensor for on-line prediction of in-cylinder pressure in a Diesel engine. Comput. Aided Chem. Eng., 33, 763–768. DOI: 10.1016/B978-0-444-63456-6.50128-9.
17. Bizon K., Continillo G., Mancaruso E., Merola S.S., Vaglieco B.M., 2010. POD-based analysis of combustion images in optically accessible engines. Combust. Flame, 157, 632–640. DOI: 10.1016/j.combustflame.2009.12.013.
18. Bizon K., Continillo G., Mancaruso E., Vaglieco B.M., 2015. Application of RBF neural networks for real-time pressure prediction in a Diesel engine. Int. J. Eng. Technol., 4, 497–508. DOI: 10.14419/ijet.v4i4.4927.
19. Bizon K., Continillo G., Russo L., Smuła J., 2008. On POD reduced models of tubular reactor with periodic regimes. Comput. Chem. Eng., 32, 1305–1315. DOI: 10.1016/j.compchemeng.2007.06.004.
20. Bizon K., Skrzypek-Markiewicz K., Pędzich D., Reczek N., 2019. Intensification of catalytic processes through the pellet structuring: Steady-state properties of a bifunctional catalyst pellet applied to generic chemical reactions and the direct synthesis of DME. Catalysts, 9, 1020. DOI: 10.3390/catal9121020.
21. Bose A., Podmore R., Spanel U., 2023. Challenges in operator training: avoiding blackouts in the evolving power grid. IEEE Power Energy Mag., 21, 61–69. DOI: 10.1109/MPE.2023.3247045.
22. Bradley W., Kim J., Kilwein Z., Blakely L., Eydenberg M., Jalvin J., Laird C., Boukovala F., 2022. Perspectives on the integration between first-principles and data-driven modeling. Comput. Chem. Eng., 166, 107898. DOI: 10.1016/j.compchemeng.2022.107898.
23. Bremer J., Goyal P., Feng L., Benner P., Sundmacher K., 2017. POD-DEIM for efficient reduction of a dynamic 2D catalytic reactor model. Comput. Chem. Eng., 106, 777–784. DOI: 10.1016/j.compchemeng.2017.02.032.
24. Broomhead D.S., Lowe D., 1988. Multivariable functional interpolation and adaptive networks. Complex Syst., 2, 321–355.
25. Carranza-Abaid A., Svendsen H.F., Jakobsen J.P., 2020. Surrogate modelling of VLE: Integrating machine learning with thermodynamic constraints. Chem. Eng. Sci.: X, 8, 100080. DOI: 10.1016/j.cesx.2020.100080.
26. Chakrabarty A., Mannan S., Cagin T., 2016. Multiscale modeling for process safety applications. Butterworth-Heinemann, Oxford.
27. Chaturantabut S., Sorensen D.C., 2010. Non-linear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput., 32, 2737–2764. DOI: 10.1137/090766498.
28. Chen X., Kurdve M., Johansson B., Despeisse M., 2023. Enabling the twin transitions: Digital technologies support environmental sustainability through lean principles. Sustain. Prod. Consum., 38, 13–27. DOI: 10.1016/j.spc.2023.03.020.
29. Correia J.B., Abel M., Becker K., 2023. Data management in digital twins: a systematic literature review. Knowl. Inf. Syst. 65, 3165–3196. DOI: 10.1007/s10115-023-01870-1.
30. Coveney P.V., Dougherty E.R., Highfield R.R., 2016. Big data need big theory too. Phil. Trans. R. Soc. A, 374, 20160153. DOI: 10.1098/rsta.2016.0153.
31. Cutillo E.A., Petito G., Bizon K., Continillo G., 2023. Analysis of an innovative sampling strategy based on k-means clustering algorithm for POD and POD-DEIM reduced order models of a 2-D reaction-diffusion system. Combust. Theory Model, 27, 508–535. DOI: 10.1080/13647830.2023.2174451.
32. Danby S.J., Echekki, T., 2005. Proper orthogonal decomposition analysis of autoignition simulation data of nonhomogeneous hydrogen-air mixtures. Combust. Flame, 144, 126–138. DOI: 10.1016/j.combustflame.2005.06.014.
33. de Beer J., Depew C., 2021. The role of process engineering in the digital transformation. Comput. Chem. Eng., 154, 107423. DOI: 10.1016/j.compchemeng.2021.107423.
34. Dhoke C., Zaabout A., Cloete S., Amini S., 2021. Review on reactor configurations for adsorption-based CO2 capture. Ind. Eng. Res., 60, 3779–3798. DOI: 10.1021/acs.iecr.0c04547.
35. Druault P., Guibert P., Alizon F., 2005. Use of proper orthogonal decomposition for time interpolation from PIV data. Exp. Fluids, 39, 1009–1023. DOI: 10.1007/s00348-005-0035-3.
36. Fernandes F.A.N., Lona L.M.F., 2002. Heterogeneous modeling of fluidized bed polymerization reactors. Influence of mass diffusion into the polymer particle. Comput. Chem. Eng., 26, 841–848. DOI: 10.1016/S0098-1354(02)00010-8.
37. Ferreira J., Pedemonte M., Torres A.I., 2022. Development of a machine learning-based soft sensor for an oil refinery’s distillation column. Comput. Chem. Eng., 161, 107756. DOI: 10.1016/j.compchemeng.2022.107756.
38. Fischer K.L., Freund H., 2020. On the optimal design of load flexible fixed bed reactors: Integration of dynamics into the design problem. Chem. Eng. J., 393, 124722. DOI: 10.1016/j.cej.2020.124722.
39. Fogleman M., Lumley J., Rempfer D., Haworth D., 2004. Application of the proper orthogonal decomposition to datasets of internal combustion engine flows. J. Turbul., 5, N23. DOI: 10.1088/1468-5248/5/1/023.
40. Froment G.F., 1974. Analysis and design of fixed bed catalytic reactors, In: Bischoff K.B. (Ed.), Chemical Reaction Engineering. American Chemical Society, Washington, D.C., 1–55. DOI: 10.1021/ba-1972-0109.ch001.
41. Galeazzi A., Prifti K., Cortellini C., Di Pretoro A., Gallo F., Manenti F., 2023. Development of a surrogate model of an amine scrubbing digital twin using machine learning methods. Comput. Chem. Eng., 174, 108252. DOI: 10.1016/j.compchemeng. 2023.108252.
42. Graham M.D., Kevrekidis I.G., 1996. Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis. Comput. Chem. Eng., 20, 495–506. DOI: 10.1016/0098-1354(95)00040-2.
43. Hesthaven J.S., Gottlieb S., Gottlieb D., 2007. Spectral methods for time-dependent problems. Cambridge University Press, Cambridge. DOI: 10.1017/CBO9780511618352.
44. Holmes P., Lumley J.L., 1996. Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, Cambridge.
45. Hou C.K.J.., Behdinan. K., 2022. Dimensionality reduction in surrogate modeling: A review of combined methods. Data Sci. Eng., 7, 402–427. DOI: 10.1007/s41019-022-00193-5.
46. Jayaweera C., Groot N., Meul S., Verliefde A., Nopens I., Hitsov I., 2022. Development of a hybrid model for reliable predicting the thermal performance of direct contact counter-current cooling towers. Int. J. Heat Mass Transf., 197, 123336. DOI: 10.1016/j.ijheatmasstransfer.2022.123336.
47. Jo T., Koo B., Kim H., Lee D., Yoon J.Y., 2019. Effective sensor placement in a steam reformer using gappy proper orthogonal decomposition. Appl. Therm. Eng., 154, 419–432. DOI: 10.1016/j.applthermaleng.2019.03.089.
48. Karhunen K., 1947. Über lineare Methoden in der Wahrschein-lichkeitsrechnung. Ann. Acad. Sci. Fennicae, 37, 3–79.
49. Kerschen G., Feeny B.F., Golinval J.-C., 2003. On the exploitation of chaos to build reduced-order models. Comput. Methods Appl. Mech. Eng., 192, 1785–1795. DOI: 10.1016/S0045-7825(03)00206-8.
50. Kestering D., Agbleze S., Bispo H., Lima F.V., 2023. Model predictive control of power plant cycling using Industry 4.0 infrastructure. Digital Chem. Eng., 7, 100090. DOI: 10.1016/j.dche.2023.100090.
51. Kosambi D., 1943. Statistics in function space. J. Ind. Math. Soc., 7, 76–88.
52. Koulouris A., Misailidis N., Petrides D., 2021. Applications of process and digital twin models for production simulation and scheduling in the manufacturing of food ingredients and products. Food Bioprod. Process., 126, 317–333. DOI: 10.1016/j.fbp.2021.01.016.
53. Krippl M., Kargl T., Duerkop M., Dürauer A., 2021. Hybrid modeling reduces experimental effort to predict performance of serial and parallel single-pass tangential flow filtration. Sep. Purif. Technol., 276, 119277. DOI: 10.1016/j.seppur.2021.119277.
54. Kurtz L.A., Smith R.E., Parks C.L., Boney L.R., 1978. A comparison of the method of lines to finite difference techniques in solving time-dependent partial differential equations. Comput. Fluids, 6, 49–70. DOI: 10.1016/0045-7930(78)90007-5.
55. Kurzina I.A., Reshetinikov S.I., Karakchieva N.I., Kurina L.N., 2017. Direct synthesis of dimethyl ether from synthesis gas: Experimental study and mathematical modeling. Chem. Eng. J., 329, 135–141. DOI: 10.1016/j.cej.2017.04.132.
56. Li S., Duan G., Sakai M., 2022a. Development of a reducedorder model for large-scale Eulerian-Lagrangian simulations. Adv. Powder. Technol., 33, 103632. DOI: 10.1016/j.apt.2022.103632.
57. Li T., Duan G., Sakai M., 2022b. POD-based identification approach for powder mixing mechanism in Eulerian-Lagrangian simulations. Adv. Powder Technol., 33, 103364. DOI: 10.1016/j.apt.2021.11.016.
58. Li T., Han D., Yu B., Li J., Sun D., 2020. Study on a POD reduced-order model for steady-state flows in fractured porous media. Int. Commun. Heat Mass Transfer, 112, 104489. DOI: 10.1016/j.icheatmasstransfer.2020.104489.
59. Loève M., 1945. Fonctions aléatoires du second ordre. C. R. Acad. Sci., 220, 469.
60. Lunev A., Lauerer A., Zborovskii V., Léonard F., 2022. Digital twin of a laser flash experiment helps to assess the thermal performance of metal foams. Int. J. Therm. Sci., 181, 107743. DOI: 10.1016/j.ijthermalsci.2022.107743.
61. Ma X., Karniadakis G.E., Park H., Gharib M., 2002. DPIV/ T-driven convective heat transfer simulation. Int. J. Heat Mass Transfer, 45, 3517–3527. DOI: 10.1016/S0017-9310(02)00071-6.
62. Makrygiorgos G., Maggioni G.M., Mesbah A., 2020. Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models. Comput. Chem. Eng., 138, 106814. DOI: 10.1016/j.compchemeng.2020.106814.
63. Marra F.S., Bizon K., Continillo G., 2015. Fast predictive model for design and optimization of a low emissions biomass fueled CHP system. 23r d European Biomass Conference and Exhibition. Vienna, Austria, 1–4 June 2015.
64. Masoudi R., McPhee J., 2021. Application of Karhunen-Loéve decomposition and piecewise linearization to a physics-based battery model. Electrochim. Acta, 365, 137093. DOI: 10.1016/j.electacta.2020.137093.
65. Matsunami K., Miura T., Yaginuma K., Tanabe S., Badr S., Sugiyama H., 2023. Surrogate modeling of dissolution behavior toward efficient design of tablet manufacturing process. Comput. Chem. Eng., 171. 108141. DOI: 10.1016/j.compchemeng.2023.108141.
66. McKay A., Ghosh D., Zhu L., Xi L., Mhaskar P., 2022. A novel linear hybrid model predictive control design: application to a fed batch crystallization process. Digital Chem. Eng., 3, 100033. DOI: 10.1016/j.dche.2022.100033.
67. McLaughlin D., Bierling A., Mayerhöfer B., Schmid G., Thiele S., 2023. Digital twin of a hierarchical CO2 electrolyzer gas diffusion electrode. Adv. Funct. Mater., 33, 2212462. DOI: 10.1002/adfm.202212462.
68. McLean K.A.P., McAuley K.B., 2012. Mathematical modelling of chemical processes – obtaining the best model predictions and parameter estimates using identifiability and estimability procedures. Can. J. Chem. Eng., 90, 351–366. DOI:10.1002/cjce.20660.
69. Moghadam S.M.A., Loosen S.L., Meinke M., Schröder W., 2020. Reduced-order analysis of the acoustic near field of a ducted axial fan. Int. J. Heat Fluid Flow, 85, 108657. DOI: 10.1016/j.ijheatfluidflow.2020.108657.
70. Moioli E., 2022. Process intensification and energy transition: A necessary coupling? Chem. Eng. Process. Process Intensif., 179, 109097. DOI: 10.1016/j.cep.2022.109097.
71. Oztruk M., Dincer I., 2021. A comprehensive review on power-to-gas with hydrogen options for cleaner applications. Int. J. Hydrogen Energy, 46, 31511–31522. DOI: 10.1016/ j.ijhyd ene.2021.07.066.
72. Padhi R., Balakrishnan S.N., 2003. Proper orthogonal decom- position based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming. Neural Networks, 16, 719–728. DOI: 10.1016/S0893-6080(03)00131-X.
73. Palys M.J., Daoutidis P., 2022. Power-to-X: A review and perspective. Comput. Chem. Eng., 165, 107948. DOI: 10.1016/j.compchemeng.2022.107948.
74. Park H.M., Cho D.H., 1996. Low dimensional modelling of flow reactors. Int. J. Heat Mass Transfer, 39, 3311–3323. DOI: 10.1016/0017-9310(96)00038-5.
75. Patle D.S., Ahmad Z., Rangaiah G.P., 2014. Operator training simulators in the chemical industry: review, issues, and future directions. Rev. Chem. Eng. 30, 199–216. DOI: 10.1515/revce-2013-0027.
76. Pearson K., 1901. On lines and planes of closest fit to systems of points in space. Philos. Mag., 2, 559–572.
77. Pergam P., Briesen H., 2023. Reduced order modeling for compressible cake filtration process using proper orthogonal decomposition. Comput. Chem. Eng., 171, 108165. DOI: 10.1016/j.compchemeng.2023.108165.
78. Pinto J., Mestre M., Ramos J., Costa R.S., Striedner G.S., Oliveira R., 2022. A general deep hybrid model for bioreactors systems: Combining first principles with deep neural networks. Comput. Chem. Eng., 165, 107952. DOI: 10.1016/j.compchemeng.2022.107952.
79. Procacci A., Amaduzzi R., Coussement A., Parente A., 2023. Adaptive digital twins of combustion systems using sparse sensing strategies. Proc. Combust. Inst., 39, 4257–4266. DOI: 10.1016/j.proci.2022.07.029.
80. Rogers A.W., Song Z., Ramon F.V., Jing K., Zhang D., 2023. Investigation ‘greyness’ of hybrid model for bioprocess predictive modeling. Biochem. Eng. J., 190, 108761. DOI: 10.1016/j.bej.2022.108761.
81. Rout K.R., Jakobsen H.A., 2015. A numerical study of fixed bed reactor modelling for steam methane reforming process. Can. J. Chem. Eng., 93, 1222–1238. DOI: 10.1002/cjce.22202.
82. Sánchez-Contador M., Ateka A., Ibáñez, M., Bilbao, J., Aguayo A.T., 2019. Influence of the operating conditions on the behavior and deactivation of a CuO-ZnO-ZrO2@SAPO-11 core-shell-like catalyst in the direct synthesis of DME. Renew. Energy, 138, 585–597. DOI: 10.1016/j.renene.2019.01.093.
83. Sansana J., Joswiak M.N., Castillo I., Wang Z., Rendall R., Chiang L.H., Reis M.S., 2021. Recent trends on hybrid modeling for Industry 4.0. Comput. Chem. Eng., 151, 107365. DOI:10.1016/j.compchemeng.2021.107365.
84. Segala D.B., Naseradinmousavi P., 2017. On the inclusion of time derivatives of state variables for parametric model order reduction for a beam on a nonlinear foundation. J. Dyn. Sys. Meas. Control., 139, 081009. DOI: 10.1115/1.4035759.
85. Shoji K., Schudel S., Onwude D., Shirvastava C., Defraeye T., 2022. Mapping the postharvest life on imported fruits from packhouse to retail stores using physics-based digital twins. Resour. Conserv. Recycl., 176, 105914. DOI: 10.1016/j.resconrec.2021.105914.
86. Siddiqui M.S., Latif S.T.M., Saeed M., Rahman M., Badar A.W., Hasan S.M., 2020. Reduced order model of offshore wind turbine wake by proper orthogonal decomposition. Int. J. Heat Fluid Flow, 82, 108554. DOI: 10.1016/j.ijheatfluid flow.2020.108554.
87. Singh M., Fuenmayor E., Hinchy E.P., Qiao Y., Murray N., Devine D., 2021. Digital twin: Origin to future. Appl. Syst. Innov., 4, 36. DOI: 10.3390/asi4020036.
88. Sirisup S., Karniadakis G.E., 2005. Stability and accuracy of periodic flow solutions obtained by a POD-penalty method. Physica D: Nonlinear Phenom., 202, 218–237. DOI: 10.1016/j.physd.2005.02.006.
89. Sirovich L., 1987. Turbulence and the dynamics of coherent structures. I. Coherent structures. Quart. Appl. Math., 45, 561–590. DOI: 10.1090/qam/910462.
90. Studer S., Bui T.B., Drescher C., Hanuschkin A., Winkler L., Peters S., Müller K.-R., 2021. Towards CRISP-ML(Q): A machine learning process model with quality assurance methodology. Mach. Learn. Knowl. Extr., 3, 392–413. DOI: 10.3390/make3020020.
91. Styring P., Duckworth E.L., Platt E.G., 2021. Synthetic fuels in a transport transition: fuels to prevent a transport underclass. Front. Energy Res., 9, 707867. DOI: 10.3389/fenrg.2021.707867.
92. Sun Y., Yang J., Wang Y., Li Z., Ma Y., 2020. A POD reduced-order model for resolving the neutron transport problem of nuclear reactor. Ann. Nucl. Energy, 149, 107799. DOI: 10.1016/j.anucene.2020.107799.
93. Sun Z., West D.H., Balakotaiah V., 2019. Bifurcation analysis of catalytic partial oxidations in laboratory-scale packed-bed reactors with heat exchange. Chem. Eng. J., 377, 119765. DOI: 10.1016/j.cej.2018.08.151.
94. Swischuk R., Mainini L., Peherstorfer B., Willcox K., 2018. Projection-based model reduction: Formulations for physics-based machine learning. Comput. Fluids, 179, 704–717. DOI: 10.1016/j.compfluid.2018.07.021.
95. van Rooij F., Scarf P., Do P., 2021. Planning the restoration of membranes in RO desalination using a digital twin. Desalination, 519, 115214. DOI: 10.1016/j.desal.2021.115214.
96. Viggiano B., Skjæraasen O., Schümann H., Tutkun M., Cal R.B., 2018. Characterization of flow dynamics and re duce d-order description of experimental two-phase pipe flow. Int. J. Multiph. Flow, 105, 91–101. DOI: 10.1016/j.ijmultiphaseflow.2018. 03.020.
97. Villadsen J., Michelsen M.L., 1978. Solution of differential equation models by polynomial approximation. Prentice Hall, Englewood Cliffs.
98. Vinokur M., 1989. An analysis of finite-difference and finite- volume formulations of conservation laws. J. Comput. Phys., 81, 1–52. DOI: 10.1016/0021-9991(89)90063-6.
99. von Stosch M., Oliveira R., Peres J., de Azevedo S.F., 2014. Hybrid semiparametric modeling in process systems engineering: Past, present and future. Comput. Chem. Eng., 60, 86–101. DOI: 10.1016/j.compchemeng.2013.08.008.
100. Wang F., Song Y., Liu C., He A., Qiang T., 2023. Multiobjective optimal scheduling of laminar cooling water supply system for hot rolling mills driven by digital twin for energy-saving. J. Process Control, 122, 134–146. DOI: 10.1016/j.jprocont.2023.01.004.
101. Wang G.G., Shan S., 2007. Review on metamodeling techniques in support of engineering design optimization. J. Mech. Des., 129, 370–380. DOI: 10.1115/1.2429697.
102. Wang L.G., Ge R., Chen X., Zhou R., Chen H.-M., 2021. Multiscale digital twin for particle breakage in milling: From nanoindentation to population balance model. Powder Technol., 386, 247–261. DOI : 10.1016/j.powtec.2021.03.005.
103. Williams B., Cremaschi S., 2021. Selection of surrogate modeling techniques for surface approximation and surrogate-based optimization. Chem. Eng. Res. Des., 170, 76–89. DOI: 10.1016/j.cherd.2021.03.028.
104. Wright L., Davidson S., 2020. How to tell the difference between a model and a digital twin. Adv. Model. Simul. Eng. Sci., 7, 13. DOI: 10.1186/s40323-020-00147-4.
105. Xing L., Jiang H., Wang S., Pinfield V.J., Xuan J., 2023. Data-driven surrogate modelling and multi-variable optimization of trickle bed and packed bubble column reactors for CO2 capture via enhanced weathering. Chem. Eng. J., 454, 139997. DOI: 10.1016/j.cej.2022.139997.
106. Yang M., Armaou A., 2018. Revisiting APOD accuracy for non-linear control of transport reaction process: A spatially discrete approach. Chem. Eng. Sci., 181, 146-158. DOI: 10.1016/j.ces.2017.12.037.
107. Yang S., Navarathna P., Ghosh S., Bequette B.W., 2020. Hybrid modeling in the era of smart manufacturing. Comput. Chem. Eng., 140, 106874. DOI: 10.1016/j.compchemeng. 2020.106874.
108. Yu J., Liu P. Li Z., 2022. Data reconciliation-based simulation on thermal power plants for performance estimation and digital twin development. Comput. Chem. Eng., 168, 108063. DOI: 10.1016/j.compchemeng.2022.108063.
109. Zendehboudi S., Rezaei N., Lohi A., 2018. Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review. Appl. Energy, 228, 2539–2566. DOI: 10.1016/j.apenergy.2018.06.051.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)

Typ dokumentu

Bibliografia

Identyfikator YADDA

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