• Nuclear Engineering and Technology
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• v.55 no.10
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• pp.3787-3800
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• 2023

Reactivity Initiated Accident (RIA) scenarios require special attention using advanced simulation techniques due to their complexity and importance for nuclear power plant (NPP) safety. While the conservative approach has traditionally been used for safety analysis, it may lead to unrealistic results which calls for the use of best estimate plus uncertainty (BEPU) approach, especially with the current advances in computational power which makes the BEPU analysis feasible. In this work an Uncontrolled Control Element Assembly (CEA) Withdrawal at Full Power accident scenario is analyzed using the BEPU approach by loosely coupling the thermal hydraulics best-estimate system code (RELAP5/SCDAPSIM/MOD3.4) to the statistical analysis software (DAKOTA) using a Python interface. Results from the BEPU analysis indicate that a realistic treatment of the accident scenario yields a larger safety margin and is therefore encouraged for accident analysis as it may enable more economic and flexible operation.

• Nuclear Engineering and Technology
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• v.53 no.8
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• pp.2523-2533
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• 2021

In the last decade, the best estimate plus uncertainty methodologies in nuclear technology and nuclear power plant design have become a trending topic in the nuclear field. Since BEPU was allowed for licensing purposes by the most important regulator bodies, different uncertainty assessment methods have become popular, overall non-parametric methods. While non-parametric tolerance regions can be well stated and used in uncertainty quantification for licensing purposes, the propagation of the uncertainty through different codes (multi-scale, multiphysics) in cascade needs a better depiction of uncertainty than the one provided by the tolerance regions or a probability distribution. An alternative method based on the parametric or distributional probability boxes is used to perform uncertainty quantification and propagation regarding statistic uncertainty from one code to another. This method is sample-size independent and allows well-defined tolerance intervals for uncertainty quantification, manageable for uncertainty propagation. This work characterizes the distributional p-boxes behavior on uncertainty quantification and uncertainty propagation through nested random sampling.

• Journal of the Korean Society of Systems Engineering
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• v.19 no.2
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• pp.18-31
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• 2023

Exploring artificial intelligence and machine learning for nuclear safety has witnessed increased interest in recent years. To contribute to this area of research, a machine learning model capable of accurately predicting nuclear power plant response with minimal computational cost is proposed. To develop a robust machine learning model, the Best Estimate Plus Uncertainty (BEPU) approach was used to generate a database to train three models and select the best of the three. The BEPU analysis was performed by coupling Dakota platform with the best estimate thermal hydraulics code RELAP/SCDAPSIM/MOD 3.4. The Code Scaling Applicability and Uncertainty approach was adopted, along with Wilks' theorem to obtain a statistically representative sample that satisfies the USNRC 95/95 rule with 95% probability and 95% confidence level. The generated database was used to train three models based on Recurrent Neural Networks; specifically, Long Short-Term Memory, Gated Recurrent Unit, and a hybrid model with Long Short-Term Memory coupled to Convolutional Neural Network. In this paper, the System Engineering approach was utilized to identify requirements, stakeholders, and functional and physical architecture to develop this project and ensure success in verification and validation activities necessary to ensure the efficient development of ML meta-models capable of predicting of the nuclear power plant response.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.20 no.1
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• pp.32-38
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• 2024

The best estimate plus uncertainty methodologies for loss-of-coolant accident analyses make use of the best-estimate codes and relevant experimental databases. Inherently, best-estimate codes have various uncertainties in the model parameters, which can be quantified by the dedicated experimental database. Therefore, this study was devoted to establishing procedures for identifying the input parameters of predictive models and quantifying their uncertainty ranges. The rod bundle heat transfer experiments were employed as a representative reflood separate effect test, and the TRACE code was utilized as a best-estimate code. In accordance with the present procedure for uncertainty quantification, the integrated list of the influential input parameters and their uncertainty ranges was obtained through local sensitivity calculations and screening criteria. The validity of the procedure was confirmed by applying it to uncertainty analyses, which checks whether the measured data are within computed ranges of the variables of interest. The uncertainty quantification procedure proposed in this study is anticipated to provide comprehensive guidance for the conduct of uncertainty analyses.

• Journal of the Korean Society of Systems Engineering
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• v.18 no.2
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• pp.75-93
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• 2022

Machine learning (ML) data-driven meta-model is proposed as a surrogate model to reduce the excessive computational cost of the physics-based model and facilitate the real-time prediction of a nuclear power plant's transient response. To forecast the transient response three machine learning (ML) meta-models based on recurrent neural networks (RNNs); specifically, Long Short Term Memory (LSTM), Gated Recurrent Unit (GRU), and a sequence combination of Convolutional Neural Network (CNN) and LSTM are developed. The chosen accident scenario is a control element assembly withdrawal at power concurrent with the Loss Of Offsite Power (LOOP). The transient response was obtained using the best estimate thermal hydraulics code, MARS-KS, and cross-validated against the Design and control document (DCD). DAKOTA software is loosely coupled with MARS-KS code via a python interface to perform the Best Estimate Plus Uncertainty Quantification (BEPU) analysis and generate a time series database of the system response to train, test and validate the ML meta-models. Key uncertain parameters identified as required by the CASU methodology were propagated using the non-parametric Monte-Carlo (MC) random propagation and Latin Hypercube Sampling technique until a statistically significant database (181 samples) as required by Wilk's fifth order is achieved with 95% probability and 95% confidence level. The three ML RNN models were built and optimized with the help of the Talos tool and demonstrated excellent performance in forecasting the most probable NPP transient response. This research was guided by the Systems Engineering (SE) approach for the systematic and efficient planning and execution of the research.

• Nuclear Engineering and Technology
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• v.55 no.9
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• pp.3423-3440
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• 2023

In this work, a multivariate time-series machine learning meta-model is developed to predict the transient response of a typical nuclear power plant (NPP) undergoing a steam generator tube rupture (SGTR). The model employs Recurrent Neural Networks (RNNs), including the Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and a hybrid CNN-LSTM model. To address the uncertainty inherent in such predictions, a Bayesian Neural Network (BNN) was implemented. The models were trained using a database generated by the Best Estimate Plus Uncertainty (BEPU) methodology; coupling the thermal hydraulics code, RELAP5/SCDAP/MOD3.4 to the statistical tool, DAKOTA, to predict the variation in system response under various operational and phenomenological uncertainties. The RNN models successfully captures the underlying characteristics of the data with reasonable accuracy, and the BNN-LSTM approach offers an additional layer of insight into the level of uncertainty associated with the predictions. The results demonstrate that LSTM outperforms GRU, while the hybrid CNN-LSTM model is computationally the most efficient. This study aims to gain a better understanding of the capabilities and limitations of machine learning models in the context of nuclear safety. By expanding the application of ML models to more severe accident scenarios, where operators are under extreme stress and prone to errors, ML models can provide valuable support and act as expert systems to assist in decision-making while minimizing the chances of human error.

• Nuclear Engineering and Technology
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• v.55 no.7
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• pp.2670-2677
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• 2023

In the nuclear safety studies, a new trend refers to the evaluation of uncertainties as a mandatory component of best-estimate safety analysis which is a modern and technically consistent approach being known as BEPU (Best Estimate Plus Uncertainty). The major objectives of this study consist in performing a study of uncertainties/sensitivities of the major analysis results for a generic CANDU 6 Nuclear Power Plant during Station Blackout (SBO) progression to understand and characterize the sources of uncertainties and their effects on the key figure-of-merits (FOMs) predictions in severe accidents (SA). The FOMs of interest are hydrogen mass generation and event timings such as the first fuel channel failure time, beginning of the core disassembly time, core collapse time and calandria vessel failure time. The outcomes of the study, will allow an improvement of capabilities and expertise to perform uncertainty and sensitivity analysis with severe accident codes for CANDU 6 Nuclear Power Plant.

• Nuclear Engineering and Technology
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• v.48 no.3
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• pp.684-701
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• 2016

The Gaussian process model (GPM) is a flexible surrogate model that can be used for nonparametric regression for multivariate problems. A unique feature of the GPM is that a prediction variance is automatically provided with the regression function. In this paper, we estimate the safety margin of a nuclear power plant by performing regression on the output of best-estimate simulations of a large-break loss-of-coolant accident with sampling of safety system configuration, sequence timing, technical specifications, and thermal hydraulic parameter uncertainties. The key aspect of our approach is that the GPM regression is only performed on the dominant input variables, the safety injection flow rate and the delay time for AC powered pumps to start representing sequence timing uncertainty, providing a predictive model for the peak clad temperature during a reflood phase. Other uncertainties are interpreted as contributors to the measurement noise of the code output and are implicitly treated in the GPM in the noise variance term, providing local uncertainty bounds for the peak clad temperature. We discuss the applicability of the foregoing method to reduce the use of conservative assumptions in best estimate plus uncertainty (BEPU) and Level 1 probabilistic safety assessment (PSA) success criteria definitions while dealing with a large number of uncertainties.

• Nuclear Engineering and Technology
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• v.46 no.5
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• pp.619-632
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• 2014

The Best Estimate Plus Uncertainty (BEPU) method has been widely used to evaluate the uncertainty of a best-estimate thermal hydraulic system code against a figure of merit. This uncertainty is typically evaluated based on the physical model's uncertainties determined by expert judgment. This paper introduces the application of data assimilation methodology to determine the uncertainty bands of the physical models, e.g., the mean value and standard deviation of the parameters, based upon the statistical approach rather than expert judgment. Data assimilation suggests a mathematical methodology for the best estimate bias and the uncertainties of the physical models which optimize the system response following the calibration of model parameters and responses. The mathematical approaches include deterministic and probabilistic methods of data assimilation to solve both linear and nonlinear problems with the a posteriori distribution of parameters derived based on Bayes' theorem. The inverse problem was solved analytically to obtain the mean value and standard deviation of the parameters assuming Gaussian distributions for the parameters and responses, and a sampling method was utilized to illustrate the non-Gaussian a posteriori distributions of parameters. SPACE is used to demonstrate the data assimilation method by determining the bias and the uncertainty bands of the physical models employing Bennett's heated tube test data and Becker's post critical heat flux experimental data. Based on the results of the data assimilation process, the major sources of the modeling uncertainties were identified for further model development.

• Nuclear Engineering and Technology
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• v.44 no.6
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• pp.611-622
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• 2012

"Scaling" plays an important role for safety analyses in the licensing of water cooled nuclear power reactors. Accident analyses, a sub set of safety analyses, is mostly based on nuclear reactor system thermal hydraulics, and therefore based on an adequate experimental data base, and in recent licensing applications, on best estimate computer code calculations. In the field of nuclear reactor technology, only a small set of the needed experiments can be executed at a nuclear power plant; the major part of experiments, either because of economics or because of safety concerns, has to be executed at reduced scale facilities. How to address the scaling issue has been the subject of numerous investigations in the past few decades (a lot of work has been performed in the 80thies and 90thies of the last century), and is still the focus of many scientific studies. The present paper proposes a "roadmap" to scaling. Key elements are the "scaling-pyramid", related "scaling bridges" and a logical path across scaling achievements (which constitute the "scaling puzzle"). The objective is addressing the scaling issue when demonstrating the applicability of the system codes, the "key-to-scaling", in the licensing process of a nuclear power plant. The proposed "road map to scaling" aims at solving the "scaling puzzle", by introducing a unified approach to the problem.