Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

Analyzing nuclear reactor simulation data and uncertainty with the group method of data handling

  • Radaideh, Majdi I. (Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana Champaign) ;
  • Kozlowski, Tomasz (Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana Champaign)
  • Received : 2019.01.30
  • Accepted : 2019.07.24
  • Published : 2020.02.25
Download PDF
⟨ Previous Next ⟩

Abstract

Group method of data handling (GMDH) is considered one of the earliest deep learning methods. Deep learning gained additional interest in today's applications due to its capability to handle complex and high dimensional problems. In this study, multi-layer GMDH networks are used to perform uncertainty quantification (UQ) and sensitivity analysis (SA) of nuclear reactor simulations. GMDH is utilized as a surrogate/metamodel to replace high fidelity computer models with cheap-to-evaluate surrogate models, which facilitate UQ and SA tasks (e.g. variance decomposition, uncertainty propagation, etc.). GMDH performance is validated through two UQ applications in reactor simulations: (1) low dimensional input space (two-phase flow in a reactor channel), and (2) high dimensional space (8-group homogenized cross-sections). In both applications, GMDH networks show very good performance with small mean absolute and squared errors as well as high accuracy in capturing the target variance. GMDH is utilized afterward to perform UQ tasks such as variance decomposition through Sobol indices, and GMDH-based uncertainty propagation with large number of samples. GMDH performance is also compared to other surrogates including Gaussian processes and polynomial chaos expansions. The comparison shows that GMDH has competitive performance with the other methods for the low dimensional problem, and reliable performance for the high dimensional problem.

Keywords

References

  1. Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (7553) (2015) 436. https://doi.org/10.1038/nature14539
  2. L. Deng, D. Yu, et al., Deep learning: methods and applications, Foundations and Trends(R) in Signal Processing 7 (3-4) (2014) 197-387.
  3. T. Poggio, H. Mhaskar, L. Rosasco, B. Miranda, Q. Liao, Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review, Int. J. Autom. Comput. 14 (5) (2017) 503-519.
  4. S.M. Erfani, S. Rajasegarar, S. Karunasekera, C. Leckie, High-dimensional and large-scale anomaly detection using a linear one-class SVM with deep learning, Pattern Recognit. 58 (2016) 121-134. https://doi.org/10.1016/j.patcog.2016.03.028
  5. E. Keogh, A. Mueen, Curse of dimensionality, in: Encyclopedia of Machine Learning, Springer, 2011, pp. 257-258.
  6. R.C. Smith, Uncertainty Quantification: Theory, Implementation, and Applications, vol. 12, Siam, 2013.
  7. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Global Sensitivity Analysis: the Primer, John Wiley & Sons, 2008.
  8. A.I. Forrester, A.J. Keane, Recent advances in surrogate-based optimization, Prog. Aerosp. Sci. 45 (1-3) (2009) 50-79. https://doi.org/10.1016/j.paerosci.2008.11.001
  9. K.K. Vu, C. D'Ambrosio, Y. Hamadi, L. Liberti, Surrogate-based methods for black-box optimization, Int. Trans. Oper. Res. 24 (3) (2017) 393-424. https://doi.org/10.1111/itor.12292
  10. J.D. Martin, T.W. Simpson, Use of kriging models to approximate deterministic computer models, AIAA J. 43 (4) (2005) 853-863. https://doi.org/10.2514/1.8650
  11. A. Marrel, B. Iooss, F. Van Dorpe, E. Volkova, An efficient methodology for modeling complex computer codes with Gaussian processes, Comput. Stat. Data Anal. 52 (10) (2008) 4731-4744. https://doi.org/10.1016/j.csda.2008.03.026
  12. M.D. Buhmann, Radial Basis Functions: Theory and Implementations, vol. 12, Cambridge university press, 2003.
  13. S. Chan, A.H. Elsheikh, A machine learning approach for efficient uncertainty quantification using multiscale methods, J. Comput. Phys. 354 (2018) 493-511. https://doi.org/10.1016/j.jcp.2017.10.034
  14. B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Saf. 93 (7) (2008) 964-979. https://doi.org/10.1016/j.ress.2007.04.002
  15. R. Tripathy, I. Bilionis, Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification, J. Comput. Phys. 375 (2018) 565-588. https://doi.org/10.1016/j.jcp.2018.08.036
  16. Y. Zhu, N. Zabaras, Bayesian deep convolutional encoderedecoder networks for surrogate modeling and uncertainty quantification, J. Comput. Phys. 366 (2018) 415-447. https://doi.org/10.1016/j.jcp.2018.04.018
  17. A.G. Ivakhnenko, The group method of data of handling; a rival of the method of stochastic approximation, Soviet Automatic Control 13 (1968) 43-55.
  18. A.G. Ivakhnenko, Polynomial theory of complex systems, IEEE Trans. Sys. Man Cybern. (4) (1971) 364-378. https://doi.org/10.1109/TSMC.1971.4308320
  19. J. Schmidhuber, Deep learning in neural networks: an overview, Neural Netw. 61 (2015) 85-117. https://doi.org/10.1016/j.neunet.2014.09.003
  20. S.J. Farlow, The GMDH algorithm of ivakhnenko, Am. Statistician 35 (4) (1981) 210-215. https://doi.org/10.2307/2683292
  21. A. Ivakhnenko, G. Ivakhnenko, The review of problems solvable by algorithms of the group method of data handling (GMDH), Pattern Recognition and Image Analysis C/C of Raspoznavaniye Obrazov I, Analiz Izobrazhenii 5 (1995) 527-535.
  22. A. Ivakhnenko, Heuristic self-organization in problems of engineering cybernetics, Automatica 6 (2) (1970) 207-219. https://doi.org/10.1016/0005-1098(70)90092-0
  23. X. Jia, Y. Di, J. Feng, Q. Yang, H. Dai, J. Lee, Adaptive virtual metrology for semiconductor chemical mechanical planarization process using GMDH-type polynomial neural networks, J. Process Control 62 (2018) 44-54. https://doi.org/10.1016/j.jprocont.2017.12.004
  24. T. Kondo, J. Ueno, Multi-layered GMDH-type neural network self-selecting optimum neural network architecture and its application to 3-dimensional medical image recognition of blood vessels, Int. J. Innov. Comput. Inf. Control 4 (1) (2008) 175-187.
  25. M. Witczak, J. Korbicz, M. Mrugalski, R.J. Patton, A GMDH neural networkbased approach to robust fault diagnosis: application to the damadics benchmark problem, Contr. Eng. Pract. 14 (6) (2006) 671-683. https://doi.org/10.1016/j.conengprac.2005.04.007
  26. S. Dolati, N. Amanifard, H.M. Deylami, Numerical study and GMDH-type neural networks modeling of plasma actuator effects on the film cooling over a flat plate, Appl. Therm. Eng. 123 (2017) 734-745. https://doi.org/10.1016/j.applthermaleng.2017.05.149
  27. X. Tian, V. Becerra, N. Bausch, T. Santhosh, G. Vinod, A study on the robustness of neural network models for predicting the break size in LOCA, Prog. Nucl. Energy 109 (2018) 12-28. https://doi.org/10.1016/j.pnucene.2018.07.004
  28. T. Cong, G. Su, S. Qiu, W. Tian, Applications of ANNs in flow and heat transfer problems in nuclear engineering: a review work, Prog. Nucl. Energy 62 (2013) 54-71. https://doi.org/10.1016/j.pnucene.2012.09.003
  29. M.-G. Park, H.-C. Shin, Reactor power shape synthesis using group method of data handling, Ann. Nucl. Energy 72 (2014) 467-470. https://doi.org/10.1016/j.anucene.2014.06.010
  30. F. Khoshahval, S. Yum, H.C. Shin, J. Choe, P. Zhang, D. Lee, Smart sensing of the axial power and offset in NPPs using GMDH method, Ann. Nucl. Energy 121 (2018) 77-88. https://doi.org/10.1016/j.anucene.2018.07.007
  31. B. Lu, B. Upadhyaya, Monitoring and fault diagnosis of the steam generator system of a nuclear power plant using data-driven modeling and residual space analysis, Ann. Nucl. Energy 32 (9) (2005) 897-912. https://doi.org/10.1016/j.anucene.2005.02.003
  32. H. Kim, M.G. Na, G. Heo, Application of monitoring, diagnosis, and prognosis in thermal performance analysis for nuclear power plants, Nucl. Eng. Technol. 46 (6) (2014) 737-752. https://doi.org/10.5516/NET.04.2014.720
  33. H.R. Madala, A.G. Ivakhnenko, Inductive Learning Algorithms for Complex Systems Modeling, vol. 368, cRc press, Boca Raton, 1994.
  34. H. Akaike, A new look at the statistical model identification, IEEE Trans. Autom. Control 19 (6) (1974) 716-723. https://doi.org/10.1109/TAC.1974.1100705
  35. C.E. Rasmussen, Gaussian processes in machine learning, in: Advanced Lectures on Machine Learning, Springer, 2004, pp. 63-71.
  36. C. Lataniotis, S. Marelli, B. Sudret, UQlab user manualekriging (Gaussian process modelling), Rep. UQLab-V0 (2015) 9-105.
  37. G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys. 230 (6) (2011) 2345-2367. https://doi.org/10.1016/j.jcp.2010.12.021
  38. R.G. Ghanem, P.D. Spanos, Stochastic finite element method: response statistics, in: Stochastic Finite Elements: A Spectral Approach, Springer, 1991, pp. 101-119.
  39. S. Marelli, B. Sudret, UQlab User ManualePolynomial Chaos Expansions, Chair of Risk, Safety & Uncertainty Quantification, ETH Zurich, 0.9-104 edition.
  40. S. Marelli, B. Sudret, UQlab: a framework for uncertainty quantification in Matlab, in: Vulnerability, Uncertainty, and Risk: Quantification, and Management, Mitigation, 2014, pp. 2554-2563.
  41. B. Neykov, F. Aydogan, L. Hochreiter, K. Ivanov, H. Utsuno, F. Kasahara, E. Sartori, M. Martin, NUPEC BWR full-size fine-mesh bundle test (BFBT) benchmark, in: Tech. rep., Organisation for Economic Co-operation and Development(OECD), Nuclear Energy Agency, 2006.
  42. M.I. Radaideh, K. Borowiec, T. Kozlowski, Integrated framework for model assessment and advanced uncertainty quantification of nuclear computer codes under bayesian statistics, Reliab. Eng. Syst. Saf. 189 (2019) 357-377. https://doi.org/10.1016/j.ress.2019.04.020
  43. X. Wu, T. Kozlowski, H. Meidani, K. Shirvan, Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 2: application to trace, Nucl. Eng. Des. 335 (2018) 417-431. https://doi.org/10.1016/j.nucengdes.2018.06.003
  44. N.V. Queipo, R.T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, P.K. Tucker, Surrogate- based analysis and optimization, Prog. Aerosp. Sci. 41 (1) (2005) 1-28. https://doi.org/10.1016/j.paerosci.2005.02.001
  45. U.S.NRC, TRACE v5.840 Theory Manual: Fields Equations, Solution Methods, and Physical Models, US Nuclear Regulatory Commission, Washington, D.C., United States.
  46. S.M. Bowman, SCALE 6: comprehensive nuclear safety analysis code system, Nucl. Technol. 174 (2) (2011) 126-148.
  47. B.T. Rearden, M.A. Jessee, SCALE Code System, Tech. rep., Oak Ridge National Lab.(ORNL), 2018. Oak Ridge, TN (United States).
  48. M.I. Radaideh, S. Surani, D. O'Grady, T. Kozlowski, Shapley effect application for variance-based sensitivity analysis of the few-group cross-sections, Ann. Nucl. Energy 129 (2019) 264-279. https://doi.org/10.1016/j.anucene.2019.02.002
  49. N. Horelik, B. Herman, B. Forget, K. Smith, Benchmark for evaluation and validation of reactor simulations (BEAVRS), v1. 0.1, in: Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuc. Sci. & Eng, 2013. Sun Valley, Idaho, United States, May 5-9.
  50. I.M. Sobol, Sensitivity estimates for nonlinear mathematical models, Math. Model. Civ. Eng. 1 (4) (1993) 407-414.
  51. G. Glen, K. Isaacs, Estimating sobol sensitivity indices using correlations, Environ. Model. Softw 37 (2012) 157-166. https://doi.org/10.1016/j.envsoft.2012.03.014

Cited by

  1. Neural-based time series forecasting of loss of coolant accidents in nuclear power plants vol.160, 2020, https://doi.org/10.1016/j.eswa.2020.113699
  2. MODELING NUCLEAR DATA UNCERTAINTIES USING DEEP NEURAL NETWORKS vol.247, 2021, https://doi.org/10.1051/epjconf/202124715016