Reactor Physics Monitoring of a Source-Driven Subcritical System in Stationary State by Deterministic and Probabilistic Deep Neural Networks

References

• “Safety of Research Reactors: Specific Safety Requirements, Revised 2016, International Atomic Energy Agency (2016).
   Google Scholar
• “Considerations of Safety and Utilization of Subcritical Assemblies,” International Atomic Energy Agency (2021).
   Google Scholar
• C. RUBBIA, J. A. RUBIO, and S. BUONO, “CERN-Group Conceptual Design of a Fast Neutron Operated High Power Energy Amplifier,” CERN/AT/95-44(ET), p. 187–312, International Atomic Energy Agency (1995).
   Google Scholar
• K. TSUJIMOTO et al., “Research and Development Program on Accelerator Driven Subcritical System in JAEA,” J. Nucl. Sci. Technol., 44, 3, 483 (2007); https://dx.doi.org/10.1080/18811248.2007.9711312.
   Web of Science ®Google Scholar
• H. NIFENECKER et al., “Basics of Accelerator Driven Subcritical Reactors,” Nucl. Instrum. Methods Phys. Res., Sect. A, 463, 3, 428 (2001); https://dx.doi.org/10.1016/S0168-9002(01)00160-7.
   Web of Science ®Google Scholar
• H. A. ABDERRAHIM, “Multi-Purpose hYbrid Research Reactor for High-Tech Applications: A Multipurpose Fast Spectrum Research Reactor,” Int. J. Energy Res., 36, 15, 1331 (2012); https://dx.doi.org/10.1002/er.1891.
   Web of Science ®Google Scholar
• J. PEVEY et al., “Genetic Algorithm Design of a Coupled Fast and Thermal Subcritical Assembly,” Nucl. Technol., 206, 4, 609 (2020); https://dx.doi.org/10.1080/00295450.2019.1664198.
   Web of Science ®Google Scholar
• K. SUN, L. HU, and C. FORSBERG, “Neutronics Feasibility of an MIT Reactor–Driven Subcritical Facility for the Fluoride-Salt–Cooled High-Temperature Reactor,” Int. J. Energy Res., 41, 14, 2248 (2017); https://dx.doi.org/10.1002/er.3786.
   Web of Science ®Google Scholar
• J. RATAJ et al., “The Project of VR-2 Subcritical Assembly,” Nucl. Eng. Des., 386, 111578 (2022); https://dx.doi.org/10.1016/j.nucengdes.2021.111578.
   Web of Science ®Google Scholar
• M. SZIEBERTH et al., “Measurement of Multiple α-Modes at the Delphi Subcritical Assembly by Neutron Noise Techniques,” Ann. Nucl. Energy, 75, 146 (2015); https://dx.doi.org/10.1016/j.anucene.2014.07.018.
   Web of Science ®Google Scholar
• A. GANDINI and M. SALVATORES, “The Physics of Subcritical Multiplying Systems,” J. Nucl. Sci. Technol., 39, 6, 673 (2002); https://dx.doi.org/10.1080/18811248.2002.9715249.
   Web of Science ®Google Scholar
• M. ROSSELET, T. WILLIAMS, and R. CHAWLA, “Subcriticality Measurements Using an Epithermal Pulsed-Neutron-Source Technique in Pebble-Bed HTR Configurations,” Ann. Nucl. Energy, 25, 4, 285 (1998); https://dx.doi.org/10.1016/S0306-4549(97)00059-5.
   Web of Science ®Google Scholar
• V. V. KULIK and J. C. LEE, “Space-Time Correction for Reactivity Determination in Source-Driven Subcritical Systems,” Nucl. Sci. Eng., 153, 1, 69 (2006); https://dx.doi.org/10.13182/NSE06-A2596.
   Web of Science ®Google Scholar
• C. A. PRESKITT et al., “Interpretation of Pulsed-Source Experiments in the Peach Bottom HTGR,” Nucl. Sci. Eng., 29, 2, 283 (1967); https://dx.doi.org/10.13182/NSE67-4.
   Web of Science ®Google Scholar
• S. BAJPAI et al., “Evaluation of Spatial Correction Factors for BRAHMMA Subcritical Assembly,” Nucl. Sci. Eng., 181, 3, 361 (2015); https://dx.doi.org/10.13182/NSE14-137.
   Web of Science ®Google Scholar
• V. BÉCARES et al., “Evaluation of the Criticality Constant from Pulsed Neutron Source Measurements in the Yalina-Booster Subcritical Assembly,” Ann. Nucl. Energy, 53, 40 (2013); https://dx.doi.org/10.1016/j.anucene.2012.10.002.
   Web of Science ®Google Scholar
• C. BERGLOF, “On Measurement and Monitoring of Reactivity in Subcritical Reactor Systems,” PhD Thesis, KTH Royal Institute of Technology, School of Engineering Sciences (2010).
   Google Scholar
• C. BERGLÖF et al., “Auto-Correlation and Variance-to-Mean Measurements in a Subcritical Core Obeying Multiple Alpha-Modes,” Ann. Nucl. Energy, 38, 2, 194 (2011); https://dx.doi.org/10.1016/j.anucene.2010.11.009.
   Web of Science ®Google Scholar
• K. NAKAJIMA et al., “Feynman-α and Rossi-α Analyses for a Subcritical Reactor System Driven by a Pulsed Spallation Neutron Source in Kyoto University Critical Assembly,” J. Nucl. Sci. Technol., 58, 1, 117 (2021); https://dx.doi.org/10.1080/00223131.2020.1806138.
   Web of Science ®Google Scholar
• C. BERGLÖF et al., “Spatial and Source Multiplication Effects on the Area Ratio Reactivity Determination Method in a Strongly Heterogeneous Subcritical System,” Nucl. Sci. Eng., 166, 2, 134 (2010); https://dx.doi.org/10.13182/NSE09-87.
   Web of Science ®Google Scholar
• H. TANINAKA et al., “Determination of Subcritical Reactivity of a Thermal Accelerator-Driven System from Beam Trip and Restart Experiment,” J. Nucl. Sci. Technol., 48, 6, 873 (2011); https://dx.doi.org/10.1080/18811248.2011.9711772.
   Web of Science ®Google Scholar
• K. NAKAJIMA et al., “Source Multiplication Measurements and Neutron Correlation Analyses for a Highly Enriched Uranium Subcritical Core Driven by an Inherent Source in Kyoto University Critical Assembly,” J. Nucl. Sci. Technol., 57, 10, 1152 (2020); https://dx.doi.org/10.1080/00223131.2020.1772896.
   Web of Science ®Google Scholar
• C.-M. PERSSON et al., “Analysis of Reactivity Determination Methods in the Subcritical Experiment Yalina,” Nucl. Instrum. Methods Phys. Res., Sect. A, 554, 1, 374 (2005); https://dx.doi.org/10.1016/j.nima.2005.07.058.
   Web of Science ®Google Scholar
• N. MARIE et al., “Reactivity Monitoring of the Accelerator Driven VENUS-F Subcritical Reactor with the ‘Current-to-Flux’ Method,” Ann. Nucl. Energy, 128, 12 (2019); https://dx.doi.org/10.1016/j.anucene.2018.12.033.
   Web of Science ®Google Scholar
• V. BÉCARES et al., “Validation of ADS Reactivity Monitoring Techniques in the Yalina-Booster Subcritical Assembly,” Ann. Nucl. Energy, 53, 331 (2013); https://dx.doi.org/10.1016/j.anucene.2012.10.001.
   Web of Science ®Google Scholar
• Y. CAO and Y. GOHAR, “YALINA-Booster Subcritical Assembly Pulsed-Neutron Experiments : Data Processing and Spatial Corrections,” ANL-10/22, Argonne National Laboratory (2010); https://dx.doi.org/10.2172/994056.
   Google Scholar
• A. TALAMO et al., “Impact of the Neutron Detector Choice on Bell and Glasstone Spatial Correction Factor for Subcriticality Measurement,” Nucl. Instrum. Methods Phys. Res., Sect. A, 668, 71 (2012); https://dx.doi.org/10.1016/j.nima.2011.11.072.
   Web of Science ®Google Scholar
• F. PERDU et al., “Prompt Reactivity Determination in a Subcritical Assembly Through the Response to a Dirac Pulse,” Prog. Nucl. Energy, 42, 1, 107 (2003); https://dx.doi.org/10.1016/S0149-1970(02)00101-4.
   Web of Science ®Google Scholar
• C. JAMMES, B. GESLOT, and G. IMEL, “Advantage of the Area-Ratio Pulsed Neutron Source Technique for ADS Reactivity Calibration,” Nucl. Instrum. Methods Phys. Res., Sect. A, 562, 2, 778 (2006); https://dx.doi.org/10.1016/j.nima.2006.02.054.
   Web of Science ®Google Scholar
• W. NAING, M. TSUJI, and Y. SHIMAZU, “Subcriticality Measurement of Pressurized Water Reactors by the Modified Neutron Source Multiplication Method,” J. Nucl. Sci. Technol., 40, 12, 983 (2003); https://dx.doi.org/10.3327/jnst.40.983.
   Web of Science ®Google Scholar
• M. TSUJI, N. SUZUKI, and Y. SHIMAZU, “Subcriticality Measurement by Neutron Source Multiplication Method with a Fundamental Mode Extraction,” J. Nucl. Sci. Technol., 40, 3, 158 (2003); https://dx.doi.org/10.1080/18811248.2003.9715346.
   Web of Science ®Google Scholar
• J. B. DOSHI and L. M. GROSSMAN, “Space-Time Dynamics of a Fast Breeder Reactor for Localized Disturbances,” Nucl. Sci. Eng., 65, 1, 106 (1978); https://dx.doi.org/10.13182/NSE78-A27130.
   Web of Science ®Google Scholar
• J. MOREIRA and J. C. LEE, “Space-Time Analysis of Reactor-Control-Rod-Worth Measurements,” Nucl. Sci. Eng., 86, 1, 91 (1984); https://dx.doi.org/10.13182/NSE84-1.
   Web of Science ®Google Scholar
• K. O. OTT and D. A. MENELEY, “Accuracy of the Quasistatic Treatment of Spatial Reactor Kinetics,” Nucl. Sci. Eng., 36, 3, 402 (1969); https://dx.doi.org/10.13182/NSE36-402.
   Web of Science ®Google Scholar
• Y. LECUN, Y. BENGIO, and G. HINTON, “Deep Learning,” Nature, 521, 7553, 436 (2015); https://dx.doi.org/10.1038/nature14539.
   PubMed Web of Science ®Google Scholar
• N. DUPIN and E.-G. TALBI, “Machine Learning–Guided Dual Heuristics and New Lower Bounds for the Refueling and Maintenance Planning Problem of Nuclear Power Plants,” Algorithms, 13, 8, 185 (2020); https://dx.doi.org/10.3390/a13080185.
   Web of Science ®Google Scholar
• R. A. B. U. SALEEM, M. I. RADAIDEH, and T. KOZLOWSKI, “Application of Deep Neural Networks for High-Dimensional Large BWR Core Neutronics,” Nucl. Eng. Technol., 52, 12, 2709 (2020); https://dx.doi.org/10.1016/j.net.2020.05.010.
   Web of Science ®Google Scholar
• A. AYODEJI et al., “Deep Learning for Safety Assessment of Nuclear Power Reactors: Reliability, Explainability, and Research Opportunities,” Prog. Nucl. Energy, 151, 104339 (2022); https://dx.doi.org/10.1016/j.pnucene.2022.104339.
   Web of Science ®Google Scholar
• J. A. AGUIAR et al., “Bringing Nuclear Materials Discovery and Qualification into the 21st Century,” Nat. Commun., 11, 1, 2556 (2020); https://dx.doi.org/10.1038/s41467-020-16406-2.
   PubMed Web of Science ®Google Scholar
• P. J. O’NEAL, S. S. CHIRAYATH, and Q. CHENG, “A Machine Learning Method for the Forensics Attribution of Separated Plutonium,” Nucl. Sci. Eng., 196, 7, 811 (2022); https://dx.doi.org/10.1080/00295639.2021.2024037.
   Web of Science ®Google Scholar
• P. BARALDI, F. MANGILI, and E. ZIO, “A Prognostics Approach to Nuclear Component Degradation Modeling Based on Gaussian Process Regression,” Prog. Nucl. Energy, 78, 141 (2015); https://dx.doi.org/10.1016/j.pnucene.2014.08.006.
   Web of Science ®Google Scholar
• M. MENDOZA and P. V. TSVETKOV, “An Intelligent Fault Detection and Diagnosis Monitoring System for Reactor Operational Resilience: Power Transient Identification,” Prog. Nucl. Energy, 156, 104529 (2023); https://dx.doi.org/10.1016/j.pnucene.2022.104529.
   Web of Science ®Google Scholar
• X. WU et al., “A Comprehensive Survey of Inverse Uncertainty Quantification of Physical Model Parameters in Nuclear System thermal–hydraulics Codes,” Nucl. Eng. Des., 384, 111460 (2021); https://dx.doi.org/10.1016/j.nucengdes.2021.111460.
   Web of Science ®Google Scholar
• L. E. MOLOKO et al., “Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks,” Ann. Nucl. Energy, 188, 109813 (2023); https://dx.doi.org/10.1016/j.anucene.2023.109813.
   Web of Science ®Google Scholar
• C. CAO et al., “A Two-Step Neutron Spectrum Unfolding Method for Fission Reactors Based on Artificial Neural Network,” Ann. Nucl. Energy, 139, 107219 (2020); https://dx.doi.org/10.1016/j.anucene.2019.107219.
   Web of Science ®Google Scholar
• S. JIANG et al., “Nuclear Reactor Reactivity Prediction Using Feed Forward Artificial Neural Networks,” Advances in Neural Networks, F. SUN et al., Eds., pp. 400–409, ISNN 2008 5263, Springer (2008); https://dx.doi.org/10.1007/978-3-540-87732-5_45.
   Google Scholar
• M. A. JIN et al., “Reactivity Estimation of Nuclear Reactor Combined with Neural Network and Mechanism Model,” presented at the 2012 IEEE Power and Energy Society General Mtg., pp. 1–6, San Diego, California, Institute of Electrical and Electronics Engineers (2012); https://dx.doi.org/10.1109/PESGM.2012.6345243.
   Google Scholar
• A. J. ARUL, “Reactivity Surveillance in a Nuclear Reactor by Using a Layered Artificial Neural Network,” Nucl. Sci. Eng., 117, 3, 186 (1994); https://dx.doi.org/10.13182/NSE94-A28533.
   Web of Science ®Google Scholar
• M. R. OKTAVIAN et al., “Preliminary Development of Machine Learning–Based Error Correction Model for Low-Fidelity Reactor Physics Simulation,” Ann. Nucl. Energy, 187, 109788 (2023); https://dx.doi.org/10.1016/j.anucene.2023.109788.
   Web of Science ®Google Scholar
• P. SELTBORG et al., “Definition and Application of Proton Source Efficiency in Accelerator-Driven Systems,” Nucl. Sci. Eng., 145, 3, 390 (2003); https://dx.doi.org/10.13182/NSE03-A2390.
   Web of Science ®Google Scholar
• M. B. CHADWICK et al., “ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data,” Nucl. Data Sheets, 112, 12, 2887 (2011); https://dx.doi.org/10.1016/j.nds.2011.11.002.
   Google Scholar
• C. J. WERNER et al., MCNP User’s Manual Code Version 6.2, LA-UR-17-29981, Los Alamos National Laboratory (2017).
   Google Scholar
• R. D. E. GATCHALIAN and P. V. TSVETKOV, “Reactor Physics Analysis of a Source-Driven TRIGA Configuration in Subcritical Domain,” Ann. Nucl. Energy, 186, 109787 (2023); https://dx.doi.org/10.1016/j.anucene.2023.109787.
   Web of Science ®Google Scholar
• Handbook of Nuclear Engineering, D. G. CACUCI, Ed., Springer (2010).
   Google Scholar
• I. GOODFELLOW, Y. BENGIO, and A. COURVILLE, Deep Learning, The MIT Press (2016).
   Google Scholar
• M. ABADI et al., “TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” [object Object] (2016). https://doi.org/10.48550/ARXIV.1603.0446.
   Google Scholar
• D. J. C. MACKAY, “Introduction to Gaussian Processes,” (1998).
   Google Scholar
• K. HORNIK, M. STINCHCOMBE, and H. WHITE, “Multilayer Feedforward Networks Are Universal Approximators,” Neural Networks, 2, 5, 359 (1989); https://dx.doi.org/10.1016/0893-6080(89)90020-8.
   Web of Science ®Google Scholar
• D.-X. ZHOU, “Universality of Deep Convolutional Neural Networks,” Appl. Comput. Harmon. Anal., 48, 2, 787 (2020); https://dx.doi.org/10.1016/j.acha.2019.06.004.
   Web of Science ®Google Scholar
• O. DÜRR, B. SICK, and E. MURINA, Probabilistic Deep Learning: With Python, Keras, and TensorFlow Probability, Manning, Shelter Island, New York (2020).
   Google Scholar
• L. LI et al., “Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization,” JMLR, arXiv 1603.06560 (2016); https://dx.doi.org/10.48550/ARXIV.1603.06560.
   Google Scholar
• T. O’MALLEY et al., “KerasTuner” (2019).
   Google Scholar
• L. BREIMAN, “Random Forests,” Mach. Learn., 45, 1, 5 (2001); https://dx.doi.org/10.1023/A:1010933404324.
   Web of Science ®Google Scholar
• T. HASTIE, R. TIBSHIRANI, and J. H. FRIEDMAN, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., Springer (2009).
   Google Scholar
• R. D. E. GATCHALIAN and P. V. TSVETKOV, “Traditional Machine Learning Methods in Predicting the Physics of Subcritical Systems in Source-Equilibrium,” Ann. Nucl. Energy, 201, 110413 (2024); 10.1016/j.anucene.2024.110413.
   Web of Science ®Google Scholar
• J. GAWLIKOWSKI et al., “A Survey of Uncertainty in Deep Neural Networks,” arXiv:2107.03342 (2022); https://dx.doi.org/10.48550/arXiv.2107.03342.
   Google Scholar
• J. V. DILLON et al., “TensorFlow Distributions,” arXiv:1711.10604 (2017); https://dx.doi.org/10.48550/ARXIV.1711.10604.
   Google Scholar
• X. WU et al., “Why Is Uncertainty Quantification Important for Machine Learning Models?,” Trans. Am. Nucl. Soc., 127, 442 American Nuclear Society (2022).
   Google Scholar
• N. SRIVASTAVA et al., “Dropout: A Simple Way to Prevent Neural Networks from Overfitting,” J. Mach. Learn. Res., 15, 1, 1929 (2014).
   Google Scholar
• Y. GAL and Z. GHAHRAMANI, “Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning,” arXiv:1506.02142 (2016); https://dx.doi.org/10.48550/arXiv.1506.02142.
   Google Scholar
• C. BLUNDELL et al., “Weight Uncertainty in Neural Network,” Proc. 32nd Int. Conf. on Machine Learning, pp. 1613–1622, Proceedings of Machine Learning Research (2015).
   Google Scholar
• C. M. BISHOP, Pattern Recognition and Machine Learning, Springer (2006).
   Google Scholar
• Y. WEN et al., “Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches,” arXiv:1803.04386v2 (Mar. 12, 2018); https://arxiv.org/abs/1803.04386v2 (current as of Aug. 26, 2023).
   Google Scholar
• J. L. LECOUEY et al., “Estimate of the Reactivity of the VENUS-F Subcritical Configuration Using a Monte Carlo MSM Method,” Ann. Nucl. Energy, 83, 65 (2015); 10.1016/j.anucene.2015.04.010.
   Web of Science ®Google Scholar