本研究使用準確可靠的SCALE程式系統計算工具TRITON與Polaris，並利用以上工具針對符合電廠之假設案例資料集進行分析，每一束燃料約有十個左右的重要物理參數與四個核子燃料特性(燃料中子、燃料光子、結構光子以及衰變熱)。除了嚴謹的燃耗計算之外，燃耗計算問題還有其它快速評估工具可以選擇，像是SCALE程式系統中，基於內插近似的分析工具ORIGEN-ARP與ORIGAMI，因此本研究挑選了假設電廠燃料束型式中的案例，資料庫中的模型參數主要來自於核一廠除役報告，同時也比較嚴謹燃耗計算與基於內插近似分析工具的差異。立基於可靠的評估技術，本研究利用嚴謹燃耗計算、內插近似法工具、Python 以及自動化模板(Jinja2)，建立假設的6870束用過核子燃料的資料庫，也拓展資料庫的冷卻時間從西元2022年至2521，同時分析案例中輻射源與衰變熱的來源核種。
建置了一個高品質的參數與特性資料庫之後，本研究透過兩種機器學習法成功預測輻射源與衰變熱，且優於文獻回顧中的誤差值1%。本研究透過嚴謹燃耗計算、內插近似與機器學習法的比較，試圖從不同角度思考輻射源與衰變熱變化與隱藏的關係，期望跨領域的合作與回饋可產生創新的見解與更好的解決方案。研究成果應可大幅提升國內用過核子燃料特性分析的能力，除了學術創新與追求卓越，相關技術與經驗可為國內面臨之核電廠除役與用過核子燃料處置提供立即協助。

All the management activities of spent nuclear fuels must start with a thorough understanding of the characteristics of the fuel inventory, with decay heat, neutron and gamma-ray sources in focus. An accurate quantitative assessment of these characteristics of each spent nuclear fuel is extremely important because the information is the basis for all safety related analyses and designs. This study aimed to investigate the characteristics of all spent nuclear fuels at the first nuclear power plant in Taiwan by using three different approaches: rigorous depletion calculation, approximate cross-section interpolation, and machine learning methods. Three nuclear analysis codes (TRITON, Polaris, and ORIGAMI) and two machine learning models (neural network and gradient boosting regression) were used in this study. TRITON and Polaris are two reactor physics codes that simulate the time-dependent transmutation of various materials in depletion models. Instead of a detailed and expensive depletion calculation, ORIGAMI enables a rapid calculation of spent fuel characterization by using ORIGEN with pre-generated reactor libraries. In addition to traditional approaches, two machine learning models, neural network and gradient boosting regression, were developed and trained to predict spent fuel characteristics based on the previous TRITON-calculated database. The outputs of these different approaches were compared and discussed in terms of computational accuracies and efficiencies. The results and experience obtained in this study provide valuable information for those performing similar analyses and may give some insights into the methods used in spent fuel characterization.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
表目錄 vii
圖目錄 x
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧與衰變熱及輻射源分析 2
1.3 研究目的與動機 7
第二章 用過核子燃料衰變熱與輻射源分析方法 8
2.1 嚴謹燃耗分析方法簡介 8
2.1.1 SCALE Code System 軟體 9
2.1.2 SCALE 4.4a / SAS2H 程式 12
2.1.3 SCALE 6.2.4/ TRITON 程式 15
2.1.4 SCALE 6.2.4/ Polaris程式 20
2.2 內插近似法簡介 23
2.2.1 SCALE 6.2.4/ ORIGEN 程式 24
2.2.2 SCALE 6.2.4/ ORIGEN REACTOR LIBRARY 程式 26
2.2.3 SCALE 6.2.4/ ORIGAMI & ARP程式 28
2.3 機器學習法 34
2.3.1 用過核子燃料資料庫簡介與前處理 34
2.3.2 梯度提升回歸(Gradient boosting regression, GBR) 37
2.3.3 神經網路深度學習法(Neural Network, NN) 40
第三章 驗證案例分析 43
3.1 驗證案例 JPDR 44
3.2 驗證案例 TAKAHAMA 49
3.2.1 案例介紹與參數設定 49
3.2.2 結果比較與討論 54
3.3 驗證案例 BWR4/6-09B 61
3.3.1 案例介紹與參數設定 61
3.3.2 結果比較與討論 64
第四章 燃料燃耗計算: 嚴謹燃耗計算與內插近似法 69
4.1 用過核子燃料分析 69
4.1.1 前言與特性介紹 69
4.1.2 燃耗計算參數與模型 72
4.2 用過核子燃料(A1案例) -嚴謹燃耗計算 74
4.2.1 Polaris 74
4.2.2 TRITON 78
4.2.3 ORIGEN 82
4.3 用過核子燃料(A1案例)-內插近似法 84
4.3.1 ORIGAMI 84
4.3.2 ARP 88
4.4 用過核子燃料衰變熱與輻射源分析與比較 91
4.4.1 B1, C1, D1, E1案例模型介紹 91
4.4.2 驗證假設案例 93
4.4.3 案例探討結論 102
第五章 自動化計算與資料庫分析 103
5.1 用過核子燃料資料庫建立(嚴謹燃耗計算方法) 103
5.1.1 資料庫簡介與參數設定 103
5.1.2 資料庫建立流程與程式介紹(TRITON為例) 109
5.2 資料庫結果分析 112
5.2.1 嚴謹燃耗計算結果 113
5.2.2 嚴謹燃耗計算(TRITON與Polaris)之間的模擬差異 119
5.2.3 嚴謹燃耗計算與內插近似法之間的差異 125
5.3 拓展資料庫分析範圍 128
5.3.1 冷卻時間範圍 128
5.3.2 資料庫燃料束核種組成 133
第六章 機器學習法與比較結果 142
6.2 梯度提升回歸(GRADIENT BOOSTING REGRESSION, GBR) 143
6.2.1 GBR 模型MDI指數 144
6.2.2 模型訓練與結果分析 148
6.3 神經網路模型 (NEURAL NETWORK, NN) 154
6.3.1 參數設定 154
6.3.2 模型結果分析 156
6.4 嚴謹燃耗計算、內插近似法與機器學習法的比較 159
6.4.1 與嚴謹燃耗計算的差距 159
6.4.2 HG誤差值解析(ORIGAMI計算) 161
第七章 結論與未來工作 167
參考文獻 169

[1] 許榮鈞，《核一廠用過核子燃料乾式貯存設施輻射屏蔽特性之確認分析研究》，台灣行政院原子能委員會，放射性物料管理局委託研究計畫研究報告，2006
[2] William. Wieselquist, Robert. Lefebvre, Matthew Jessee, Editors “Scale code system”, Oak Ridge National Laboratory, ORNL/TM-2005/39, 2020
[3] Matthew Jessee, William Wieselquist, Thomas Evans, Steven Hamilton, Joshua Jarrell, Kang Seog Kim, Jordan Lefebvre, Robert Lefebvre, Ugur Mertyurek, Adam Thompson, and Mark Williams “POLARIS: A new two-dimensional lattice physics analysis capability for the scale code system” Oak Ridge National Laboratory, PHYSOR 2014
[4] Mark Williams and Kang Seog Kim, “THE EMBEDDED SELF-SHIELDING METHOD”, Oak Ridge National Laboratory, PHYSOR 2012
[5] Matthew Jessee, William Wieselquist, Ugur Mertyurek, Kang Seog Kim, Thomas Evans, Steven Hamilton and Cole Gentry “Lattice physics calculations using the embedded self-shielding method in POLARIS, Part I: Methods and implementation” Oak Ridge National Laboratory, Annals of Nuclear Energy 150, 2021
[6] Ugur Mertyurek, Matthew Jessee, Benjamin Betzler, “Lattice physics calculations using the embedded self-shielding method in POLARIS, Part II: Benchmark assessment” Oak Ridge National Laboratory, Annals of Nuclear Energy 150, 2021
[7] Otto Hermann and Mark DeHart “Validation of SCALE (SAS2H) Isotopic Predictions for BWR Spent Fuel” Oak Ridge National Laboratory, ORNL/TM-13315, 1998
[8] 許榮鈞，《核二廠用過核子燃料乾式貯存護箱系統輻射屏蔽分析技術研究》，台灣行政院原子能委員會，放射性物料管理局委託研究計畫研究報告， 2011
[9] Bénédicte Roque and Mary Erlund “International Comparison of a Depletion Calculation Benchmark on Fuel Cycle Issues” Nuclear Science, NEA/NSC/DOC, 2013
[10] NAC international INC.Modular “Advanced Generation Nuclear All-purpose Storage (MAGNASTOR®) dry cask storage system” certificate of compliance no. 1031, amendment no. 3 docket NO. 72-1031, 2004
[11] Labarile, Miró, Barrachina and Verdú “TRITON vs Polaris. Comparison Between Two Modules for LWRs Modelling in SCALE 6.2” Institute for Industrial, Radiophysical and Environmental Safety (ISIRYM) Universitat Politècnica de València, Camí de Vera, s/n, 46022 Valencia, Spain, 2015
[12] James Duderstadt “Nuclear Reactor Analysis” University of Michigan Ann Arbor, Michigan, John Wiley & Sons Inc., 1976
[13] Baptiste Leniau, Baptiste Mouginot, Nicolas Thiolliere, Xavier Doligez, Adrien Bidaud, Fanny Courtin, Marc Ernoult and Sylvain David. “A neural network approach for burn-up calculation and its application to the dynamic fuel cycle code CLASS” Subatech EMN-IN2P3/CNRS-Université, Nantes F-44307, France, Annals of Nuclear Energy 81 125–133, 2015
[14] Kathryn Huff, Matthew Giddenb, Robert Carlsen, Robert Flanagan, Meghan McGarry, Arrielle Opotowsky, Erich Schneider, Anthony Scopatz, and Paul Wilson, “Fundamental concepts in the Cyclus nuclear fuel cycle simulation framework”, University of California- Berkeley, Department of Nuclear Engineering, Berkeley, United States, Advances in Engineering Software 94 46–59, 2016
[15] Bae, Betzler, and Worrall, “Neural Network Approach to Model Mixed Oxide Fuel Cycles in Cyclus a Nuclear Fuel Cycle Simulator” Oak Ridge National Laboratory, Fuel Cycle and Waste Management: General—II, 2019
[16] Jin Whan Bae, Andrei Rykhlevskii, Gwendolyn Chee, and Kathryn Huff, “Deep learning approach to nuclear fuel transmutation in a fuel cycle simulator”, Dept. of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, Annals of Nuclear Energy 139, 2020
[17] Bamidele Ebiwonjumi, Alexey Cherezov, Siarhei Dzianisau, and Deokjung Lee, “Machine learning of LWR spent nuclear fuel assembly decay heat measurements”, Department of Nuclear Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan, 44919, Republic of Korea, Nuclear Engineering and Technology 53 3563-3579, 2021
[18] Jerome Friedman “Greedy Function Approximation: A Gradient Boosting Machine” IMS 1999 Reitz Lecture, 1999
[19] Artificial neural network from Wikipedia article https://en.wikipedia.org/wiki/Artificial_neural_network, Feb 2022
[20] Diederik Kingma, and Jimmy Ba, “ADAM: A METHOD FOR STOCHASTIC OPTIMIZATION” University of Amsterdam, OpenAI, ICLR 2015
[21] Germina Ilas, and Henrik Liljenfeldt “Decay heat uncertainty for BWR used fuel due to modeling and nuclear data uncertainties” Oak Ridge National Laboratory, Nuclear Engineering and Design 319 176–184, 2017
[22] Bé, Chisté, Dulieu, Mougeot, Chechev, Kuzmenko, Kondev, Luca, Galán, Nichols, Pearce, Arinc, Huang “Monographie BIPM-5 Table of Radionuclides (Vol. 1 - A = 1 to 150)” Édité par le BIPM, Pavillon de Breteuil, F-92312 Sèvres Cedex France, 2011
[23] Tae SoonPark, Jong Man Lee, Han Yull Hwang “Standardization of Eu-152 and Y-88” Applied Radiation and Isotopes, Volume 56, Issues 1–2, 2002