Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

Prediction of the remaining time and time interval of pebbles in pebble bed HTGRs aided by CNN via DEM datasets

  • Mengqi Wu (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Xu Liu (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Nan Gui (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Xingtuan Yang (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Jiyuan Tu (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Shengyao Jiang (Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University) ;
  • Qian Zhao (Beijing Institute of Spacecraft Environment Engineering (BISEE), China Academy of Space Technology)
  • Received : 2022.01.29
  • Accepted : 2022.09.20
  • Published : 2023.01.25
Download PDF
⟨ Previous Next ⟩

Abstract

Prediction of the time-related traits of pebble flow inside pebble-bed HTGRs is of great significance for reactor operation and design. In this work, an image-driven approach with the aid of a convolutional neural network (CNN) is proposed to predict the remaining time of initially loaded pebbles and the time interval of paired flow images of the pebble bed. Two types of strategies are put forward: one is adding FC layers to the classic classification CNN models and using regression training, and the other is CNN-based deep expectation (DEX) by regarding the time prediction as a deep classification task followed by softmax expected value refinements. The current dataset is obtained from the discrete element method (DEM) simulations. Results show that the CNN-aided models generally make satisfactory predictions on the remaining time with the determination coefficient larger than 0.99. Among these models, the VGG19+DEX performs the best and its CumScore (proportion of test set with prediction error within 0.5s) can reach 0.939. Besides, the remaining time of additional test sets and new cases can also be well predicted, indicating good generalization ability of the model. In the task of predicting the time interval of image pairs, the VGG19+DEX model has also generated satisfactory results. Particularly, the trained model, with promising generalization ability, has demonstrated great potential in accurately and instantaneously predicting the traits of interest, without the need for additional computational intensive DEM simulations. Nevertheless, the issues of data diversity and model optimization need to be improved to achieve the full potential of the CNN-aided prediction tool.

Keywords

Acknowledgement

The authors are grateful for the support of this research by the National Science and Technology Major Project (2011ZX06901-003), and the Fund of Nuclear Power Technology Innovation Centre (Grant No. HDLCXZX-2021-ZH-024)

References

  1. J.M. Ryskamp, E.A. Harvego, S.T. Khericha, E.J. Gorski, G.A. Beitel, D.J. Harrell, Next generation nuclear plant: high-level functions and requirements, in: Proceedings of the 12th International Conference on Nuclear Engineering, 2004, pp. 395-402.
  2. L. Shi, J.Q. Zhao, B. Liu, X.W. Li, X.W. Luo, Z.M. Zhang, P. Zhang, L.B. Sun, X.X. Wu, Development strategy of key materials technology for the high temperature gas-cooled reactor, J. Tsinghua Univ. (Sci. Technol.) 61 (4) (2021) 270-278.
  3. D. Wang, R.G. Ballinger, H.J. Maclean, TIMCOAT: an integrated fuel performance model for coated particle fuel, Nucl. Technol. 148 (2004) 68-96. https://doi.org/10.13182/NT04-A3549
  4. X.T. Yang, W.P. Hu, S.Y. Jiang, K. Wong, J.Y. Tu, Mechanism analysis of quasi-static dense pebble flow in pebble bed reactor using phenomenological approach, Nucl. Eng. Des. 250 (2012) 247-259. https://doi.org/10.1016/j.nucengdes.2012.06.011
  5. S. Wang, S. Wang, B.W. Wu, Y.L. Lu, K.F. Zhang, H.L. Chen, Effect of packing structure on anisotropic effective thermal conductivity of thin ceramic pebble bed, Nucl. Eng. Technol. 53 (7) (2021) 2174-2183. https://doi.org/10.1016/j.net.2021.01.013
  6. M.A. Alzamly, M. Aziz, A.A. Badawi, H.A. Gabal, A.,R.A. Gadallah, Burnup analysis for HTR-10 reactor core loaded with uranium and thorium oxide, Nucl. Eng. Technol. 52 (4) (2020) 674-680. https://doi.org/10.1016/j.net.2019.09.012
  7. N. Gui, X. Yang, J. Tu, S. Jiang, Effect of bed configuration on pebble flow uniformity and stagnation in the pebble bed reactor, Nucl. Eng. Des. 270 (2014) 295-301. https://doi.org/10.1016/j.nucengdes.2013.12.055
  8. C.H. Rycroft, G.S. Grest, J.W. Landry, M.Z. Bazant, Analysis of granular flow in a pebble-bed nuclear reactor, Phys. Rev. 74 (2) (2006), 021306.
  9. X. Jia, N. Gui, H. Wu, X.T. Yang, J.Y. Tu, S.Y. Jiang, Numerical study and analysis of the effects of recirculation flow rates in drained pebble flow, Powder Technol. 314 (2016) 608-619.
  10. V.B. Khane, Experimental and Computational Investigation of Flow of Pebbles in a Pebble Bed Nuclear Reactor, Missouri University of Science and Technology, Rolla, Missouri, USA, 2014.
  11. D. Sohn, Y. Lee, M.Y. Ahn, Y.H. Park, S. Cho, Numerical prediction of packing behavior and thermal conductivity of pebble beds according to pebble size distributions and friction coefficients, Fusion Eng. Des. 137 (2018) 182-190. https://doi.org/10.1016/j.fusengdes.2018.09.012
  12. Y.A. Hassan, E.E. Dominguez-Ontiveros, Flow visualization in a pebble bed reactor experiment using PIV and refractive index matching techniques, Nucl. Eng. Des. 238 (11) (2008) 3080-3085. https://doi.org/10.1016/j.nucengdes.2008.01.027
  13. A. Shams, F. Roelofs, E. Komen, E. Baglietto, Quasi-direct numerical simulation of a pebble bed configuration. Part I: flow (velocity) field analysis, Nucl. Eng. Des. 263 (2013) 473-489. https://doi.org/10.1016/j.nucengdes.2012.06.016
  14. V.B. Khane, M.M. Taha, M.H. Al-Dahhan, Experimental investigation of the overall residence time of pebbles in a pebble bed reactor (PBR) using radioactive pebble[J], Prog. Nucl. Energy 93 (2016a) 267-276. https://doi.org/10.1016/j.pnucene.2016.09.001
  15. X. Liu, N. Gui, X. Yang, J.Y. Tu, S.Y. Jiang, A new discrete element-embedded finite element method for transient deformation, movement and heat transfer in packed bed, Int. J. Heat Mass Tran. 165 (2021a), 120714.
  16. Y.J. Liu, S.F. Peng, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, An improved high accuracy PTV algorithm for pebble flow, Powder Technol. 387 (2021b) 227-238. https://doi.org/10.1016/j.powtec.2021.04.025
  17. A.C. Kadark, M.Z. Bazant, Pebble Flow Experiments for Pebble Bed Reactors, 2nd International Topical Meeting on High Temperature Reactor Technology, Beijing, 2004.
  18. V.B. Khane, I.A. Said, M.H. Al-Dahhan, Experimental investigation of pebble flow dynamics using radioactive particle tracking technique in a scaled-down Pebble Bed Modular Reactor (PBMR), Nucl. Eng. Des. 302 (2016b) 1-11. https://doi.org/10.1016/j.nucengdes.2016.03.031
  19. P.Y. Zhang, Q.Q. Guo, S. Pang, Y.L. Sun, Y. Chen, Experimental research on vertical mechanical performance of embedded through-penetrating steel-concrete composite joint in high-temperature gas-cooled reactor pebble-bed module, Nucl. Eng. Technol. 54 (1) (2022) 357-373. https://doi.org/10.1016/j.net.2021.07.014
  20. D. Matzner, PBMR Project status and the way ahead, in: 2nd International Topical Meeting on High Temperature Reactor Technology. Beijing, September, 2004, pp. 22-24.
  21. X.T. Yang, W.P. Hu, S.Y. Jiang, Experimental investigation on feasibility of two region-designed pebble-bed high-temperature gas-cooled reactor, J. Nucl. Sci. Technol. 46 (4) (2009) 374-381. https://doi.org/10.1080/18811248.2007.9711543
  22. X. Jia, N. Gui, X. Yang, J. Tu, H. Jia, S. Jiang, Experimental study of flow field characteristics on bed configurations in the pebble bed reactor, Ann. Nucl. Energy 102 (2017) 1-10. https://doi.org/10.1016/j.anucene.2016.12.009
  23. L. Liu, J. Deng, D. Zhang, C. Wang, S.Z. Qiu, G. Su, Experimental analysis of flow and convective heat transfer in the water-cooled packed pebble bed nuclear reactor core, Prog. Nucl. Energy 122 (2020), 103298.
  24. J. Haervig, U. Kleinhans, C. Wieland, H. Spliethoff, A.L. Jensen, K.S. Rensen, T.J. Condra, On the adhesive JKR contact and rolling models for reduced particle stiffness discrete element simulations, Powder Technol. 319 (2017) 472-482. https://doi.org/10.1016/j.powtec.2017.07.006
  25. S.S. Park, E.S. Kim, Jamming probability of granular flow in 3D hopper with shallow columns: DEM simulations, Granul. Matter 22 (4) (2020) 77.
  26. H. Wu, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal radiation, Int. J. Heat Mass Tran. 110 (2017) 393-405. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.035
  27. Y. Lee, S. Yu, M.Y. Ahn, Y.H. Park, D. Sohn, Numerical investigation of mechanical and thermal characteristics of binary-sized pebble beds using discrete element method, Fusion Eng. Des. 146 (2019) 2285-2291. https://doi.org/10.1016/j.fusengdes.2019.03.173
  28. G.K.P. Barrios, N. Jimenez-Herrera, L.M. Tavares, Simulation of particle bed breakage by slow compression and impact using a DEM particle replacement model, Adv. Powder Technol. 31 (7) (2020) 2749-2758. https://doi.org/10.1016/j.apt.2020.05.011
  29. M. Ebrahimi, A. Yaraghi, B. Jadidi, F. Ein-Mozaffari, A. Lohi, Assessment of bi-disperse solid particles mixing in a horizontal paddle mixer through experiments and DEM, Powder Technol. 381 (2020) 129-140. https://doi.org/10.1016/j.powtec.2020.11.041
  30. L. Benvenuti, C. Kloss, S. Pirker, Identification of DEM simulation parameters by artificial neural networks and bulk experiments, Powder Technol. 291 (2016) 456-465. https://doi.org/10.1016/j.powtec.2016.01.003
  31. F. Ye, C. Wheeler, B. Chen, J. Hu, K. Chen, W. Chen, Calibration and verification of DEM parameters for dynamic particle flow conditions using a backpropagation neural network, Adv. Powder Technol. 30 (2019) 292-301. https://doi.org/10.1016/j.apt.2018.11.005
  32. R. Kumar, C.M. Patel, A.K. Jana, S.R. Gopireddy, Prediction of hopper discharge rate using combined discrete element method and artificial neural network, Adv. Powder Technol. 29 (2018) 2822-2834. https://doi.org/10.1016/j.apt.2018.08.002
  33. H. Wu, S. Hao, A deep neural network model of particle thermal radiation in packed bed, Proc. AAAI Conf. Artif. Intell. 34 (1) (2020) 1029-1036.
  34. X.J. Huang, Q.J. Zheng, A.B. Yu, W.Y. Yan, Shape optimization of conical hoppers to increase mass discharging rate, Powder Technol. 361 (2020) 179-189. https://doi.org/10.1016/j.powtec.2019.09.043
  35. R. Hesse, F. Krull, S. Antonyuk, Prediction of random packing density and flowability for non-spherical particles by deep convolutional neural networks and Discrete Element Method simulations, Powder Technol. 393 (2021) 559-581. https://doi.org/10.1016/j.powtec.2021.07.056
  36. Z. Liang, Z. Nie, A. An, J. Gong, X. Wang, A particle shape extraction and evaluation method using a deep convolutional neural network and digital image processing, Powder Technol. 353 (2019) 156-170. https://doi.org/10.1016/j.powtec.2019.05.025
  37. Z. Liao, Y. Yang, C. Sun, R. Wu, Z. Duan, Y. Wang, X. Li, J. Xu, Image-based prediction of granular flow behaviors in a wedge-shaped hopper by combing DEM and deep learning methods, Powder Technol. 383 (2021) 159-166. https://doi.org/10.1016/j.powtec.2021.01.041
  38. P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47-65. https://doi.org/10.1680/geot.1979.29.1.47
  39. H.P. Zhu, Z.Y. Zhou, R.Y. Yang, A.B. Yu, Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci. 62 (2007) 3378-3396. https://doi.org/10.1016/j.ces.2006.12.089
  40. P.A. Cundall, O. Strack, A discrete numerical model for granular assemblies, Geotechnique 30 (3) (2008) 331-336. https://doi.org/10.1680/geot.1980.30.3.331
  41. J. Horabik, M. Molenda, Parameters and contact models for DEM simulations of agricultural granular materials: a review, Biosyst. Eng. 147 (2016) 206-225. https://doi.org/10.1016/j.biosystemseng.2016.02.017
  42. Y. Li, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Effect of a flow-corrective insert on the flow pattern in a pebble bed reactor, Nucl. Eng. Des. 300 (2016) 495-505. https://doi.org/10.1016/j.nucengdes.2016.02.002
  43. M.Q. Wu, N. Gui, H. Wu, X.T. Yang, J.Y. Tu, S.Y. Jiang, Numerical study of mixing pebble flow with different density in circulating packed bed, Ann. Nucl. Energy 130 (2019a) 483-492. https://doi.org/10.1016/j.anucene.2019.03.020
  44. M.Q. Wu, N. Gui, H. Wu, X.T. Yang, J.Y. Tu, S.Y. Jiang, Effects of density difference and loading ratio on pebble flow in a three-dimensional two-region-designed pebble bed, Ann. Nucl. Energy 133 (2019b) 924-936. https://doi.org/10.1016/j.anucene.2019.07.032
  45. S.Y. Jiang, X.T. Yang, Z.W. Tang, W.J. Wang, J.Y. Tu, Z.Y. Liu, J. Li, Experimental and numerical validation of a two-region-designed pebble bed reactor with dynamic core, Nucl. Eng. Des. 246 (2012) 277-285. https://doi.org/10.1016/j.nucengdes.2012.02.005
  46. S. Jiang, J. Tu, X. Yang, N. Gui, A review of pebble flow study for pebble bed high temperature gas-cooled reactor, Exp. Comput. Multiphase Flow 1 (3) (2019) 159-176. https://doi.org/10.1007/s42757-019-0006-1
  47. A. Krizhevsky, I. Sutskever, G. Hinton, ImageNet classification with deep convolutional neural networks, Advances in neural information processing systems 25 (2012) 1097-1105.
  48. K. Simonyan, A. Zisserman, Very deep convolutional networks for large-scale image recognition, Computer Science (2015) 1409-1556.
  49. K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, IEEE (2016) 770-778.
  50. Y.L. Boureau, F. Bach, Y. LeCun, J. Ponce, Learning mid-level features for recognition, IEEE.Comput. Soc. Conf. Comput. Vis. Pattern Recogn. (2010) 2559-2566.
  51. Y. LeCun, B. Boser, J.S. Denker, D. Henderson, R.E. Howard, W. Hubbard, L.D. Jackel, Backpropagation applied to handwritten zip code recognition, Neural Comput. 1 (1989) 541-551. https://doi.org/10.1162/neco.1989.1.4.541
  52. W.A. Beverloo, H.A. Leniger, J. Velde, The flow of granular solids through orifices, Chem. Eng. Sci. 15 (3-4) (1961) 260-269. https://doi.org/10.1016/0009-2509(61)85030-6
  53. M.Q. Wu, N. Gui, X. Liu, X.T. Yang, J.Y. Tu, S.Y. Jiang, Numerical analysis of the effects of different outlet sizes on pebble flows in HTR-10 pebble beds, Nucl. Eng. Des. 387 (2022), 111620.
  54. W.P. Hu, Experimental and Theoretical Research on Pebble Flow in two-Region Pebble Bed Doctor Thesis, Tsinghua University, Beijing, China, 2009.
  55. S. Zaghbani, N. Boujneh, M.S. Bouhlel, Age estimation using deep learning, Comput. Electr. Eng. 68 (2018) 337-347. https://doi.org/10.1016/j.compeleceng.2018.04.012
  56. W.Z. Cao, V. Mirjalili, S. Raschka, Rank consistent ordinal regression for neural networks with application to age estimation, Pattern Recogn. Lett. 140 (2020) 325-331. https://doi.org/10.1016/j.patrec.2020.11.008
  57. D.P. Kingma, J. Ba, Adam: A Method for Stochastic Optimization, International Conference on Learning Representations, San Diego, CA, USA, 2015.
  58. Z.H. Liu, R.H. Meng, H.X. Dai, Q.Y. Hong, Q.H. Yan, Y.T. Liu, H.T. Wang, T. Chen, Evaluation of heavy metals pollution in surface sediments using an improved geo-accumulation index method, J.Agro.Environ.Sci 38 (9) (2019) 2157-2164.
  59. S. Urolagin, K.V. Prema, N.V.S. Reddy, Generalization capability of artificial neural network incorporated with pruning method, Int. Conf.Adv.Comput vol. 7135 (2011) 171-178. Networking and Security. Springer, Berlin, Heidelberg.
  60. H. Wu, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Parameter analysis and wall effect of radiative heat transfer for CFD-DEM simulation in nuclear packed pebble bed, Exp.Comput. Multiphase Flow 3 (4) (2021a) 250-257. https://doi.org/10.1007/s42757-020-0058-2
  61. M.Q. Wu, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Effects of 3D contraction on pebble flow uniformity and stagnation in pebble beds, Nucl. Eng. Technol. 53 (5) (2021b) 1416-1428. https://doi.org/10.1016/j.net.2020.10.022
  62. B. Yan, R.A. Regueiro, S. Sture, Three-dimensional ellipsoidal discrete element modeling of granular materials and its coupling with finite element facets, Eng. Comput. 27 (3-4) (2009) 519-550. https://doi.org/10.1108/02644401011044603