Research on a strongly generalizable fault diagnosis method based on adversarial transfer learning

1 Introduction

Nuclear power plants are complex nonlinear systems with high safety requirements, where safety and economic efficiency are two critical aspects that cannot be overlooked throughout all stages of development. Due to the potential radiological risks, serious failures of critical equipment may lead to shutdowns and other accidents, threatening the safe operation of the plant. On the other hand, reasonably reducing operation and maintenance (O&M) costs while ensuring safety is also of great significance (Zhaojun et al., 2024; Jung-Wun et al., 2024). Statistics show that O&M costs account for as much as 60%–70% of the total electricity generation cost (Coble et al., 2012). Moreover, the prevailing maintenance strategy in current nuclear power plants remains scheduled preventive maintenance—regular inspections and servicing regardless of the actual condition of equipment—which not only wastes O&M resources but also fails to effectively ensure operational safety. Therefore, research on operational status identification based on multi-dimensional monitoring parameters at the system level is crucial. Meanwhile, leveraging emerging technologies such as artificial intelligence, the Internet of Things, and big data can enhance intelligence and digitalization, helping to achieve a unified goal of safe, economical, high-quality, and efficient plant operation (Gursel et al., 2023; Chen et al., 2026; Youndo et al., 2026).

The generalization ability and stability of machine learning models developed by artificial intelligence in instrumentation and control systems are critical to their successful deployment (Nilsson, 1982). However, traditional machine learning-based fault diagnosis models often suffer from poor generalization in practice due to discrepancies between the distributions of training and real-world test data (Liu et al., 2025; Jiang et al., 2025; Kim et al., 2022). There is thus an urgent need for intelligent fault diagnosis techniques to address challenges such as small sample sizes, data distribution shifts, and class imbalance. Nuclear power plants have a substantial body of research and theoretical achievements in intelligent fault diagnosis, which is essential for advancing diagnosis methods toward greater applicability, intelligence, and accuracy (Wang and Liu, 2026; Li et al., 2026; Liu et al., 2026).

According to the nature of fault reasoning methods in the diagnostic process, the fault diagnosis methods for nuclear power plants can be divided into knowledge-based methods and data-based methods. Knowledge-based methods conduct fault diagnosis by simulating the thinking abilities of domain experts such as analysis, reasoning and logical judgment, and they are qualitative diagnostic methods. Commonly used knowledge-based methods mainly include expert systems, signed directed graphs, fault trees and fuzzy logic (Wang et al., 2025). Data-based fault diagnosis methods can be mainly divided into signal processing-based methods and machine learning-based methods. Signal processing-based methods are mainly applied to the diagnosis of equipment vibration signals, and the commonly used signal processing methods in nuclear power plants include Fourier transform, spectral analysis, Short-time Fourier Transform (STFT), wavelet transform and Hilbert-Huang Transform (HHT) (Su et al., 2025; Valipi et al., 2025). Xia Hong et al. aimed at the problems of difficulty in identifying abrupt signals and frequency aliasing existing in wavelet transform, and realized the accurate identification and localization of abrupt stiffness signals of the main pump rotating shaft in nuclear power plants by using an improved single subband algorithm and introducing a transition function (Xia et al., 2012). GAO et al. proposed a VMD-MDI-ISSA-RF model fusing variational mode decomposition, mutual dimensionless indices and random forest optimized by an improved sparrow search algorithm for the fault diagnosis of electric gate valves in nuclear power plants, and experimental verification showed that the average fault diagnosis accuracy of the model can reach 96.375% (Gao et al., 2024). Meiru Liu et al. adopted HHT to analyze the vibration signals of the main pump flywheel, and successfully realized the extraction and identification of vibration features of local defects of the flywheel (Bin, 2015). Chauhan et al. proposed a hybrid method combining Discrete Wavelet Transform (DWT) and Convolutional Neural Network (CNN), which takes voltage signals under different loads as input to achieve accurate diagnosis of rotor bar breakage faults of squirrel-cage induction motors, and experimental verification showed that the classification accuracy of this method can reach 99%, with performance superior to the traditional CNN model based on raw signals (Chauhan et al., 2026). In recent years, with the rise of artificial intelligence technology, machine learning-based diagnostic methods have developed rapidly in the nuclear energy field. Relying on strong computing power, machine learning can realize feature extraction and classification of a large number of samples with only a small amount of prior knowledge. The commonly used machine learning methods in nuclear power plant fault diagnosis mainly include neural networks, support vector machines, naive Bayes, decision trees, K-nearest neighbors, clustering and ensemble methods (Gong et al., 2024; Ben et al., 2023). Among them, clustering is an unsupervised learning method, while the others are all supervised learning methods. Ensemble methods mainly combine the outputs of several base classifiers through specific rules to obtain the final classification results. Such classifier design can effectively solve the overfitting problem and thus improve classification accuracy. Commonly used ensemble methods mainly include Bagging series algorithms, Boosting series algorithms and random forest algorithms (Huang et al., 2026). Mao Wei et al. used the least square support vector machine to classify typical faults such as unbalance, misalignment and rub-impact of the main pump rotor, and achieved high accuracy, verifying the effectiveness of the algorithm (Mao et al., 2012). Duan Zhiyong et al. established a corresponding fault diagnosis model by using the random forest algorithm for 5 typical faults of canned motor pumps, and the test results showed that the model can effectively identify the 5 typical faults of canned motor pumps (Duan et al., 2020). Qinghu Meng et al. developed fault diagnosis software for the main pump by using PCA and support vector machine, and applied it to the fault detection and diagnosis of the main pump in Qinshan Nuclear Power Plant (Meng et al., 2012). GUO et al. aimed at the problem of poor model effect caused by unbalanced samples and excessive redundant data in nuclear power plant fault diagnosis, and proposed the CVGR method, which combines random forest feature selection, convolutional variational autoencoder gradient penalty Wasserstein generative adversarial network and convolutional neural network to solve the problem. Experimental verification on the full-scope simulator of Fuqing Unit 2 showed that this method can effectively alleviate the data imbalance problem and provide ideas for intelligent fault diagnosis of nuclear power plants (Guo et al., 2024). Liu et al. proposed a Crossformer-SVM hybrid diagnosis framework to capture the spatiotemporal dependence of multi-variate time series data in nuclear power plants and improve fault diagnosis accuracy. After constructing noisy and noise-free fault datasets, Crossformer is used to extract spatiotemporal features and SVM to complete fault pattern recognition. Experimental verification showed that the diagnosis accuracy of the model is superior to models such as CNN-LSTM, and it performs excellently on both noisy and noise-free data (Liu et al., 2026). SUN et al. proposed an FDD-CVS intelligent fault detection and diagnosis model based on KPCA combined with decision tree and SVM to improve the detection and diagnosis effect of internal faults in the chemical and volume control system of nuclear power plants. Verification with data from the passive nuclear power simulation analyzer showed that the model has good detection and diagnosis accuracy, and also has the characteristics of clear principle, fast diagnosis speed and visualizable results (Sun et al., 2025).

Deep learning can automatically mine multiple complex features from data by using a deep architecture composed of multiple layers of data processing units. Against the background of industrial big data, it shows great advantages in solving the learning problems of complex high-dimensional data. Typical deep learning network architectures mainly include deep belief networks, deep Boltzmann machines, stacked autoencoders, Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN). Among them, CNN is the most representative deep network, and its characteristics such as local perception, weight sharing and downsampling can effectively reduce the parameters and complexity of the network, making its performance in information processing superior to that of the standard fully connected network (Dhillon and Verma, 2020; Cui et al., 2025; Wang H. et al., 2026). However, when the number of CNN network layers increases to a certain extent, the model will degenerate, with the problems of gradient vanishing or gradient exploding. To solve this problem, Dr. He Kaiming greatly improved the performance of CNN by introducing cross-layer connections (He et al., 2016), and the network composed of this structure is called Residual Network (ResNet). Although deep learning has achieved promising fault diagnosis results in the past few years, its application in nuclear power plant fault diagnosis still faces two challenges. First, nuclear power plant fault diagnosis tasks are usually carried out based on the assumption that the training set and test set follow the same distribution, that is, the model trained on a part of the data is used to test another part of the homologous data (Wang et al., 2021; Ayo-Imoru and Cilliers, 2018; Yin et al., 2025). However, in the complex actual monitoring environment of nuclear power plants, fluctuations in operating conditions, environmental noise interference and differences in component materials will all lead to inconsistent distribution of monitoring data (Liang et al., 2026). Data distribution differences will reduce the classification accuracy of the trained model on test data (Guo et al., 2018). Second, the high safety requirements of nuclear power plants do not allow component-level or system-level faults to occur, resulting in the scarcity of available nuclear power plant monitoring data for research, especially the difficulty in obtaining labeled system-level fault data (Li et al., 2022a). It is unrealistic to establish fault diagnosis models for data under all distributions based on traditional intelligent methods. Not only does the small sample problem affect the generalization ability of data-driven methods, but unlabeled data is also a challenge for intelligent fault diagnosis. To solve the problem of low model generalization ability caused by data distribution differences and unlabeled data in the above-mentioned nuclear power plant fault diagnosis, a feasible intelligent technology is needed to reliably apply the trained model to fault identification of test data with different probability distributions. As an emerging technology in the field of machine learning, transfer learning is a solution, which has developed rapidly and been extensively studied in the fields of image recognition, text classification and fault diagnosis in recent years (Lei et al., 2020). For source domain data and target domain data with different probability distributions, transfer learning reduces data distribution differences by extracting domain-invariant features, and then applies the model learned from the source domain to the target domain (Long et al., 2015; Ma et al., 2025).

According to the transfer content, transfer learning can be divided into four types, namely Instance-Transfer (Pan et al., 2008), Feature-Representation-Transfer (Evgeniou and Pontil, 2004), Parameter-Transfer (Mihalkova et al., 2007) and Relational-Knowledge-Transfer (Mihalkova et al., 2007). Instance-Transfer refers to applying source domain data to the target domain by assigning weights to the source domain data. Feature-Representation-Transfer refers to extracting features from the source domain and target domain data to make their distributions consistent. Model-based transfer mainly refers to the transfer applied to neural networks, that is, directly transferring parameters such as weights in neural networks, among which Fine-tune is a classic example. Relational-Knowledge-Transfer refers to mining the mapping of relational knowledge between the source domain and the target domain.

For deep transfer learning, researchers have carried out many experimental studies on the transferability of deep neural networks. The experiments have proved that neural networks are transferable for related tasks, especially the first few layers with better effects. Moreover, adding fine-tuning operation after network transfer will greatly improve the network performance. For the case where the distribution of training data and test data is similar, LI et al. proposed a transfer learning framework with multiple transfer strategies based on the pre-trained CNN model to solve the problem of limited labeled data in the target domain in nuclear power plant fault diagnosis. Verification showed that this framework can significantly improve the diagnostic performance compared with training CNN from scratch, confirming the feasibility and superiority of transfer learning in this scenario (Li et al., 2022b). Qian et al. proposed a GRU-AM-TL method fusing attention mechanism and transfer learning to address the small sample problem in the fault diagnosis of rotating machinery in nuclear power plants, which strengthens the extraction of effective features and reuses existing diagnostic knowledge. Multi-dataset verification showed that the diagnostic accuracy of this method under small sample conditions is superior to many classical methods (Qian and Liu, 2023). WANG et al. aimed at the multi-source domain data problem in cross-condition fault diagnosis of the secondary loop of marine nuclear power systems, first constructed a simulation model to obtain fault data under multiple operating conditions, then improved the MLDAN domain adaptation algorithm. Comparative experiments proved that the improved method achieves the highest diagnostic accuracy in various cross-condition diagnosis scenarios (Wang Y. et al., 2026). Wang et al. proposed a diagnostic method fusing deep learning and transfer learning to solve the problem of poor generalization of system-level fault diagnosis models caused by inconsistent data distribution at different power levels of nuclear power plants. Simulation verification showed that it can effectively reduce the feature distribution difference and realize fault diagnosis at the target power level, and feature visualization also intuitively confirmed the improvement effect of data difference (Wang et al., 2022). However, in the cross-condition fault diagnosis of nuclear power plants, when transferring fault knowledge from the source condition to fault identification in the target condition, the distribution of fault features under different operating conditions has great differences. Simply reducing the overall data distribution difference between domains tends to ignore the detailed feature space structure within the domain. Therefore, in the research of the fault diagnosis method in this paper, it is necessary to consider the problem of reducing the distribution of relevant local domains within different domains, so as to reduce the data distribution difference in more detail. To better reduce the data distribution difference and realize the enhancement of data quality, researchers have further combined generative adversarial networks with transfer learning.

The classic generative adversarial transfer learning method is the Domain-Adversarial Neural Network (DANN) model published by Ganin and Lempitsky (2015), which introduces an adversarial training mechanism into the neural network (Ganin and Lempitsky, 2015). In recent years, many excellent improved generative adversarial transfer learning methods have emerged for cross-domain fault diagnosis scenarios with large data distribution differences. Wang et al. proposed a deep transfer learning method based on a hybrid domain adversarial learning strategy to solve the problem that inconsistent data distribution at different power levels of rotating machinery in nuclear power plants limits the application of traditional models. Experimental and feature visualization verification showed that this method can effectively reduce feature differences and show superiority in fault diagnosis at the target power level (Wang et al., 2023). Li et al. proposed a TF-DLGAN model framework to address the problems of lack of a universal fault diagnosis model and insufficient fault data for the sliding bearing-rotor system in nuclear power plants, built an experimental platform to obtain fault data under multiple operating conditions and completed the verification. The model can solve the problem of insufficient data and has excellent fault diagnosis performance (Li et al., 2024). Xia et al. proposed a collaborative conditional deep adversarial network, which combines cross-scale collaboration and adversarial learning to improve the discriminability of features in the target domain (Xia et al., 2022). Meneses et al. proposed a design method based on Wasserstein generative adversarial network for the NP-hard combinatorial optimization problem of nuclear fuel loading pattern design in pressurized water reactors. Verification with the IAEA-2D benchmark showed that this method can generate loading patterns that meet safety constraints and design objectives, and can autonomously learn the implicit probability distribution of nuclear fuel and design high-quality loading patterns (Meneses and Araujo, 2026).

Aiming at the problem of low model generalization performance caused by changes in monitoring data distribution due to material differences and changes in similar reactor types (Li et al., 2018), a Hybrid Domain Adversarial Learning (HDAL) model is proposed, which combines deep learning (Lecun et al., 2015) and transfer learning technology to realize transferable feature extraction between the source reactor type and the target reactor type, thereby improving the classification accuracy under the unlabeled target reactor type. The model uses deep convolutional neural networks for feature extraction, thus providing sufficient data mining capabilities for cross-domain fault diagnosis tasks. The research results of this paper can be used to improve the safety and reliability of nuclear power plants, improve the economic efficiency and operational efficiency of nuclear power plants, and effectively enhance the intelligent level and automatic decision-making ability of nuclear power plants.

Section 2 of the paper introduces the overall framework of fault diagnosis based on the HDAL model, the basic theories of adversarial transfer learning and domain adaptation, and the mathematical principles of the proposed HDAL model in detail. Section 3 describes the implementation process of the cross-type fault diagnosis method for nuclear power plants based on the HDAL model. Section 4 constructs a cross-type fault dataset based on the PCTRAN simulation platform to conduct verification experiments, comparative experiments, and result analysis. Section 5 summarizes the research findings, innovations, and engineering application value of the paper, and provides an outlook on future research directions.

2 Fault diagnosis method transfer learning

2.1 Fault diagnosis framework based on HDAL transfer learning

Data distribution differences in system-level monitoring parameters of nuclear power plants can degrade the generalization performance of fault diagnosis models. However, cross-reactor-type fault diagnosis can effectively leverage fault diagnosis knowledge from source reactors to identify faults in target reactors. Similar reactor types exhibit analogous qualitative changes in parameters under certain faults, enabling knowledge transfer via deep transfer learning strategies. This paper proposes a subdomain-adaptation-driven adversarial training strategy to finely reduce data discrepancies between similar reactor types, combined with a pre-trained ResNet-18 network to extract domain-invariant features for cross-reactor fault diagnosis knowledge transfer, The specific framework is shown in Figure 1.

2.2 Adversarial transfer learning model

Traditional data generation models include restricted Boltzmann machines, deep belief networks, generative stochastic networks, and autoregressive models. However, their development and deployment efficiency is low, and the quality of generated data is limited (Ming-Fei et al., 2022; Chen et al., 2021; Jian-Wei et al., 2020).

The HDAL transfer learning model proposed in this paper is an improved adversarial transfer learning model, whose underlying architecture is based on the Generative Adversarial Network (GAN). GAN, introduced by Goodfellow et al., in 2014, frames the sample generation problem as an adversarial zero-sum game between two models (Goodfellow et al., 2014), making adversarial networks a powerful tool for enhancing network performance (Jin-Dong, 2021). A classical GAN consists of at least four components: 1) real data, serving as genuine samples. 2) random noise, drawn from a specific distribution and acting as the source for generated samples. 3) a generator, which takes noise as input and produces synthetic data. And 4) a discriminator, which evaluates both real and generated data to determine their authenticity, as illustrated in Figure 1. GANs can be composed of various fundamental units—such as autoencoders, fully connected layers, and CNNs—to accommodate different input data types and application scenarios. GAN models are commonly used to generate data under imbalanced conditions, and data generation techniques have been widely studied and applied to mitigate the issue of insufficient training datasets.

Based on the adversarial principle of GAN, deep adversarial networks can be effectively applied to transfer learning problems. Similar to deep network adaptation methods, the loss of a deep adversarial network consists of two parts: the classification loss L c and the domain discrimination loss L a d v as shown in Equation 1:where λ denotes the weight of the loss function, D s represents labeled source domain data, and D t represents unlabeled target domain data.

L = L c D s + λ L a d v D s , D t (1)

In generative adversarial transfer learning-based fault diagnosis, constructing an effective model loss function is critical to improving cross-domain diagnostic accuracy. Given the large discrepancies in data probability distributions across reactor types, demands on the model’s feature extraction and fault classification performance are significantly heightened. Therefore, in the proposed HDAL model, we intend to integrate both implicit and explicit transfer learning strategies to enhance the extraction of domain-invariant features and ensure stability in cross-reactor-type fault diagnosis under multiple monitoring parameters. The ResNet-18 feature extraction method adopted in this paper can specifically capture the temporal and local features of thermal-hydraulic transients in nuclear power plants (such as sudden changes in coolant flow and abnormal fluctuations in core temperature). For example, in LOCA (Loss of Coolant Accident) transients, it can quickly extract the sudden change features of coolant pressure and flow, providing reliable feature support for subsequent fault classification.

2.3 Transfer learning based on domain adaptation

The objective of this paper is to achieve fault diagnosis with strong generalization capability, making feature-based transfer learning strategies particularly suitable. By leveraging labeled source domain data and unlabeled target domain data, shared latent features—known as Domain-Invariant Features (DIF)—are extracted to minimize the data distribution discrepancy between source and target domains, ultimately enabling accurate fault classification in the target domain. Given the assumption that source and target domains share the same classification space, the strong generalization fault diagnosis technology developed in this paper falls within the domain of Domain Adaptation (DA) (Guan and Liu, 2021).

Domain adaptation addresses the problem of inconsistent data distributions between training and test sets while maintaining the same classification task. Assuming identical class labels between source and target domains, let the labeled source domain samples be X s = x i s , y i s i = 1 n s with probability distribution U, and the unlabeled target domain samples be X t = x j t j = 1 n t with probability distribution V. For domain adaptation, the condition U ≠ V is explicitly permitted. To solve domain adaptation problems, model performance can be enhanced from two perspectives: feature extraction capability and transfer learning strategy.

Classic deep domain adaptation models include Deep Domain Confusion (DDC), Deep Adaptation Network (DAN), and Deep Subdomain Adaptation Network (DSAN) (Tzeng et al., 2014; Long et al., 2015; Zhu et al., 2020), all of which are explicit feature-based methods that define a fixed distribution metric to quantify distribution discrepancy and minimize it through model training.

Maximum Mean Discrepancy (MMD) is one of the most widely used discrepancy metrics in transfer learning. Compared with Kullback-Leibler (K-L) divergence, MMD avoids calculating the intermediate density of the distribution. Based on nonlinear feature kernel functions, it maps the original sample data into a Reproducible Kernel Hilbert Space (RKHS) and measures the distance between two distributions as the feature distribution discrepancy. To address the limitation of Maximum Mean Discrepancy (MMD)—which may lead to low transfer efficiency due to its neglect of internal data structure—Local Maximum Mean Discrepancy (LMMD) has been introduced to achieve finer-grained distribution alignment (Gao et al., 2024). For a source domain dataset X s = x i s , y i s i = 1 n s following distribution U and a target domain dataset X t = x j t j = 1 n t following distribution V, the formulation is:

L M U , V = E Z E U z ϕ X s − E V z ϕ X t H 2 = 1 Z ∑ z = 1 Z ∑ i = 1 n s ω i s z ϕ x i s − ∑ j = 1 n t ω j t z ϕ x j t H 2 (2)

In the equation, U z and V z denote the probability distributions of sub-domain z in the source and target domains, respectively, In the fault diagnosis task of this paper, each sub-domain z corresponds to an independent fault type (i.e., a classification label). Samples in the same sub-domain are all monitoring data under the same fault condition, with consistent internal data distribution. Weight coefficients ω i s z and ω j t z are introduced to facilitate the computation of sub-domain expectations, representing the probabilities that samples x i s and x j t belong to sub-domain z, satisfying ∑ i = 1 n s ω i s z = ∑ j = 1 n t ω j t z = 1. ϕ is the feature mapping function, whose function is to map the original input data into the high-dimensional Reproducing Kernel Hilbert Space (RKHS), and calculate the mean difference between the two distributions in the high-dimensional space, solving the problem that the nonlinear distribution is difficult to measure in the original space. Equation 2 is the calculation formula of Local Maximum Mean Discrepancy (LMMD), and its core function is to quantify the feature distribution difference between each corresponding fault subdomain in the source domain and the target domain. By minimizing this loss value, fine-grained alignment of features of the same fault type in the source and target domains is realized, so that the model can learn cross-reactor invariant features of the same fault type. It solves the problem that the traditional global MMD ignores the intra-class data structure, and improves the accuracy of cross-domain fault diagnosis. The computation of these weights depends on the sub-domain partitioning method, where the weight of sample x k for sub-domain z is:

ω k z = y k z ∑ y z (3)

Where y k z denotes the classification label of sample x k for sub-domain z, encompassing both y k s z and y k t z. ∑ y z represents the total classification sum of samples in this domain for sub-domain z. The source domain weight ω i s z is computed using labeled data, while the target domain weight ω j t z is calculated based on the probability distribution output by the classifier. The sub-domain distribution discrepancy of extracted features can be measured across multiple network layers. Assuming the output of layer l is o i s l i = 1 n s and o j t l j = 1 n t, Equation 3 can be expanded into Equation 4.

L M U , V = 1 Z ∑ z = 1 Z [ ∑ i = 1 n s ∑ j = 1 n s ω i s z ω j s z k o i s l , o j s l + ∑ i = 1 n t ∑ j = 1 n t ω i t z ω j t z k o i t l , o j t l − 2 ∑ i = 1 n s ∑ j = 1 n t ω i s z ω j t z k o i s l , o j t l (4)

Where k , is the kernel function, which is used to calculate the inner product of two sample features in the high-dimensional feature space. In this paper, the Gaussian kernel function is adopted as the kernel function.

The DSAN model implements subdomain adaptation based on the LMMD metric, computing the distribution distances between subdomains within each domain. Compared to global distribution alignment using MMD, it accounts for fine-grained data structures within domains, enabling the extraction of more detailed information for domain adaptation tasks. The subdomain adaptation theory can effectively alleviate the distribution difference of thermal-hydraulic transient data between different reactor types. For example, in the steam generator tube rupture condition of EPR reactor and PWR 3-loop (3-loop pressurized water reactor), it can specifically align the temperature and pressure temporal data distribution of the two reactor types, solving the domain shift problem in cross-reactor fault diagnosis.

2.4 Improved adversarial transfer learning method

Based on the deep learning and feature-based transfer learning strategies described above, this paper proposes a Hybrid Domain Adversarial Learning (HDAL) model to enhance the generalization performance of fault diagnosis under varying operating conditions and without labeled target samples. The model employs a deep convolutional neural network to adaptively process input data and select features, ensuring robust feature extraction capability. Within the feature-based transfer learning framework, a subdomain-adaptive adversarial training strategy is introduced across multiple network layers to perform domain adaptation of features, thereby transferring source domain features to enable classification in the target domain and improving cross-domain diagnostic performance. In feature-based transfer learning, methods that dynamically and implicitly measure distribution discrepancies without predefined metrics are termed implicit feature transfer methods—such as the Domain-Adversarial Neural Network (DANN) (Kim et al., 2022). In the HDAL model, to effectively enhance the extraction of domain-invariant features, we integrate the strengths of both explicit and implicit approaches by combining subdomain adaptation with adversarial training, thereby minimizing the distribution discrepancy of extracted features and achieving effective fault feature transfer from source to target domains.

The deep convolutional neural network and the designed optimization objective function are critical to the model’s ability to extract domain-invariant features. The architecture of the proposed HDAL model is illustrated in Figure 2. The feature extractor G is constructed based on an improved ResNet-18 network, with pooling layers used to output high-dimensional features. Subsequently, subdomain adaptation is performed at the first fully connected layer (F _*C*), followed by two separate fully connected layers that feed into the classifier C and domain discriminator D, respectively. Classifier C consists of one fully connected layer and a Softmax function, while discriminator D comprises three fully connected layers and a Sigmoid function.

As shown in Figure 2, after the source and target domain data pass through the feature extractor G, three types of network losses are computed: source classification loss L _*C*, subdomain adaptation loss L _*M*, and domain discriminator loss L _*D*.

2.4.1 Source classification loss

The source domain data X s = x i s , y i s i = 1 n s are processed by the feature extractor G to obtain features G x s. These features are fed into the classifier C, yielding C G x i s, and the source classification loss is computed using the ground-truth labels. This process resembles conventional supervised learning, enabling the model to retain as much discriminative information from the source domain as possible. The source domain classification loss L C is expressed as Equation 5.where n s denotes the number of source domain samples. K represents the number of classes. l y i s = k is an indicator function. And G x i s denotes the output of multiple class scores. In traditional supervised learning models, where the training and test sets share the same probability distribution, training the model solely on the source classification loss is sufficient for accurate test set classification. However, in unlabeled cross-reactor-type fault diagnosis tasks, multiple transfer learning strategies must be integrated to extract domain-invariant features, enabling effective application of source-extracted features for classification in the target domain.

L C C G x i s , y i s = − 1 n s ∑ i = 1 n s ∑ k = 1 K l y i s = k log 1 C G x i s (5)

2.4.2 Subdomain adaptation loss

After extracting high-dimensional features via the feature extractor, subdomain adaptation is performed through the following adjustments: 1) In the subdomain partitioning method, each fault type in the cross-reactor-type diagnosis task is treated as a subdomain, where internal data distributions are consistent, enabling effective subdomain feature alignment. 2) Subdomain adaptation is applied at a single network layer. As training converges, the features output by this fully connected layer exhibit strong subdomain alignment, significantly improving the efficiency of subsequent adversarial training. 3) When computing ω j t z in Equation 2, since target domain samples are unlabeled, pseudo-labels derived from the classifier’s output are used as target domain labels in the computation, and convergence is achieved through iterative training. The classifier’s output serves as the predicted classification for the target domain. Ultimately, the subdomain adaptation loss L M is computed using Equation 2.

2.4.3 Domain discriminator loss

The domain discriminator loss is computed after the second fully connected layer following the feature extractor. In generative adversarial transfer learning, a GAN is introduced with modified generator and discriminator roles to effectively reduce the data discrepancy between source and target domains (Kim et al., 2022). Specifically, the feature extractor G is treated as the generator, responsible for extracting high-dimensional features G x i from both domains. Crucially, in the adversarial training framework, the domain discriminator D takes the mixed features from both domains as input and outputs a binary domain label D G x i. The discriminator D is trained to distinguish whether a given feature originates from the source or target domain. Conversely, at convergence, if the discriminator cannot reliably determine the domain origin of the extracted features, it indicates that G has successfully learned domain-invariant shared features. The domain discriminator loss L D is computed using Equation 6.where d i is the domain label indicating whether the extracted feature originates from the source or target domain.

L D D G x i , d i = d i ⁡ log 1 D G x i + 1 − d i log 1 1 − D G x i (6)

2.4.4 Overall objective function and optimization

Unlike conventional fault diagnosis models, the HDAL model performs explicit and implicit domain adaptation at different network layers, with its overall objective function comprising the three aforementioned losses, as shown in Equation 7:where μ and λ are weight coefficients. θ g , θ c , θ d denote the network parameters of G, C, and D, respectively, explicitly included in the loss functions (e.g., L C θ g , θ c and L M θ g , θ c) to clarify parameter optimization targets. The domain discriminator D is trained to maximize its ability to distinguish the domain origin of features. Conversely, the feature extractor G, acting as the generator in the adversarial framework, aims to maximize confusion of D by extracting domain-invariant features. During subdomain-driven adversarial iterations, θ g is optimized to maximize D, θ c is trained to minimize C, and θ d is updated to minimize D. The final parameter optimization process for all components is given in Equation 8.

L t o t a l θ g , θ c , θ d = L C θ g , θ c + μ L M θ g , θ c − λ 1 n s ∑ i = 1 n s L d i θ g , θ d + 1 n t ∑ i = 1 n t L d i θ g , θ d (7)

θ g ← θ g − η ∂ L C ∂ θ g + μ ∂ L M ∂ θ g − λ ∂ L D ∂ θ g θ c ← θ c − η ∂ L C ∂ θ c + μ ∂ L M ∂ θ c θ d ← θ d − η λ ∂ L D ∂ θ d (8)

The HDAL model proposed in this paper builds on the advantages of traditional adversarial transfer learning, incorporating a single layer of subdomain adaptation to more finely reduce domain discrepancies. Additionally, a Gradient Reversal Layer (GRL) is integrated into the model architecture to ensure proper parameter updates during adversarial training, thereby maximizing the reduction of feature distribution differences across reactor types in fault diagnosis tasks.

3 Fault diagnosis model based on HDAL transfer learning

The specific implementation process of cross-type fault diagnosis based on HDAL transfer learning mainly includes three parts: data preprocessing, transfer model training, and target reactor type testing, as detailed below:

3.1 Data preprocessing

System-level monitoring parameters from nuclear power plants are acquired via the I&C system and preprocessed through dimensionality reduction and normalization. For cross-similar-reactor fault diagnosis, the input parameter matrix must remain consistent. To suit the input requirements of subsequent deep convolutional neural networks, the normalized multidimensional monitoring parameters related to selected faults are converted from sequences to images. These monitoring parameter images are then divided into source and target domain datasets according to reactor type. Source domain signals are labeled with corresponding fault types, while target domain labels are unavailable. The training set is composed of randomly sampled samples from both source and target domains, while the test set consists of remaining randomly sampled target domain samples.

3.2 Transfer model training

The training set samples are fed into the HDAL transfer diagnosis model, whose architecture is shown in Figure 3. To reduce the feature distribution discrepancy between source and target domains, appropriate optimization objectives and transfer strategies are configured. The GAN encourages the feature extractor to mine as many transferable features as possible—features indistinguishable in origin between domains. To further fine-tune distribution alignment, a subdomain-adaptation-driven adversarial training strategy is incorporated. After passing through the feature extractor G, three losses are computed: source classification loss L _*C*, single-layer subdomain adaptation loss L _*M*, and domain discrimination loss L _*D*. Deep fault features are extracted using the ResNet-18 network, and the three loss functions are combined to form the model’s optimization objective. The model is optimized using the Stochastic Gradient Descent (SGD) algorithm, with parameters iteratively updated via backpropagation until convergence to the optimal solution.

Specifically, the role of each module in reactor fault diagnosis is as follows.

Feature extractor: Constructed by an improved ResNet-18 network, it can extract deep temporal features such as coolant pressure drop rate and core level change trend for LOCA transients, filter out irrelevant environmental interference signals, and convert raw monitoring data into high-dimensional feature vectors usable for fault identification.

Subdomain adaptation module: Divide the thermal-hydraulic transient data of the source domain (PWR 3-loop, 3-loop pressurized water reactor) and target domain (EPR reactor) into subdomains by fault type. For example, take the ‘steam generator tube rupture' condition as an independent subdomain, and reduce the feature distribution difference of the same fault condition between different reactor types through the subdomain alignment loss function to ensure the accuracy of feature transfer.

Classifier: Constructed based on a fully connected neural network, it inputs the feature vectors after feature extraction and subdomain alignment, and performs multi-classification for 13 thermal-hydraulic transient conditions. For example, it can accurately distinguish LOCA from other similar faults, avoiding misjudgment caused by similar pressure change features in different faults.

Domain discriminator: Learn the feature distribution difference between the source domain and target domain through adversarial training, feedback and adjust the parameters of the feature extractor, so that the extracted features have domain invariance. For example, in the transient condition diagnosis of EPR reactor, it can ignore the influence of parameter distribution difference between EPR and PWR 3-loop reactor types, realizing accurate identification of cross-reactor faults.

Each component works together to form a complete link of “feature extraction - distribution alignment - fault classification - parameter optimization,” effectively solving the core problem of cross-reactor thermal-hydraulic transient fault diagnosis in nuclear power plants.

3.3 Target reactor testing

After training, the test set from the target reactor is input into the transfer learning-based fault diagnosis model to obtain fault identification results.

The adversarial learning mechanism of the model can adapt to the complexity of thermal-hydraulic transient faults in nuclear power plants, effectively distinguish normal transients from fault transients, and avoid diagnostic errors caused by similar working conditions.

4 Validation

4.1 Simulation based on PCTRAN

To validate the effectiveness of the proposed deep transfer learning method for fault diagnosis across different reactor types in nuclear power plants, system-level parameters related to faults under various reactor types must be obtained. The nuclear power plant simulation software (Personal Computer Transient Analyzer, PCTRAN)—an effective tool for simulating various transient conditions and faults in nuclear power plants (Cheng et al., 2012; Wang et al., 2020)—is employed in this project to simulate transient operations and acquire data for the EPR pressurized water reactor, the schematic diagram of the operating conditions in PCTRAN is shown in Figure 4. Specifically, 13 operational transients are introduced at 100% power level, including normal conditions, loss-of-coolant accidents (LOCA) in cold legs, LOCA in hot legs, internal steam line rupture, external steam line rupture, steam generator tube rupture, and load rejection, the specific operating conditions are shown in Table 1. Each fault condition is simulated at two severity levels: 10% and 20%, resulting in a total of 13 fault scenarios. The severity of LOCA and steam line ruptures is defined as the break area divided by 100 cm². The severity of steam generator tube rupture is defined as the ratio of one fully ruptured tube. And the severity of load rejection is defined as the ratio of load reduction to full power (100%). After 50 s of steady-state operation, time-series data for 84 parameters under each of the 13 transients are recorded. The 205-s time series of these 84 parameters, collected following the insertion of each transient at 100% power, serve as the analysis dataset, representing the parameter evolution and automated system compensation responses post-transient.

TABLE 1. Operational conditions and corresponding labels.

4.2 Data preprocessing

4.2.1 Elimination of irrelevant parameters

In fault diagnosis testing, fault knowledge from a 1,000 MWe PWR 3-loop reactor (hereafter referred to as the source reactor) is intended to be transferred to fault identification in the EPR reactor (hereafter referred to as the target reactor). Therefore, the fault parameter selection strategy for the target reactor must align with that of the source reactor, resulting in the selection of 64 consistent parameters, as listed in Table 2. Ultimately, the 64-dimensional parameter patterns and their correlations with the 13 operational conditions from the source reactor are applied to diagnose the same 13 conditions in the target reactor.

TABLE 2. List of 64-dimensional parameters.

4.2.2 Normalization

After selecting normalized monitoring parameters with high relevance to the 13 operational conditions chosen for case testing, as shown in Equation 9.where x n is the set of all operational data for the parameter under the same condition, x * n is the normalized value, x min n 及x max n and x max n are the minimum and maximum values of the parameter, and N is the total number of samples for all faults under the same condition.

x * n = x n − x min n x max n − x min n , n ∈ N (9)

4.2.3 Sequence-to-image conversion

The data must be converted from sequences to images to be fed into the feature extractor in image form. This conversion must preserve information integrity and avoid distortion, ensuring compatibility with deep convolutional neural networks while maintaining the fidelity of embedded features. Accordingly, the 64-dimensional parameters recorded at the same time step are sequentially reshaped into an 8 × 8 matrix, where the normalized value at each matrix position is mapped to a corresponding pixel color in the image. Thus, the RGB values extracted by the deep convolutional neural network directly represent the operational state information encoded in the parameters. For parameters that cannot be directly converted into equal-sized matrices, appropriate padding or interpolation methods are applied to ensure uniform dimensionality. The conversion schematic is illustrated in Figure 5.

4.3 Deep learning fault diagnosis testing

Before conducting cross-reactor transfer learning-based fault diagnosis, a fault diagnosis test is performed on the target reactor simulation data using a non-transfer DCNN model. Since each transient in the target reactor simulation spans 205 s with fault insertion at the 50th second and a sampling interval of 5 s, each class contains 31 image samples. Specifically, the 403 samples across the 13 classes of the target reactor data are divided into training and test sets at a 7:3 ratio. The feature extraction and classification model parameters are optimized using the Stochastic Gradient Descent (SGD) algorithm with a Momentum of 0.9, Weight Decay of 0.01, and a learning rate of 0.01. The Batch Size and maximum number of Epochs are set to 32 and 300, respectively. After 300 training iterations, a DCNN fault diagnosis model without transfer learning is obtained, with its training accuracy shown in Figures 6–8.

Figure 9 compares the behavior of parameters 1, 2, 3, and 4 under Condition 12 and Condition 13. It is evident that parameters 1, 2, and 3 exhibit identical trends under both faults and are indistinguishable, while only parameter 4 shows a distinct variation pattern. Consequently, in the target reactor simulation data, Conditions 12 and 13 share highly similar multivariate trend characteristics, making it difficult for the fault diagnosis model to differentiate between test samples of these two conditions, resulting in a final diagnostic accuracy of 92.556%.

4.4 Transfer fault diagnosis testing

4.4.1 Transfer diagnosis testing based on HDAL

Before conducting cross-reactor transfer learning for fault diagnosis, the preprocessed data must be organized. The preprocessed dataset contains data from two reactor types—designated as Domain A (source reactor) and Domain B (target reactor), as shown in Table 3. Each domain includes 13 operational transients, corresponding to 13 fault classes. This dataset encompasses system-level faults across multiple severity levels, enabling reliable evaluation of transfer learning performance between different reactor types. For the source reactor (Domain A), multidimensional data at identical time points are extracted for each condition, resulting in 31 image samples per class. The project evaluates transfer performance between Domains A and B by performing the transfer task A → B: Domain A (source) provides labeled data for all 13 classes, while Domain B (target) provides unlabeled data. The transfer learning fault diagnosis model is trained to learn the mapping between parameters and operational states in Domain A, enabling classification of operational states in the unlabeled Domain B.

TABLE 3. Data preparation for transfer tasks.

By integrating adversarial learning with the TLMMD metric in the HDAL model, the probability distribution discrepancy between domains is effectively reduced, while the fault classification error from the source reactor is jointly optimized as the training objective. With iterative training, the model achieves strong classification performance while simultaneously minimizing inter-domain differences. The HDAL model combines the transfer advantages of both DANN and DSAN, enabling fine-grained alignment of fault features across subdomains. As shown in the accuracy curve of Figure 10, during 300 training epochs, accuracy rises rapidly in the first 50 epochs and then stabilizes at a fixed value. The final fault diagnosis accuracy achieved by the HDAL model is 91.067%. The training process and results are illustrated in Figures 10–12.

As shown in Figures 11, 12, misclassifications occur in Conditions 2, 3, and 12, with the highest number of errors in Condition 12, primarily due to data quality issues in this condition.

4.4.2 Reverse transfer diagnosis testing based on HDAL

This section evaluates the HDAL model on the reverse transfer task from target to source reactor. Due to the minimal discriminability between Conditions 12 and 13, transferring fault knowledge to the source reactor in this case leads to reduced diagnostic efficiency and blurred classification boundaries. Therefore, Conditions 12 and 13 are excluded, and only fault knowledge from Conditions 1–11 (11 classes total) is transferred. This eliminates the influence of low-quality simulated conditions. As shown in Figure 13, the accuracy curve rises sharply within the first 50 epochs and then stabilizes at a fixed value. The final fault diagnosis accuracy under this transfer task reaches 98.53%. The training process and results are presented in Figures 13–15. The model misclassifies only five samples across Conditions 2 and 3. After excluding Conditions 12 and 13, the proposed HDAL model successfully achieves cross-reactor transfer learning for fault diagnosis and effectively extracts transferable features.

4.4.3 Comparative testing across multiple methods

In addition to the HDAL transfer learning fault diagnosis method primarily studied in this paper, three other comparative methods were selected to test the transfer tasks: 1) DCNN: Trained only with labeled source domain data, using target domain data as the test set, and calculating the model classification accuracy via the output labels and actual labels. 2) DANN: A classic algorithm in the field of transfer learning, which reduces the discrepancy of extracted features based on generative adversarial strategies to achieve the transfer of fault knowledge between different domains. 3) DSAN: Deep Subdomain Adaptation Network (DSAN), which aligns feature distributions in a fine-grained manner based on the Local Maximum Mean Discrepancy (LMMD) metric to extract transferable features. The convolutional networks for feature extraction and model training parameters in these three comparative methods are consistent with those of the method proposed in this project. Meanwhile, to further highlight the performance and robustness of the proposed algorithm, comparative tests were also conducted with current advanced nuclear power plant fault diagnosis algorithms, including Attention-based CNN (Attention-CNN), Transformer, and TCN.

For the DCNN-based cross-reactor transfer learning fault diagnosis test, the absence of any transfer learning strategy causes the feature extractor to randomly capture source reactor fault features and directly apply them to target reactor fault identification. Over 300 training epochs, the accuracy curve exhibits significant fluctuations, as shown in Figure 16, indicating poor convergence. DCNN fails to extract effective transferable features for cross-reactor diagnosis, resulting in misclassifications across Conditions 2, 3, 7, 12, and 13—particularly low accuracy in Conditions 3, 12, and 13. The final fault diagnosis accuracy is 79.901%.

By introducing an adversarial learning strategy into the DANN model, the extraction of high-quality transferable features between the two reactor types becomes the joint objective of the generator and discriminator, enabling cross-reactor transfer learning. Over 300 training epochs, the accuracy curve rises rapidly and then stabilizes within a limited range of fluctuations, indicating partial convergence. DANN achieves basic extraction of transferable features for cross-reactor fault diagnosis, with accuracy maintained between 85% and 90%. As shown in Figure 17, misclassifications occur in Conditions 2, 3, 6, 7, 12, and 13—particularly in Conditions 12 and 13. As a baseline adversarial transfer learning model, DANN achieves a final fault diagnosis accuracy of 89.330%. It demonstrates moderate efficiency in cross-reactor transfer, outperforming DCNN in target reactor diagnostic accuracy.

By incorporating the TLMMD metric into the DSAN model to measure the probability distribution discrepancy between domains and jointly optimizing it with source-domain classification error, the model achieves strong classification performance while effectively reducing inter-domain differences. DSAN is a variant of MMD-based feature transformation transfer learning models, capable of fine-grained alignment of fault features across subdomains. Over 300 training epochs, the accuracy curve rises sharply within the first 100 epochs and then stabilizes at a fixed value, as shown in Figure 18, enabling effective extraction of transferable features for cross-reactor fault diagnosis. The final diagnostic accuracy of the DSAN model is 89.082%. While its accuracy is nearly identical to that of DANN, DSAN demonstrates superior training efficiency and stability.

Comparing the test results of the four methods (using the average of 5 independent repeated trials), the HDAL model has the highest training efficiency and the most stable test performance among the four classification models. The results are shown in Table 4. It can be seen from the table that under noise-free conditions, the standard deviations of DSAN and HDAL are zero. This is because both the HDAL and DSAN models introduce explicit distribution alignment constraints, and the models fully converge after 300 rounds of training. Moreover, the PCTRAN simulation dataset used in this paper possesses high reproducibility without random noise interference. In the 5 independent repeated experiments, the final classification accuracy is completely consistent after model convergence, so the standard deviation is 0. After adding noise, the accuracy decreases to some extent due to the increased data complexity, but HDAL still maintains a high accuracy. It should be noted that the signal noise added in this paper is within the accuracy range of nuclear power plant measuring instruments, adding a random white noise. Specifically, the temperature instrument has Class A accuracy (0.015 ± 0.002t)°C, where t is the measured temperature. The pressure instruments (including pressure, differential pressure, flow, and liquid level) and other instruments have an accuracy of 0.5% FS, where FS is the full scale of the instrument.

TABLE 4. Cross-type fault diagnosis results of each model at the same power level.

Furthermore, it can be seen from the table that models such as DCNN, Attention-CNN, Transformer, and TCN perform poorly. This is because these models are trained only using labeled source domain data without any domain adaptation or transfer learning strategies, making them unable to mitigate the data distribution discrepancy between the source and target domains. Meanwhile, they suffer from severe overfitting to the source domain data during the training process, resulting in extremely poor generalization performance on the target domain test set. Therefore, further tests were conducted on the source domain test set using DCNN, achieving a test accuracy of 98.635%. This forms a sharp contrast with the accuracy of 79.901% on the target domain, directly proving that the DCNN model experienced severe overfitting on the source domain and failed to adapt to the data distribution of the target domain. This further highlights the superiority of the HDAL transfer learning method proposed in this paper in addressing cross-domain generalization and suppressing overfitting.

Finally, to further increase the discrepancy between the source domain and target domain data and verify the robustness of the proposed algorithm, cross-power level tests under cross-type conditions were conducted. The power level of the target reactor type B in Table 3 was adjusted to 80%, and multi-method comparative tests were carried out. All methods were tested on data with noise, and the results are shown in Table 5. It can be seen from the data in the table that under cross-type conditions, if the power level is further crossed, the accuracy of all models decreases to some extent. The accuracy of non-transfer learning algorithms decreases significantly, indicating that the data discrepancy has further increased. Compared with the cross-type data, the accuracy of the proposed algorithm, HDAL, decreases by 2.66% under the cross-type and cross-power scenario, yet it still maintains a high accuracy of 88.642%, verifying the superiority of the algorithm.

TABLE 5. Cross-type and cross-power level fault diagnosis results of each model.

5 Conclusion

To address the low efficiency of shallow machine learning algorithms in fault diagnosis under small-sample and unlabeled data conditions, this study investigates a cross-reactor fault diagnosis method based on adversarial transfer learning. The proposed approach leverages the strengths of generative adversarial networks and deep transfer learning, enabling effective extraction of transferable features between related reactor types through an integrated overall loss function. First, common system-level faults and associated monitoring parameters across reactor types are identified to define the source and target domains for transfer learning. A shared fault diagnosis model is trained using labeled source domain data, with an improved generative adversarial strategy introduced to extract deep fault features and classify unlabeled target domain operational data.

By integrating transfer learning, simulation modeling, deep learning, and data analysis techniques, this study on cross-reactor fault diagnosis based on multidimensional nuclear power plant monitoring parameters holds significant value for enhancing model generalization, breakthroughs in fault diagnosis paradigms, and improved plant operational efficiency. As one of the pioneering explorations of deep transfer learning in cross-domain nuclear power plant fault diagnosis, this work demonstrates the feasibility and applicability of cross-reactor diagnosis, effectively increasing the utilization rate of monitoring parameters and expanding the scope of fault diagnosis applications—thereby advancing the implementation of condition-based maintenance strategies and further promoting the intelligence and informatization of nuclear power plants.

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Footnotes

Edited by: Nicola Pedroni, Polytechnic University of Turin, Italy

Reviewed by: Guohua Wu, Harbin Institute of Technology, China

Ugur Mertyurek, Oak Ridge National Laboratory (DOE), United States