Ensemble-Based Inverse Model for Multiple Radionuclide Source Term Estimation in Nuclear Accidents = 핵사고시 다중 방사성 핵종 선원항 역추정을 위한 앙상블 기반 역모델

국문 초록 (Abstract)

희소하고 이종적인 관측 데이터만으로 미지의 방사성 핵종의 선원항(source term)을 정확하고 신뢰성 있게 추정 및 재구성하는 문제는 방사선 비상 대응에 있어 중요한 과제이다. 대기 확산은 비선형적인 기상 요인에 의해 지배되며, 환경 모니터링 네트워크는 서로 다른 시공간 척도로 데이터를 수집한다. 한편, 음수 형태의 역추정 결과값은 물리적 해석을 어렵게 하므로 방사성 농도 및 선량 정보는 반드시 비음수성 물리제약을 준수해야 한다. 본 논문에서는 이러한 도전 과제를 해결하기 위하여 i-STAR-GPU(Inverse-integrated Source Term Assessment with Radiological-emergency focus, GPU 가속)라는 통합 프레임워크를 제안한다. 이 체계는 방사성 핵종 대기 확산 모델, 앙상블 기반 베이지안 역추정, 엄밀한 부등식 제약 처리, 그리고 대규모 병렬 연산을 하나의 플랫폼으로 결합한다.
통합 역추정의 이론적 핵심인 앙상블 칼만 역추정(EKI: Ensemble Kalman Inversion)은 미분 없는(derivative-free) 베이지안 최적화 관점에서 선원항 추정을 재해석한다. 정방향 모델은 가우시안 플룸 및 퍼프 모델에 방사성 붕괴와 건식 및 습식 침적 과정을 결합했으며, EKI는 수반 모델(adjoint solvers) 없이도 사후분포 공분산을 자연스럽게 제공한다. 앙상블 동역학에 대한 엄밀한 섭동 분석을 통해 고차원 문제에서 일부 입자가 음수 영역으로 진입하여 앙상블 붕괴가 발생할 수 있음을 규명하였다. 따라서 이를 해결하기 위해 평균 지향 로그 장벽, 적응형 확률 투사, 제어된 공분산 팽창을 결합한 하이브리드 제약 전략을 도입하여 앙상블 다양성을 유지하고 역추정 결과의 물리적 비음수성을 보장한다.
이종 관측 데이터를 동시 반영하기 위해 감마선량(전체 핵종 기여)과 시간 평균 농도(개별 핵종)를 칼만 업데이트 과정에서 통합하는 융합 기법을 제안한다. 완전 결합, 블록 대각 결합, 순차 결합, 정규화 결합의 네 가지 방식은 측정 오차 구조를 유지하면서 통계적 최적화와 계산 효율 간의 균형을 조절한다. 이종 관측 데이터를 결합하여 역추정하는 방식은 개별 관측 데이터를 활용했을 때에 대비하여 더 나은 역추정 결과를 얻을 수 있음을 밝혔다.
또한 실시간 분석을 위해 전체 역추정 과정을 텐서 연산으로 표현하고, 맞춤형 CUDA 커널에 구현하였다. 퍼프 이동 및 제거 과정의 물리 모델 연산, 공동 우도 계산, 앙상블 공분산 연산이 수천 개 GPU 코어에서 병렬 실행되며, 적응형 및 지역화된 EKI 서브루틴이 실행 시간을 단축하고 메모리 요구량을 최소화하여 준실시간 역추정을 가능하게 한다.
제안된 통합 체계는 정상 및 과도 방출, 단일 및 다중 사고, 다핵종 시나리오와 후쿠시마 원전사고 초기 사례 연구를 통해 유연성과 효용성을 검증하였다. 각 사례에서 제약 조건이 강화된 EKI는 빠른 수렴과 물리적 왜곡 회피를 보였으며, 수반(adjoint) 방식이나 경사하강법보다 높은 정밀도와 불확실성 분석을 동시에 제공함을 입증하였다. 정교한 확산 모델과 엄밀한 부등식 제약 처리, 이종 관측 동화, 다중 병렬 GPU 연산을 결합함으로써, 본 연구에서 개발한 i-STAR-GPU는 선원항 역추정의 이론 및 응용 범위를 크게 확장시키고, 방사선 비상 상황에서 준실시간 의사결정을 지원하는 첨단기술 기반의 견고한 플랫폼을 제공할 것으로 기대된다.

다국어 초록 (Multilingual Abstract)

The reliable reconstruction of unknown radionuclide releases from sparse and heterogeneous environmental observations remains a critical challenge in radiological emergency response science. Atmospheric dispersion is governed by highly nonlinear meteorological processes, and observation networks collect data at disparate spatiotemporal scales. Moreover, any plausible source term estimate should enforce the fundamental physical constraint of non‐negative activity and dose-rate, since negative values are physically meaningless and undermine interpretability. To address these challenges, this dissertation introduces i-STAR-GPU (Inverse-integrated Source Term Assessment with Radiological-emergency focus, GPU-accelerated), an end-to-end framework that integrates atmospheric transport physics, ensemble-based Bayesian inversion, inequality-constraint enforcement, and massively parallel processing into a single operational pipeline.
At its core, this work recasts Ensemble Kalman Inversion (EKI) as a derivative‐free Bayesian optimization framework for the source term. Forward uncertainty propagation employs Gaussian plume and puff solvers augmented with radioactive decay, dry deposition, and wet scavenging, eliminating the need for adjoint solvers while naturally producing posterior covariance estimates. A rigorous perturbation analysis of ensemble dynamics reveals that, in high‐dimensional inverse settings, unconstrained updates can drive all particle states into the negative orthant, leading to catastrophic ensemble collapse. Therefore, we propose a hybrid constraint strategy, encompassing a mean-based log-barrier, adaptive stochastic projection, and controlled ensemble covariance inflation, that rigorously preserves ensemble diversity and enforces physical non-negativity.
To assimilate heterogeneous data streams, we develop a unified algebraic framework that simultaneously incorporates time-averaged gamma-dose-rates (aggregating all radionuclide contributions) and radionuclide-specific concentrations within a single Kalman update. We derive four fusion schemes: fully coupled, block-diagonal, sequential, and normalized. Each of these schemes preserves the integrity of measurement‐error structure while also offering adjustable trade-offs between statistical optimality and computational cost.
Furthermore, to meet real-time emergency response requirements, the entire inversion workflow is expressed in tensor form and mapped to custom CUDA kernels that execute concurrently across thousands of GPU cores. Adaptive and localized ensemble subroutines further reduce runtime and memory footprint, enabling near-real-time inversions in commodity hardware.
The methodological versatility of i-STAR-GPU is demonstrated through comprehensive synthetic experiments, including scenarios such as steady-state and transient releases, single- and multi-unit accidents, and multi-radionuclide plumes, alongside a case study of the early Fukushima Daiichi release informed by spatial dose‐rate observations. In every scenario, our constraint-enhanced EKI converges rapidly, avoids non‐physical artifacts, and produces posterior uncertainty bounds that are tighter and more interpretable than those from conventional adjoint- or gradient-based approaches. By uniting faithful dispersion physics, rigorous inequality-constraint enforcement, heterogeneous-data fusion, and high-throughput GPU computation, i-STAR-GPU both extends the theoretical foundations of ensemble data assimilation under hard bounds and delivers a practical, scalable, and scientifically robust platform for near-real-time decision support in radiological emergencies.

목차 (Table of Contents)

• Abstract i
• Table of Contents v
• List of Figures xi
• List of Tables xix
• Chapter 1. Introduction 1
• 1.1. Background and Motivation 1
• 1.2. Objective and Scope 5
• Chapter 2. Previous Studies 7
• 2.1. Historical Perspective 7
• 2.1.1. Before the Fukushima Nuclear Accident 8
• 2.1.2. After the Fukushima Nuclear Accident 8
• 2.2. Source Term Estimation Study in Nuclear Accidents 10
• 2.2.1. Back-Trajectory Model 11
• 2.2.2. Reverse Model 12
• 2.2.3. Inverse Model 14
• 2.2.4. Metaheuristic Algorithm 16
• 2.2.5. Machine Learning Algorithm 17
• 2.3. Gap Analysis 19
• 2.4. Integrated Inverse Estimation Research from Regulatory and Emergency response Perspectives 22
• 2.4.1. Global Regulatory Status of Level 3 Probabilistic Safety Assessment 22
• 2.4.2. Mandates, Risk Criteria, and Regulatory Evolution 24
• 2.4.3. International Emergency response Platforms and Inversion Methodologies 24
• 2.4.4. Legal Foundations and Practical Performance Requirements 26
• Chapter 3. Development of the Integrated Inverse Estimation Framework 27
• 3.1. Basic Concept 27
• 3.2. Source Term Information 30
• 3.3. Atmospheric Dispersion Models 33
• 3.3.1. Gaussian Plume Model 34
• 3.3.2. Gaussian Puff Model 36
• 3.3.3. Radionuclide Removal Process 37
• 3.4. Environmental Monitoring Data 38
• 3.4.1. Gamma-dose-rate 39
• 3.4.2. Concentration 40
• 3.5. Ensemble Kalman Inversion (EKI) 40
• 3.5.1. Inverse Modeling: Bayesian Optimization 41
• 3.5.2. Standard Ensemble Kalman Inversion 43
• 3.5.3. Regularized Ensemble Kalman Inversion 47
• 3.5.4. Adaptive Ensemble Kalman Inversion 49
• 3.5.5. Localized Ensemble Kalman Inversion 52
• 3.6. Ensemble Kalman Inversion under Inequality Constraints 54
• 3.6.1. Non-physical (Negative value) Phenomena on Ensemble Kalman Inversion 54
• 3.6.2. Ensemble Collapse Mechanism 55
• 3.6.3. Box-Constraints for Ensemble Kalman Inversion 55
• 3.6.4. Log-Barrier Formulations on Ensemble Kalman Inversion 56
• 3.6.5. Inflation Formulations on Ensemble Kalman Inversion 56
• 3.6.6. Tikhonov Regularization under Inequality Constraints 57
• 3.6.7. Combined Approaches 57
• 3.7. Ensemble Kalman Inversion for Multi-Type Observation 58
• 3.7.1. Spatiotemporal Difference for Each Observation Type 59
• 3.7.2. Combined Method for Ensemble Kalman Inversion Algorithm 59
• 3.7.3. Sequential Method for Ensemble Kalman Inversion Algorithm 62
• 3.7.4. Normalized Method for Ensemble Kalman Inversion Algorithm 64
• 3.7.5. Comparison of Combined, Sequential and Normalized Approach 65
• 3.8. Code Architecture and GPU Parallelization 67
• 3.8.1. Integrated Code Structure 67
• 3.8.2. Connection between Inverse Modeling and Forward Physics Model 69
• 3.8.3. GPU Parallelization 70
• 3.9. Summary 73
• Chapter 4. Performance Evaluation of Integrated Inverse Source Term Estimation Method 75
• 4.1. Introduction 75
• 4.2. Case 1: Source Term Estimation for Steady-State Scenarios 75
• 4.2.1. Source Term Information 76
• 4.2.2. Simulation Settings 76
• 4.2.3. Case 1-1: Single Radionuclide Release 78
• 4.2.4. Case 1-2: Multiple Radionuclide Release 82
• 4.2.5. Case 1-3: Multi-Unit and Multiple radionuclides Release 90
• 4.2.6. Uncertainty Quantifications 91
• 4.2.7. Results and Discussions 100
• 4.3. Case 2: Source Term Estimation for Transient Scenarios 101
• 4.3.1. Source Term Information 102
• 4.3.2. Simulation Settings 104
• 4.3.3. Case 2-1: Single Radionuclide Release 109
• 4.3.4. Case 2-2: Multiple Radionuclide Release 113
• 4.3.5. Uncertainty Quantifications 117
• 4.3.6. Impact of Deposition Effects 119
• 4.3.6. Impact of Inverse Time Step 121
• 4.3.7. Results and Discussions 123
• 4.4. Summary 124
• Chapter 5. Improvements for Inverse Source Term Estimation Methods 127
• 5.1. Accuracy Improvements 127
• 5.1.1. Prior Information Effects 130
• 5.1.2. Uncertainty Removal Techniques 132
• 5.1.3. Measurement Points Placement Optimization 140
• 5.1.4. Results and Discussions 143
• 5.2. Computational Performance Improvements 145
• 5.2.1. Adaptive Ensemble Kalman Inversion 145
• 5.2.2. Localized Ensemble Kalman Inversion 147
• 5.2.3. GPU Parallelization 150
• 5.2.4. Results and Discussions 154
• 5.3. Summary 155
• Chapter 6. Robust Constraint-Handling for Non-Negative (physical bounds) Ensemble Kalman Inversion for Multi-Radionuclide Source Term Estimation 157
• 6.1. Main Problem and Need for Appropriate Constraints 158
• 6.2. Kalman Update with Log-Barrier Constraints 160
• 6.3. Projection Operators After Kalman Update 163
• 6.3.1. Deterministic Clipping 167
• 6.3.2. Uniform Soft Projection with Jitter 167
• 6.3.3. Gaussian Soft Projection 167
• 6.3.4. Adaptive Uniform / Gaussian Soft Projection 168
• 6.4. Space-Transformation-Based Kalman Update 168
• 6.5. Summary 169
• Chapter 7. Multi-Radionuclide Inverse Estimation using Ensemble Kalman Inversion with Multi-Type Environmental Monitoring Data 171
• 7.1. Introduction 171
• 7.2. Multi-Observation Extension Methods for Ensemble Kalman Inversion 173
• 7.2.1. Combined Update for Gamma-dose-rates and Concentrations 173
• 7.2.2. Sequential Update Approach 174
• 7.2.3. Normalization of Both Gamma-dose-rates and Concentrations 174
• 7.2.4. Results and Discussions 174
• 7.3. Summary 177
• Chapter 8. Real-World Application: Fukushima Daiichi Nuclear Power Plant Accident 179
• 8.1. Context and Data Set 179
• 8.1.1. Benchmark Study of the Accident at Fukushima (BSAF) 181
• 8.2. Forward and Inverse Models 183
• 8.3. Reconstructed Release History 184
• 8.3.1. Major Accident Events and Integrated Re-Interpretation 185
• 8.3.2. Impact of Wind-Field Representation on the Inverse Estimation of I-131 Releases 188
• 8.3.3. Oscillatory Behavior of the Inverse Source Term: Diagnosis and Mitigation 196
• 8.4. Impact of Non-Negativity Handling on the Reconstructed I-131 Release History (12 – 16 March 2011) 209
• 8.4.1. Visual consistency with the dose-rate record 210
• 8.4.2. Amplitude fidelity and non-physical artefacts 211
• 8.4.3. Temporal resolution of pulsed emissions 211
• 8.4.4. Operational implications 212
• 8.4.5. Summary of findings 213
• 8.5. Summary 213
• Chapter 9. Conclusions 215
• Bibliography 219
• Appendix 231
• Appendix A. Forward Physics Model 231
• Appendix B. Model Validation and Comparative Analysis 235
• Appendix C. Performance Evaluation of EKI in Estimating Release-rate and Spatial Positioning 239
• Appendix D. Impact of Wind Speed Variations on Radionuclide Estimation and Dispersion Modeling 243
• Appendix E. Genetic Algorithm 247
• Appendix F. Particle Swarm Optimization 249
• Appendix G. Evaluation Metrics 251
• Abstract in Korean (국문 초록) 253