AI-Assisted Forecasting of a Mitigated Multiple Steam Generator Tube Rupture Scenario in a Typical Nuclear Power Plant

Abstract

This study is focused on developing a machine learning (ML) meta-model to predict the progression of a multiple steam generator tube rupture (MSGTR) accident in the APR1400 reactor. The accident was simulated using the thermal–hydraulic code RELAP5/SCDAPSIM/MOD3.4. The model incorporates a mitigation strategy executed through operator interventions. Following this, uncertainty quantification employing the Best Estimate Plus Uncertainty (BEPU) methodology was undertaken by coupling RELAP5/SCDAPSIM/MOD3.4 with the statistical software, DAKOTA 6.14.0. The analysis concentrated on critical safety parameters, including Reactor Coolant System (RCS) pressure and temperature, as well as reactor vessel upper head (RVUH) void fraction. These simulations generated a comprehensive dataset, which served as the foundation for training three ML architectures: Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), and Convolutional LSTM (CNN+LSTM). Among these models, the CNN+LSTM hybrid configuration demonstrated superior performance, excelling in both predictive accuracy and computational efficiency. To bolster the model’s transparency and interpretability, Integrated Gradients (IGs)—an advanced Explainable AI (XAI) technique—was applied, elucidating the contribution of input features to the model’s predictions and enhancing its trustworthiness.

1. Introduction

The 2011 Fukushima Nuclear Power Plant (NPP) accident highlighted the critical need to enhance safety measures during extreme events exceeding Design Basis Accidents (DBAs). In response, the concept of Design Extension Conditions (DECs) was introduced to evaluate NPP resilience to severe accidents and to develop effective mitigation strategies. Among DEC scenarios, the multiple steam generator tube rupture (MSGTR) accident stands out due to its rapid progression and heightened potential for radioactive release compared to a single-tube rupture scenario [1]. During an MSGTR accident, a void fraction in the reactor vessel upper head (RVUH) can lead to core uncovering and melting if not mitigated in a timely manner. This underscores the importance of initial operator actions within a response time shorter than the standard 30 min to ensure safe plant shutdown. Due to the risk of reactor core damage, potential radiological leakage, and stringent operator requirements, the MSGTR scenario demands thorough thermal–hydraulic analysis and drives the exploration of AI-based technologies to ensure safety.

Although the safety analysis of APR1400 in the Design Safety Document was conducted using a conservative approach, the IAEA recommended the Best Estimate Plus Uncertainty (BEPU) approach as a tool for a more realistic safety assessment. The BEPU methodology emerged as a key approach, offering realistic alternatives to conservative analyses by integrating practical assumptions and considering a spectrum of uncertainties [2]. BEPU allows for realistic safety analyses that enhance thermal–hydraulic system modeling and provide solutions to technical issues in NPPs [3]. This led the IAEA to recommend the adoption of the BEPU approach given its potential benefits for operational flexibility and cost-effectiveness [4]. Due to its irrefutable advantages, BEPU is now applied both in the licensing process of reactors and extensively by researchers. Zhang [3] detailed the application process and examples of BEPU in system thermal–hydraulic and multi-physics codes, emphasizing its necessity for compliance with updated safety criteria for DBAs and quantifying margins in DECs. For example, Rey et al. [5] applied BEPU to analyze the control element assembly withdrawal at full power accident scenario in the APR1400 reactor, demonstrating its capability to provide accurate safety margins. Similarly, Lee [6] employed BEPU to calculate the Peak Cladding Temperature (PCT) and Maximum Cladding Temperature (MCT) in a CANDU spent fuel storage canister, utilizing a robust uncertainty analysis method to achieve high confidence in the results. IAEA guidelines, as well as numerous scientific publications, highlight the many advantages of conducting analyses using the BEPU method. Moreover, BEPU enables the generation of multiple possible outcomes for a single-accident scenario, providing a valuable dataset for training machine learning models. For these reasons, the present study is based on a thermal–hydraulic analysis using the BEPU approach.

Considering its potential consequences, the MSGTR accident warrants detailed analysis and careful evaluation of the operator’s actions. Due to the specific and stringent requirements placed on the operator, many researchers have investigated the development of an effective mitigation strategy. In his work, Bang [7] presents two main strategies for mitigating the effects of an MSGTR accident. The first approach involves supplementing the RCS inventory with high-pressure safety injection (HPSI) and using the pressurizer’s main spray along with the intact steam generator (SG) for partial cooling. This strategy helps prevent the core from being uncovered by stabilizing the RCS inventory, yet it may increase RCS pressure, raising the likelihood of the MSSVs opening, which could lead to radiation release into the environment. The second strategy focuses on cooling the RCS through the intact SG while limiting safety injections. This approach minimizes the chance of MSSV activation by quickly depressurizing the RCS; however, it also lowers the RCS inventory and can result in backflow.

Bae et al. [8] developed a set of operator’s actions to mitigate a MSGTR accident scenario for OPR1000 system. Dzien and Diab [9] verified the efficacy of this strategy for APR1400 in consideration of various operational and design uncertainties in alignment with IAEA recommendation. Lim [10] conducted a best-estimate analysis of the MSGTR accident in CANDU-6 plants using the MAAP-ISAAC code, applying Severe Accident Management Guidance (SAMG) to limit fission product release and conducting radiological analysis. Jeong [11] identified tube ruptures on the hot side of the steam generator as the most hazardous, emphasizing the complexity of MSGTR scenarios. Additional research includes Yoon’s [12] RELAP5-based modeling of MSGTR in APR1400. In the present study, the analysis by Dzien and Diab [9] was used as a starting point, revised and improved, and then integrated with AI technology to enhance plant safety during the MSGTR accident.

Artificial Intelligence (AI) is poised to become a cornerstone of future advancements in almost all aspects of our society. Machine learning (ML), particularly deep learning, has emerged as a powerful tool for solving complex problems across various domains, including image and speech recognition, natural language processing, and predictive modeling [13]. Its ability to automatically learn and identify patterns from large datasets has led to transformative advancements in research and practical applications.

The integration of deep learning methods into fields such as nuclear engineering and safety analysis further underscores its versatility and potential for advancing complex analytical frameworks [14]. One of its promising applications lies in predicting accidents in NPPs. Additionally, the concept of virtual twins is gaining traction [15], offering virtual replicas of physical assets or systems that can simulate real-world scenarios for testing, optimization, and predictive maintenance.

Deep learning, a subset of ML employing multi-layered neural networks, captures hierarchical data representations with remarkable precision [16]. Architectures such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) excel in image analysis and sequential data processing, respectively, while more specialized networks like Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRUs) effectively address long-range dependencies in time-series data [17]. Nanjappan [18] showed the effectiveness of LSTM and GRU architectures in internet of things (IoT) intrusion detection, highlighting the computational efficiency of GRUs in real-world applications. Nguyen and Diab [19] demonstrated the utility of LSTM and GRUs in forecasting the transient response of the APR1400 plant to a steam generator tube rupture (SGTR) accident. Despite their strengths, these models often exhibit black-box characteristics, limiting their interpretability and acceptance in high-stakes fields like nuclear safety analysis.

Explainable Artificial Intelligence (XAI) bridges this gap by enhancing the interpretability of complex ML models. Among XAI techniques, Integrated Gradients (IGs) method effectively attributes model predictions to input features, enabling transparent and trustworthy decision-making [20]. This method has been effectively applied across diverse domains. For instance, Bhat and Raychowdhury proposed a non-uniform interpolation scheme to accelerate IG computations, achieving significant performance improvements in real-time applications [21]. They similarly utilized IGs to select textural characteristics in chest X-rays for pneumonia lesion classification, demonstrating their utility in medical image analysis [22]. These studies underscore the versatility and effectiveness of Integrated Gradients in enhancing model interpretability across critical and responsible fields such as medicine, highlighting the potential application of IGs in nuclear safety analysis, where understanding model predictions is essential for regulatory compliance and operational reliability.

Building on foundational studies, this work seeks to harness its potential in thermal–hydraulic safety analysis. Specifically, we aim to develop, optimize, and explain a machine learning model that utilizes the Integrated Gradients XAI method to forecast the progression of MSGTR accidents in the APR1400 reactor. This effort represents a step toward integrating AI into safety analysis, enhancing the safe and reliable operation of NPPs.

2. Methodology

The research work focused on key safety parameters relevant to the accident: RCS temperature, RCS pressure, and RVUH void fraction. Unlike temperature and pressure, the RVUH void fraction cannot be accurately or directly measured during accident events in the APR1400; thus, computational methods using thermal–hydraulic codes is essential to estimate this parameter.

Figure 1 provides a detailed documentation of the entire workflow of this study. The main building blocks are as follows: thermal hydraulic model, uncertainty quantification and data generation, and machine learning model. For brevity, the development of the thermal–hydraulic model and uncertainty quantification framework is not detailed here; readers are encouraged to consult the work by Dzien and Diab [9].

The MSGTR accident, involving the rupture of five tubes in the APR1400, was initially modeled as a double-ended guillotine break on the hot leg side, as this scenario is shown to potentially lead to the shortest MSSV opening time and the largest discharge flow [12]. The simulation was performed using the thermal–hydraulic code RELAP5/SCDAPSIM/MOD3.4, incorporating operator mitigation actions. The initial conditions were set as close as possible to APR1400 nominal conditions to reflect realistic operating conditions, following the BEPU methodology.

Given the rapid progression of an MSGTR accident, prompt and effective operator actions are essential to mitigate the event and ensure plant safety. Building on the work of Bae et al. [8], the first operator action is modeled to occur 10 min after the reactor trip, involving a manual trip of all four RCPs. Five minutes later, a temporary RCS cooldown is initiated through the manual operation of the main steam isolation bypass valve (MSIBV) and the Steam Blowdown Control System (SBCS) to discharge steam from the affected SG to the condenser.

Table 1. Operator’s actions timeline.

	Timeline	Operator Action
#1	Reactor trip + 10 min	Manual trip of 4 RCPs
#2	Reactor trip + 15 min	Manual opening of MSIBVs and TBVs for temporary RCS cooldown
#3	OA#2 + 2 min	Pressurizer Auxiliary Spray activation
#4	OA#3 + 2 min	Affected steam generator blowdown operation (200 s)
#5	OA#4 + 2 min	Manual opening of ADV in unaffected steam generator
#6	OA#5 + 1 h	Restarting one RCP per loop

outlines all operator actions along with their respective timelines.

The next step encompasses the generation of a database for training the machine learning model. This is achieved by developing an uncertainty analysis framework to simulate the accident using the BEPU method. Here, the statistical software, DAKOTA, is coupled with the RELAP5/SCDAPSIM/MOD3.4 code via a Python interface.

The IAEA has outlined multiple sources of uncertainty that need to be considered in a BEPU analysis. These include uncertainties in input data, models, numerical methods, experiments, scaling, extrapolation, assumptions, simplifications, code reliability, and human errors [19]. Furthermore, for each accident scenario, it is possible to identify the key phenomena causing uncertainties via a Phenomena Identification and Ranking Table (PIRT). Westinghouse [23] and Ahn [24] developed PIRT methods for SGTR accidents, with Youn [25] focusing on the MSGTR scenario for APR1400 reactors.

Following their work, the critical phenomena associated with MSGTR were identified and utilized to define the key uncertain parameters. These include 13 uncertain parameters modeled with normal distributions and 19 with uniform distributions, each within specified ranges. For each simulation run, DAKOTA randomly selected uncertain parameters from specified probability distributions and ranges. The software used the Latin Hypercube Sampling (LHS) technique for parameter sampling. These parameters were then inserted into the RELAP5/SCDAPSIM/MOD3.4 simulation input file to model the system’s response under varying uncertain conditions.

The number of iterations was determined using Wilk’s k-order formula. The choice of Wilk’s method for this study was driven by its simplicity, accuracy, and acceptance in regulatory contexts as specified by the USNRC 95/95 rule. Wilks’ 5th order was selected given the recognition that 3rd order or higher typically produce more precise and reliable outcomes [26]. A database is generated that comprises 600 potential MSGTR accident progression scenarios, and stored in a mySQL database due to the large amount of data that would not fit into standard CSV files. This dataset is then used to develop and train three ML models, namely: GRU, LSTM, and LSTM + CNN.

Finally, the best-performing model was analyzed using the XAI technique known as Integrated Gradients to explain its prediction-making process and enhance model credibility. The development of the ML meta-models will be delineated next.

2.1. Machine Learning Model Development

Machine learning, a branch of AI, focuses on developing algorithms and meta-models that enable computers to learn from data and make predictions or decisions without explicit programming. By identifying patterns and relationships within datasets, machine learning algorithms continuously improve their performance. Deep learning, a subset of machine learning, utilizes artificial neural networks with multiple layers to capture complex data representations. Recurrent neural networks (RNNs), a type of deep learning architecture, are designed to process sequential data by maintaining a hidden state that retains information from previous time steps. This makes RNNs particularly effective for tasks such as time series forecasting, where the sequence and context of data are crucial. The basic architecture of the RNN model is presented in Figure 2.

2.1.1. Model Selection

To predict the APR1400 reactor’s response to MSGTR accidents, three deep learning models based on RNN architectures were selected and developed:

▪

Gated Recurrent Unit (GRU)

GRUs are a simplified type of RNN architecture designed specifically for time series data. They incorporate two gates: reset and update. The reset gate determines which parts of the previous information should be discarded, whereas the update gate controls how much information from the previous time step should be retained and passed forward. GRUs use sigmoid and tanh activation functions to manage the flow of information, balancing simplicity and performance. Their streamlined design reduces computational complexity while maintaining essential information, making them highly effective for sequential data tasks, such as predicting accident progression over time. The basic architecture of the GRU model is presented in Figure 3.

▪

Long Short-Term Memory (LSTM)

LSTMs improve upon standard RNNs by incorporating three gates: forget, update and output gates. The forget gate discards irrelevant information from the previous state, while the update gate decides what new information to add to the next state, and the output gate filters the information to be passed as its output. This gated structure enables LSTMs to manage long-term dependencies effectively, making them particularly useful for multivariate time series forecasting. Despite their robustness, LSTMs may still face issues like vanishing and exploding gradients, though their advanced design helps mitigate these challenges and enhances dependency modeling. The basic architecture of the RNN model is presented in Figure 4.

▪

Hybrid Convolutional Neural Network-LSTM (CNN-LSTM)

The CNN-LSTM model combines the strengths of CNNs and LSTMs, leveraging their complementary abilities. While the CNN layer identifies patterns and extracts features from input data, filtering out noise, the LSTM layer processes the refined data for time series predictions. Although CNNs are primarily used for image classification due to their grid-like two-dimensional topology, they can be adapted to time series data using 1D, 2D, or 3D convolutions. The input is filtered through convolutional layers where weighted summation and feature extraction occur. The final fully connected and dense layers label the input data. In this hybrid model, the dataset undergoes preprocessing (normalization, reshaping, and inverse transformation), passes through the CNN layer for noise reduction, and is then processed by the LSTM for prediction. This combination enhances computational efficiency and performance in time series prediction tasks, making it a robust choice for forecasting complex accident scenarios. The detailed architecture of the CNN-LSTM model used in the study is shown in Figure 5.

2.1.2. Parameters Selection and Database Generation

The foundation of training machine learning (ML) models lies in the database, which enables the models to identify and learn dependencies. Given the impossibility of replicating nuclear power plant (NPP) accidents in real-world conditions, simulation data were used. Through logical reasoning, 34 parameters critical to the progression of the accident were identified, including reactor power, decay heat, RCS pressure, RCS temperature, pressurizer water level, SG pressure and water level, steam blowdown flow, safety injection pump (SIP) flow, auxiliary spray flow, main steam isolation bypass valve (MSIBV) flow, auxiliary feedwater (AFW) flow, RCS flow, hot leg (HL) and cold leg (CL) temperatures, and reactor vessel upper head (RVUH) void fraction.

The dependencies among these parameters were confirmed by constructing a covariance matrix (Figure 6). To predict the key parameters for the MSGTR accident—RCS pressure, RCS temperature, and RVUH void fraction—Spearman’s rank correlation coefficient was calculated between these parameters and the rest of the dataset. Parameters with an absolute correlation value greater than 0.25 were retained, resulting in a preliminary set of 25 parameters.

To enhance model efficiency, parameters with overlapping trends, such as temperature and saturation temperature in hot and cold legs, were removed. The final list contained 17 essential parameters: reactor power, SG pressure and water level, RCS pressure and temperature, MSIBV mass flows, MFW mass flows, UH temperature, RCP mass flow, and AFW mass flow.

Using the RELAP5/SCDAPSIM/MOD3.4 code coupled with DAKOTA software, a simulation database was generated with 600 iterations over 14,000 s, resulting in a dataset with 8.4 million rows and 18 columns, with time as an additional parameter. By applying the BEPU methodology and the statistical software, the simulations produced varying results as uncertain parameters were considered. Consequently, a broad range of possible accident outcomes were obtained.

2.1.3. Data Preprocessing

Data scaling is essential due to the wide range of parameter magnitudes, where large values could skew the model’s accuracy. A standard scaler is employed to normalize the data. The dataset is then partitioned into training (80%) and testing (20%) subsets, with an additional 80:20 split applied to the training set for validation purposes. The training dataset is used for model learning by adjusting weights and biases. The validation dataset monitors the model’s learning progress, whereas the testing dataset is used to predict NPP responses to unseen data.

A dataset of dependent (y) and independent (x) variables is created, where the time step is set to 10 s. This allowed the model to predict the value of the 18th parameter at the 11th second based on the preceding 10 s. Finally, the dataset was reshaped into the format (samples, time steps, and features) as required by the ML models.

2.1.4. Training and Evaluation of the Models

The models were designed to predict three critical safety-related parameters: RCS pressure, RCS temperature, and RVUH void fraction. Using a trial-and-error approach, the hyperparameters were fine-tuned to optimize the model’s accuracy and efficiency. Given the lengthy duration of each simulation (14,000 s), the large dataset posed computational challenges. To mitigate this, the number of epochs was capped at 10 as accuracy gains were negligible beyond this point, enhancing computational efficiency. A list of the hyperparameters with specific details are summarized in

Table 2. Hyperparameters of ML models.

Hyperparameters	GRU	LSTM	CNN + LSTM
Optimizer	Adam	Adam	Adam
Epoch	10	10	10
Batch size	700	700	700
Activation function	relu	relu	relu
Hidden layers	1	1	2
Units in hidden layers	3 × 50	3 × 50	110 + 120 + 3 × 50
Hidden architecture	2× GRU + Dense	2× LSTM + Dense	2× Conv1D 2× LSTM + Dense
Kernel regularizes	1	1	1

. The hyperparameters were chosen through trial and error, and by referencing open-source models and those previously used by Nguyen and Diab [19].

Subsequent to training, the model performance was evaluated using several metrics including: mean absolute error (MAE), mean square error (MSE), root-mean-square error (RMSE), the coefficient of determination (R²), and prediction accuracy. It is crucial to monitor errors using multiple metrics during training, as certain metrics may be more sensitive to outliers than others.

MAE measures the average absolute difference between actual and predicted values:

$$MAE={\displaystyle \frac{1}{n}}{\sum }_i^n|y_i^{actual}-y_i^{predicted}|$$

(1)

MSE calculates the average squared difference, penalizing larger errors more heavily due to the squaring operation:

$$MSE={\displaystyle \frac{1}{n}}{\sum }_i^n{(y_i^{actual}-y_i^{predicted})}^2$$

(2)

RMSE is the square root of MSE, and also penalizes larger errors while providing error magnitudes in the target variable’s units:

$$RMSE=\sqrt{MSE}$$

(3)

The R² metric indicates how well the model predicts variance in the target variable, while the prediction accuracy is computed by dividing the average of predicted values by actual values and multiplying by 100%. The ideal performance targets are 0 for MAE, MSE, and RMSE, 1 for R², and 100% for accuracy. These metrics ensure comprehensive error monitoring, as different metrics respond differently to outliers, making them essential for robust model validation.

Based on the results accuracy and training duration, the most effective model was selected. To gain insight into the selected model’s prediction process and demonstrate its reliability through logical reasoning, the model was analyzed using the Explainable AI (XAI) technique of Integrated Gradients, as described in the following section.

2.1.5. Explainable Artificial Intelligence (XAI)

Explainable AI (XAI) has become an essential element of machine learning, providing methods to enhance the transparency and interpretability of complex models. By providing insight into the model’s decision-making process, XAI methods enable stakeholders to verify, trust, and refine predictive systems, ensuring they meet critical safety standards. In the final stage of this study, the Integrated Gradient (IG) method was employed to explain the model’s prediction process. The IG method attributes importance to input features based on their contribution to the output, offering a clear understanding of how changes in input features affect predictions.

The IG method operates by computing the path integral of the output gradients with respect to the input, which is traced along a straight-line path from a baseline input to the actual input. This ensures that each feature’s attribution is based on its value’s deviation from the baseline, which is often an input with minimal or zeroed values. The IG method is both theoretically robust and practically interpretable, adhering to the principles of sensitivity and implementation invariance, making it ideal for safety-critical applications. The IG calculation is expressed as follows:

$${IG}_i\left(x\right)=\left(x_i-x_i^{\mathrm{\prime }}\right){\int }_{\alpha =0}^1{\displaystyle \frac{\partial F\left(x^{\mathrm{\prime }}+\alpha ·\left(x-x^{\mathrm{\prime }}\right)\right)}{\partial x_i}}d\alpha$$

(4)

where

• $F\left(x\right)$—the predictive model output to be explained.
• $x—$ the input vector used to explain the prediction.
• $x\mathrm{\prime }—$ the baseline vector, representing a reference point (often a zero vector).
• $\alpha —$ the path parameter, which scales from the baseline $x\mathrm{\prime }$ to the actual input $x$.
• ${\displaystyle \frac{\partial F\left(x\right)}{\partial x_i}}—$ the partial derivative of the model output with respect to the ith feature of the input.

This equation calculates the integral of the model’s gradient along a path from the baseline x′ to the actual input, x, assigning an importance score to each feature based on how its change influences the output. A positive IG value indicates that increasing the feature moves the prediction towards the current output, meaning it positively contributes to the predicted outcome. Conversely, a negative IG value suggests that increasing the feature would push the prediction away from the output, indicating a negative correlation.

For the selected best performing model, IGs were calculated and averaged across all input features throughout the entire transient. The only exception was the parameter that was both predicted and used as an input feature, given its influence on the model’s prediction. The objective was to understand how the model interprets the remaining features, shedding light on their relative importance in the prediction process.

3. Results

3.1. MSGTR Simulation Results

To maintain brevity, the condensed results of the thermal–hydraulic model and the uncertainty quantification are presented below. Readers are encouraged to refer to the work of Dzien and Diab [9] for detailed information. Sequences of events and corresponding operator actions are summarized in

Table 3. Sequence of events.

Time [s]	Event
0.0	Rupture of five u-tubes
151.0	Reactor trip
191.0	SIP starts
751.0	RCPs trip (OA#1)
858.0	Affected SG isolation due to high SG water level
1051.0	MSIBVs and TBV open (OA#2)
1171.0	Pressurizer Auxiliary Spray operation (OA#3)
2514.0	MSIBVs and TBV close
2634.0	SGBD operation (OA#4)
2954.0	ADV open in unaffected SG (OA#5)
4739.0	AFW activation in unaffected SG
6554.0	RCP restart—1 per loop (OA#6)
11,250.0	SCS entry condition

.

The simultaneous rupture of five u-tubes at 0 s in the affected SG results in the leakage of RCS inventory into the secondary side. This, in turn, leads to a rapid decline in the primary side pressure and a corresponding drop in the pressurizer water level. The reduction in the RCS pressure results in a decrease in the saturation temperature of the primary side. When the difference between the temperature of the hot leg and that of the saturation temperature becomes less than 7.2 K, the reactor is tripped after 151 s. Concurrent with the reactor trip, the turbine is also tripped, and the feedwater flow to the down comer region is terminated. When the pressure of the primary side drops below 80 Pa, the low pressurizer pressure (LPP) signal initiates the activation of SIP at 199 s. The initiation of safety injection causes the RCS pressure to drop at a slower rate.

Ten minutes after the reactor trip, i.e., at 751 s, the operator manually stops all four RCPs. Subsequently, at 858 s, the MSIS signal is generated given the continuous leakage of RCS coolant, which increases the affected SG water level. The isolation of the affected SG results in a loss of its heat removal capability, leading to a pressure peak.

In order to implement a temporary RCS cooldown, the operator manually opens the MSIBVs and TBVs at 1051 s. This enables the generated steam to be dumped into the condenser. The process allows the generated steam to be discharged into the condenser, which results in a decline in temperature and pressure below the MSSV opening setpoint.

Then, 2 min after, at 1171 s, the operator activates the PZR auxiliary spray, which causes the pressurizer water level to rise, and subsequently depressurizes the RCS and affected SG. When the hot leg temperature reaches 558.15 K, the MSIBVs and TBVs are closed at 2514 s, causing the pressure in the affected SG to start rising again. Due to the continuous leakage of the RCS coolant through the break, the water level of the affected SG exceeded 100%. In response, the operator initiates the SGBD operation at 2634 s. Following the completion of the SG emergency blowdown procedure, the operator opens the unaffected SG’s ADV at 2954 s to continue the cooldown and depressurization of the RCS. This procedure leads to a pressure drop in the unaffected SG (Figure 7). A reduction in the unaffected steam SG water level results in the activation of the auxiliary feedwater system at 4739 s. The system remains active until the SG is filled with water to the closing setpoint. From this point until the end of the simulation, the AFW system is activated whenever the water level fell below the setpoint due to evaporation and discharge through the ADV. The system is then deactivated once the water level is restored to the closer setpoint.

The coordinated operation of the AWF and ADV systems significantly enhances the heat removal from the unaffected SG, leading to a reduction in its pressure. The RCS temperature also begins to steadily decrease. However, natural circulation is insufficient to depressurize the primary side. Therefore, one hour after the ADV is opened, the operator manually starts one RCP per loop. The initial startup of the pumps results in a pressure peak in the unaffected SG. However, the pressure throughout the entire system begins to decrease afterwards. The increased coolant flow leads to an effective cooldown and depressurization of the RCS, enabling the plant to reach safe SCS conditions at 11250 s.

The uncertainty analysis revealed that in all cases, the MSSVs remained closed, preventing any radiological release. The RCS pressure and temperature followed the nominal response without significant deviations. Thanks to the implementation of operator actions, the accident can be successfully mitigated, and the system is brought to a safe shutdown condition, as evidenced by Figure 8.

Figure 9 presents the void fraction of the reactor vessel upper head (RVUH), which is filled with vapor. This occurs as a consequence of inventory leakage due to the break and the decline in saturation temperature. The void persisted until the restart of RCPs, at which point the vapor collapsed and a flow was once again established. Furthermore, the restart of RCPs resulted in a reduction in the break flow to a value of approximately 0 kg/s. The break flow was driven by the pressure differential between the primary and secondary sides. As this differential decreased, the leakage was constrained. In the interval of 3413.0–7316.0 s, the natural circulation caused a backflow, which was initially exacerbated by the restart of the RCPs. This was due to the pressure and temperature dropping more rapidly in the cooled RCP than in the isolated affected SG. In each iteration, the plant successfully achieved SCS conditions, the MSSVs were not activated, and the RVUH void fraction collapsed. In conclusion, the simulation demonstrated that the accident was successfully mitigated with the appropriate operator actions.

3.2. Machine Learning Model Results

The collected results of the fitted and evaluated models are summarized in

Table 4. ML models’ performance results.

Parameter	Model	MSE	MAE	R2	Accuracy (%)	Step Time (ms/Step)
RCS pressure	GRU	0.00167	0.0021	0.998	99.60	25.3
	LSTM	0.00170	0.0895	0.998	98.81	30.0
	CNN + LSTM	0.00160	0.0019	0.998	99.64	7.0
RCS temperature	GRU	0.00064	0.0012	0.999	99.58	25.3
	LSTM	0.00064	0.0015	0.999	98.94	30.3
	CNN + LSTM	0.00065	0.0029	0.999	98.80	7.0
RVUH void	GRU	0.00044	0.0152	0.999	99.73	26.5
	LSTM	0.00065	0.0018	0.999	99.58	31.0
	CNN + LSTM	0.00013	0.0029	0.999	99.37	7.0

. All models delivered outstanding prediction accuracy, consistently exceeding 98.8%. The CNN + LSTM model showed superior overall performance, with an exceptionally short training time and a step time of 7.0 ms/step, which was nearly four times faster than other models. In comparison, the LSTM model required the longest training time, with an average step time of 30.5 ms/step, making the model impractical.

Due to its accuracy and training time, the CNN + LSTM model was recognized as the best performing model with the most practical potential.

Figure 10, Figure 11 and Figure 12 below show the training and validation losses recorded during the fitting process. Overall, the training was smooth and effective for all parameters and models. However, slight fluctuations and minor noise were observed in the GRU model for RCS temperature and the LSTM model for RVUH void fraction. The CNN + LSTM model showed the most consistent performance during training and validation. All models were also tested with 20 training epochs instead of 10, but this did not result in significant changes, confirming that 10 epochs are sufficient to fit the models while saving time.

Figure 13, Figure 14 and Figure 15 illustrate the models’ excellent forecasting performance for the parameters, with minimal observable differences between the predicted and actual values. Notably, slight variations in accuracy and output graphs were observed across multiple training sessions. These differences stem from the inherent uncertainty in the characteristics of machine learning models. Quantifying this uncertainty is essential in order to improve the models’ reliability and credibility.

3.3. Integrated Gradients Results

In

Table 5. Integrated gradient results.

Predicted Parameter	Key Input Parameters	Integrated Gradients (×1000)
RCS pressure	Affected SG pressure RCP A1 mass flow RCP B1 mass flow	168.29 −78.17 −73.79
RCS temperature	UH temperature Unaffected SG pressure RCP A1 mass flow	95.52 30.19 −25.61
RVUH void fraction	RCP B1 mass flow RCP B2 mass flow RCS temperature	−190.07 −80.34 70.04

, the summed Integrated Gradient (IG) results for the three most important features influencing each model’s predictions during the whole transient are presented. As shown, the most significant influence on predicting the RCS pressure was the pressure in the affected SG. Since the affected SG reduced the pressure throughout the entire system, the correlation was justified and positive. The next important features were the mass flow rates in the RCPs, which were restarted during the second part of the transient. The pumps were responsible for cooling, which lowered the pressure; therefore, the IG values were negative. In predicting the RCS temperature, the most significant influence was the UH temperature, as it exhibited a similar response throughout most of the accident. The second most important parameter was the pressure in the unaffected SG, which maintained its cooling function and was responsible for temperature regulation. The mass flow of the restarted RCP in the affected SG also had a significant impact on the predicted values. In predicting the formation of the RVUH void fraction, the greatest negative influence was from the mass flows of the RCPs in the unaffected loop, which were responsible for cooling and thus prevented the formation of voids. An additional significant parameter was the RCS temperature.

As mentioned in the methodology, IG values were not calculated for the impact of the same parameter on their own prediction (for example, IG of RCS pressure for predicting RCS pressure), as its influence was obviously high. The aim of this study was to determine which additional features significantly influenced the model’s predictions.

4. Conclusions and Future Work

This study focused on developing a machine learning (ML) model to predict the progression of a multiple steam generator tube rupture (MSGTR) accident in the APR1400 reactor. The initial phase involved conducting a Best Estimate Plus Uncertainty (BEPU) analysis to simulate two scenarios: a simultaneous guillotine rupture of five tubes and a mitigation strategy involving specific operator actions at defined intervals. Following uncertainty quantification and the phenomena identification and ranking table (PIRT) process, 181 simulations were performed using the RELAP5/SCDAPSIM/MOD3.4 code coupled with Dakota statistical software. Critical safety parameters such as Reactor Coolant System (RCS) pressure and temperature, reactor vessel upper head (RVUH) void fraction, and Main Steam Safety Valve (MSSV) activation were monitored. Across all scenarios, the plant successfully transitioned to Shutdown Cooling System (SCS) conditions, void fractions collapsed, and no MSSVs were activated, demonstrating that the proposed mitigation strategy effectively prevents core damage and ensures safety during the accident.

To support ML model development, the accident scenario was simulated 600 times, generating a comprehensive database. Three ML architectures, namely, GRU, LSTM, and CNN+LSTM, were trained to predict the value of one parameter at the 11th second based on the preceding 10 s of data across 18 parameters. All models achieved high accuracy, exceeding 98.8%, with CNN+LSTM selected as the optimal model due to its superior training efficiency. To enhance model transparency, IG, an XAI technique, was applied to assess input features importance. The most influential parameters were identified as the RCP mass flows and the SG pressure.

While this study made significant advancements, there remain opportunities for refinement and future enhancements. A sensitivity study highlighted that using MSSV setpoints from the DCD for an SGTR accident results in valve activation, necessitating the further quantification of radiological leakage and comprehensive radiological analysis.

The current ML models were designed to predict a single parameter based on all 18 input parameters from the preceding 10 s. However, for real-world applications, models capable of predicting one parameter using only the remaining 17 parameters would be more practical. Such models would be invaluable during accident conditions where certain instruments may be non-functional or specific measurements unavailable. While excluding the predicted parameter from the input may reduce accuracy and necessitate the use of a larger dataset, it is a critical step towards integrating AI into thermal–hydraulic safety analysis and nuclear safety frameworks.

Additionally, minor fluctuations in model accuracy were observed during training due to inherent ML characteristics. Addressing this variability through formal classification of uncertainty bounds will improve model reliability and establish a consistent range of expected performance.

To further validate the insights derived from IGS, it is recommended to employ an additional XAI technique, such as Shapley additive explanations (SHAP). SHAP leverages game theory to quantify each feature’s contribution, offering a complementary perspective on feature importance. Integrating SHAP can enhance model interpretability by providing a more robust and reliable assessment of feature impact, confirming or refining the findings from IGS, and strengthening stakeholder confidence in the ML-driven safety analysis framework.