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. 2023 Feb 22;9(3):e13883. doi: 10.1016/j.heliyon.2023.e13883

A review of the application of artificial intelligence to nuclear reactors: Where we are and what's next

Qingyu Huang 1,, Shinian Peng 1, Jian Deng 1,∗∗, Hui Zeng 1, Zhuo Zhang 1, Yu Liu 1, Peng Yuan 1
PMCID: PMC9988575  PMID: 36895398

Abstract

As a form of clean energy, nuclear energy has unique advantages compared to other energy sources in the present era, where low-carbon policies are being widely advocated. The exponential growth of artificial intelligence (AI) technology in recent decades has resulted in new opportunities and challenges in terms of improving the safety and economics of nuclear reactors. This study briefly introduces modern AI algorithms such as machine learning, deep learning, and evolutionary computing. Furthermore, several studies on the use of AI techniques for nuclear reactor design optimization as well as operation and maintenance (O&M) are reviewed and discussed. The existing obstacles that prevent the further fusion of AI and nuclear reactor technologies so that they can be scaled to real-world problems are classified into two categories: (1) data issues: insufficient experimental data increases the possibility of data distribution drift and data imbalance; (2) black-box dilemma: methods such as deep learning have poor interpretability. Finally, this study proposes two directions for the future fusion of AI and nuclear reactor technologies: (1) better integration of domain knowledge with data-driven approaches to reduce the high demand for data and improve the model performance and robustness; (2) promoting the use of explainable artificial intelligence (XAI) technologies to enhance the transparency and reliability of the model. In addition, causal learning warrants further attention owing to its inherent ability to solve out-of-distribution generalization (OODG) problems.

Keywords: Artificial intelligence, Causal learning, Nuclear reactors, SciML, XAI

1. Introduction

With the rapid development of the global economy, low-carbon policies that aim to reduce the consumption of high-carbon resources and greenhouse gas emissions as much as possible by altering the energy composition are being increasingly advocated by governments worldwide in order to achieve sustainable economic development while ensuring environmental protection. Among the various components of non-fossil energy, wind power and solar energy are competitive owing to their renewable nature. However, the energy supply instability resulting from their volatility, intermittency, and other drawbacks will persist until energy storage technologies become adequately mature [1,2]. Under these circumstances, nuclear energy, as a stable base-load zero-carbon energy source, can be leveraged as a powerful strategic option for ensuring the stable supply of electricity [3] .

However, for nuclear energy to be more competitive and integrable in modern energy systems, nuclear power plants (NPPs) must be not only economical and efficient but also safe, reliable, and sustainable [4]. Recent years have witnessed a trend of deep integration of information technology and industry. Consequently, various digital technologies represented by artificial intelligence (AI) have been rapidly deployed in many high-tech fields to help reduce costs, improve profit margins, and enhance industrial competitiveness. Owing to the strong dependence of modern AI technology on data, the nuclear energy field has considerable potential, because many NPPs have accumulated a large amount of underutilized data in recent decades. Although research on the combination of the nuclear industry and AI has been recently conducted by many nuclear scientists, most applications of AI for empowering the nuclear industry remain in the experimental stage and cannot be implemented in real-world scenarios owing to some unavoidable problems (such as algorithm robustness). Therefore, exploring the correct, effective, and in-depth use of AI technology is expected to be one of the most important paths toward fostering sustainable innovation in nuclear power reactor research.

The entire life cycle of a nuclear reactor involves multiple steps, such as design, manufacture, operation, maintenance, refueling, and decommissioning. The present study investigates the application of AI to nuclear reactor design and operation & maintenance (O&M) by considering that the two fields are particularly pertinent to AI in terms of the proportion of existing research cases.

The remainder of this paper is organized as follows. Section 1.1 provides a brief introduction to some mainstream AI technologies. Sections 2, 3 describe the application of AI to nuclear reactor design optimization and O&M, respectively. Section 4 focuses on the existing bottlenecks and open issues in the combination of AI technology and nuclear reactor research. Section 5 discusses some directions for future work based on existing technologies. Finally, Section 6 concludes the paper.

1.1. A brief introduction to modern AI technologies

AI is the science domain concerned with the theory and practice of explaining and implementing intelligent behavior using computational processes [5]. AI has a broad and rich research history, covering the issues of knowledge representation [6], evolutionary computing [7,8], machine learning [9], and intelligent system construction [10]. A brief framework of AI technologies is shown in Fig. 1.

Fig. 1.

Fig. 1

Brief framework of AI technologies.

Machine learning (ML), as a specialized research field that falls under the umbrella of modern AI technology, acquires knowledge through the automatic analysis of data and utilizes the acquired knowledge to perform tasks such as the prediction or classification of unknown data. Machine learning can be broadly divided into three categories: supervised, unsupervised, and reinforcement learning. Supervised learning refers to learning a pattern from the labeled input-output training set, and inferring new instance patterns based on it. The output can be a continuous value (regression analysis task), or a classification label (classification task). Unsupervised learning refers to a class of algorithms that learn patterns from unlabeled data. From a probabilistic perspective, unsupervised and supervised learning are in stark contrast: supervised learning aims to infer conditional probability distributions conditioned on the labels of the input data, while unsupervised learning aims to infer prior probability distributions. Reinforcement learning (RL) [11] is a type of machine learning used to address the problem of agents learning strategies to maximize rewards or achieve specific goals during the interaction with the environment. Typical ML algorithms, such as linear regression [12,13], support vector machine (SVM) [14,15], random forest (RF) [16], and artificial neural network (ANN) [17,18], have been widely explored and adopted in the field of nuclear energy. However, the process of determining the optimal feature expression in ML often involves high costs, which is a significant challenge for further improving the efficiency of ML.

With continuous advances in computational capabilities and optimization techniques, deep learning (DL) [19], as the main representative of the AI connectionism/bionicsism, has witnessed a quantum leap in the fields of computer vision and natural language processing [20,21]. In general, DL refers to network models composed of multiple nonlinear transformations, which are mainly used for the simulation (representation, feature extraction) of the data generation mechanism and the approximation of arbitrary unknown mapping relationships. Common DL models, such as deep neural network (DNN), convolutional neural network (CNN) [22], recurrent neural network (RNN) [23,24], and long short-term memory neural network (LSTM) [25], are being increasingly leveraged in the modern world. ML and DL have grown exponentially in the past decade in the field of data mining, while Python programming language [26] is one of the indispensable tools in the field of data science because of its concise and easy-to-read code, and extensive open-source libraries. Here some currently widely used machine learning/deep learning libraries are listed and recommended: Scikit-learn [27], TensorFlow [28] and PyTorch [28].

Moreover, as a nuclear reactor is a complex system involving numerous nonlinear parameters, solutions to global optimal issues remain elusive and demanding in terms of the design process. Therefore, it is necessary to focus on the evolutionary algorithm (EA). In addition to the genetic algorithm (GA) [29], and with a deeper understanding of its nature, researchers have proposed many EA paradigms. For instance, Dorigo and Di Caro [30] proposed ant colony optimization, while Eberhart and Kennedy [31] proposed particle swarm optimization (PSO). Subsequently, additional EAs such as the artificial bee colony algorithm [32], cuckoo search [33], and the bat algorithm [34] have been proposed to promote the exploration of optimization problems.

2. Application of AI to nuclear reactor design optimization

A nuclear reactor is a complex nonlinear system involving multiple disciplines such as materials science, nuclear physics, chemistry, heat transfer, fluid mechanics, and radiation shielding. To fully exploit the massive data accumulated by nuclear reactors, optimizing the reactor design for improving the safety and economy of the reactor is an important direction for AI technology to empower the field of nuclear energy. Some novel studies (See Table 1) that have focused on integrating the capabilities of AI into nuclear industry design optimization are briefly reviewed below:

Table 1.

Summary of previous application of AI in nuclear reactor design optimization.

Application Method Findings References
In-Core fuel management GA GA shows the advantage of global search and is more suitable for parallel computing in comparison with simulated annealing algorithm [35]
Fuel loading pattern GA A program based on GAs and a code-independent interface was developed to optimize nuclear reactor loading patterns [36]
Fuel loading pattern GA (constrained optimization with penalty function) A program based on the proposed methods was developed for BWR fuel assembly axial optimization [37]
Core design Multi Objective GA Advantages of the proposed approach over the single-objective GAs in a multi- criteria and multi- constraint optimization problem were found [38]
Fuel loading pattern Multi Objective GA Design parameters of the fast breeder were improved properly [39]
Core design Parallel GA Parallel GA provides gains in both computational efficiency and optimization outcome [40]
Fuel lattice design Ant colony Ant colony algorithm was proven to be an effective tool for BWR fuel lattice arrangement [41]
Fuel loading pattern Ant colony An automatic PWR core reload design tool was developed [42]
In-Core fuel management Artificial bee colony The proposed approach can reduce the computational cost by employing significantly fewer control parameters compared to other population-based algorithms [43]
Fuel management HANN A set of two basic parameters: Power peaking factor and Reactivity coefficient, was obtained appropriately [44]
Fuel loading pattern HANN Best axial variation distributions of enrichment were determined in order to reach the flattening neutronic flux [45]
Nuclear assembly design RL RL shows better computational efficiency than traditional stochastic optimization algorithms in addressing high-dimensional problems [46]
Nuclear assembly design RL-guided EA RL-guided EA outperforms standalone algorithms by a wide margin in exploration capabilities and computational efficiency [47]
Thermal-hydraulic simulation computation acceleration Deep neural network Developed model can achieve rapid and accurate prediction of key thermal-hydraulic parameters [48]
Thermal-hydraulic simulation computation acceleration A physical simulation and deep learning coupled framework Capable of accelerating the convergence of RANS simulations [51]
Thermal-hydraulic simulation computation acceleration Deep neural network A surrogate model to predict turbulent eddy viscosity in RANS simulation [52]
Thermal-hydraulic simulation computation acceleration A neural network model introducing the FVM with unique architecture Significantly improved accuracy of multistep time series prediction with much faster speed [53]
Thermal-hydraulic simulation computation acceleration A model combines modal decompositions with DL architectures The speed-up factor in the numerical simulations using this ROM is remarkably high [55]
Thermal-hydraulic simulation computation acceleration A deep 3D-convolutional neural network A novel architecture based on 3D convolutional layers was proposed, showing good performance in predicting future velocity fields of a complex fluid flow [54]
Thermal-hydraulic simulation computation acceleration DL-based ROMs A method to avoid the expensive training stage of the model was proposed, and tested on several examples, showing the good generality [56]
Thermal-hydraulic simulation computation acceleration DL-based ROMs Computational runtime of iterative solvers was reduced by nearly two orders of magnitude with an acceptable error threshold [57]
Data-driven-based key parameters prediction BPNN Capable of accurately estimating supercritical water heat transfer coefficient [58]
Data-driven-based key parameters prediction A multitask-based temporal-channelwise CNN A novel DL based soft measure technique to predict the gas void fraction [59]
Data-driven-based key parameters prediction Lasso regression, SVM, RF, BPNN RF performs more prominently than other ML paradigms on tabular data prediction tasks [60]
CHF prediction ANN The network architecture is general and can be used for continuous learning beyond the training data range [63]
Wall temperature prediction at CHF ANN Highly enhanced the calculation speed corresponding to a maximum 86%-time reduction [62]
CHF prediction ANN The effects of main parameters such as pressure, mass flow rate and equilibrium quality on CHF were analyzed [64]
CHF prediction PIMLAF The proposed framework takes advantage domain knowledge and uses machine learning (ML) to capture undiscovered information from the mismatch, achieving superior predictive capabilities. [61]
Radiation shielding design GA The multi-objective optimization design method can be used to find a better scheme more comprehensively. [70]
Radiation shielding design MACNOS Able to seek for the shielding design that minimizes the total weight by changing the thickness and the material of the shield with constraints satisfied [71]
Mass attenuation coefficient prediction for shielding material ANN A high determination coefficient of 1 and a root mean square error of 0.0033 [72]
Radiation shielding design BPNN and GA Significantly reducing the computational cost of shielding structure design optimization for marine reactors [73]
Radiation shielding design PSO An automatic optimization program was developed and proved effective on marine reactors [74]

2.1. Nuclear reactor core design

The nuclear reactor core is inherently the most critical part among the various complex systems of an NPP. It consists of nuclear fuel assemblies, control rods, neutron reflectors, in-core instrumentation, etc. The nuclear fuel assemblies are arranged in a pressure vessel in a specific form to ensure continuous thermal power output through chain nuclear reactions under controllable conditions. Nuclear fuel management is critical to the design of the core, as it determines the core power distribution and fuel economy. Therefore, to improve the neutron fluence rate and burnup depth, it is necessary to optimize the nuclear fuel layout of the core in order to minimize the cost of electrical energy generation while considering the operational and safety constraints.

As a classical and versatile optimization search strategy, GA imitates the mechanism of biological genetics and natural selection, and it has been shown to be a robust tool in nuclear fuel management studies. Poon and Parks [35] were the first researchers to apply GA to nuclear fuel management. Later, Dechaine and Feltus [36] developed a GA-based system for in-core fuel design optimization, and they showed that GA significantly outperforms the random search method. Subsequently, other variants of GA (including constrained optimization with penalty function [37], multi-objective GA [38,39], and parallel GA [40]) were used for different types of nuclear reactor core optimization.

Montes and Francois [41], Lin and Lin [42] applied ant colony algorithm to water reactor radial fuel lattice design optimization and pressurized water reactor (PWR) loading pattern design optimization, respectively. de Oliveira and Schirru [43] adopted the artificial bee colony method for solving the combinatorial problems of in-core fuel management optimization. Remarkably, this approach can reduce the computational cost by employing significantly fewer control parameters, thereby achieving considerable performance improvement. Pazirandeh and Tayefi [44] employed a Hopfield artificial neural network (HANN) to obtain a suitable power peaking factor and evaluate the effective multiplication factor for VVER-1000 reactors in order to optimize fuel management. Tayefi and Pazirandeh [45] used HANN to determine the best axial variation distributions of enrichment in order to reach the flattening neutronic flux and guarantee safe operation. Radaideh, Wolverton [46] successfully applied RL to the optimization of fuel assemblies by establishing a connection between RL and the strategy of moving the fuel rods to meet specific constraints. Further, they showed that RL outperforms other methods in the case of boiling water reactor (BWR) assemblies and demonstrated that RL is a feasible and efficient tool for fuel management. Furthermore, a novel rule-based hybrid framework of RL and evolutionary computing was developed to reduce the computing time and improve the optimization performance [47].

2.2. Thermal-hydraulic simulation analysis

Thermal-hydraulic analysis mainly focuses on the flow and heat transfer process of the coolant in the nuclear reactor. Essentially, the reactor is a heat source with a compact structure and a high heat release rate per unit volume. Timely and efficient transfer of heat by the coolant, which guarantees that the core will not melt under transient or accident conditions, plays an important role in ensuring the safety of nuclear reactors and improving their economics. However, the traditional thermal-hydraulic design strategy has the following drawbacks: (1) the workload of the model development/mesh design based on experience is complicated and time-consuming. (2) The working conditions are numerous and complex, resulting in a long calculation time.

To make the computation tractable, AI-based surrogate models have been developed in order to accelerate the computation for nuclear reactor analysis, such as computational fluid dynamics (CFD) and system analysis code. Lu and Yuan [48] adopted a deep neural network model with the scaled exponential linear unit (SELU) as the activation function to realize rapid prediction of multiple important thermal parameters of the KLT-40S nuclear reactor [49] core and tube-in-tube once-through steam generator; the results were in good agreement with the RELAP5/SCDAPSIM program [50]. Obiols-Sales and Vishnu [51] proposed a physics–DL coupled framework for accelerating the convergence of Reynolds-averaged Navier–Stokes (RANS) simulations. Ayodeji and Amidu [52] developed a surrogate model based on a deep feedforward neural network to predict the turbulent eddy viscosity in RANS simulations; the results closely matched those of an actual turbulent model. Jeon and Lee [53] constructed a neuron-network-based model to simulate the principles of the finite volume method (FVM) in fluid dynamics. The performance was evaluated using unsteady reacting flow datasets and showed good agreement with reference data at one-tenth of the computational cost. In addition, several studies have shown that it is feasible to use machine learning methods to develop hydrodynamic reduced order models (ROMs) in order to achieve substantial computational acceleration [[54], [55], [56], [57]].

In the calculation of two-phase flows and boiling heat transfer phenomena, empirical or semi-empirical formulas are widely employed owing to the complexity of the physical mechanisms, and they usually involve problems such as a limited model application range. AI-based methods can reliably guarantee the establishment of data-driven models and pave the way for exploring intrinsic physical mechanisms. Ma and Zhou [58] used back-propagation neural networks to determine the heat transfer coefficient within the scope of the supercritical water pressure on the basis of parameters such as heat flux, mass flux, pipe diameter, and pressure as inputs. Gao and Hou [59] designed a novel CNN-based soft measuring method to predict the void fraction of two-phase flows and achieved good performance. Huang and Yu [60] comparatively employed four machine learning paradigms to predict the two-phase interfacial key parameters of a rectangular channel and verified the reliability and superiority of the ensemble learning method in the application of tabular data. Furthermore, the determination of the critical heat flux (CHF) is crucial for the safe operation of a water-cooled reactor. In addition to traditional empirical relations, look-up table methods, and mechanism-/phenomenon-based models, AI-based methods have been extensively explored in recent years [[61], [62], [63], [64]]. Besides, some public CHF datasets are available for deeper investigation and optimization of AI algorithms [65,66].

2.3. Radiation shielding design

The radiation generated by the operation of a nuclear reactor can cause ionizing radiation damage to the surrounding environment and personnel. Therefore, it is necessary to select materials for effective shielding. Thus, radiation shielding design is of great importance in reactor engineering design, especially for special nuclear power devices such as marine reactors and nuclear-powered spacecraft. Radiation shielding design requires not only the specified area to meet the radiation dose limit but also the weight and volume of the shielding system to be strictly controlled, which is an inherently “dose–weight–volume” multi-objective optimization problem [67]. The two main methods of shielding calculation presently adopted in the field of nuclear engineering are the discrete ordinate method (DOM) and the Monte Carlo method (MCM). However, the low computational efficiency in multi-dimensional shielding calculation problems has been a long-standing issue for both methods [68,69].

The GA method has been effectively adopted [70] for single-objective and multi-objective optimization problems of the reactor shielding design. Kim and Moon [71] proposed an improved method based on GA, called macroscopic near-optimal shielding (MACNOS), to determine the optimal space nuclear reactor radiation shielding design configuration (weight, thickness, and material) under the given constraints. Gencel [72] established an ANN-based model with the dose and thickness as the inputs for estimating the mass attenuation coefficient of the shielding barrier; the error between the predicted results and the MCM calculation results did not exceed 0.0033. Song and Li [73] used a back-propagation neural network (BPNN) and GA to determine the best shielding parameters for a marine nuclear reactor. Further, a multi-objective optimization method for the shielding design based on PSO with MCM was proposed [74], and the material type and thickness of the reactor shield were adjusted automatically. This method was proven to be reliable and effective by applying it to a Savannah marine reactor and comparing it with the original scheme.

3. Application of AI to nuclear reactor O&M

Improving the O&M capability plays an important role in enhancing the safety and economy of NPPs. In terms of safety, with the extended service life of the NPP equipment, the materials will inevitably degrade over time, which will adversely affect the equipment and prevent it from fulfilling its designed function. In the case of active equipment (such as pumps, valves, and electronic devices), aging increases the probability of failure over time, In the case of passive equipment (such as pipes and pressure vessels), aging decreases the safety margin. In terms of economy, to meet the challenges of various other emerging forms of energy supply, such as natural gas and wind power, there is an urgent need for the nuclear power industry to improve its economic level in order to enhance its market competitiveness. O&M costs account for around 60%–70% of the total operating costs of a nuclear power plant, compared to fuel costs, which account for only around 15%–30% of the total operating costs [[75], [76], [77]]. Therefore, reducing the O&M costs is an effective measure for improving the economics of nuclear power plants. Table 2 provides a summary of research focused on use of AI technologies for nuclear reactor O&M.

Table 2.

Summary of previous application of AI in nuclear reactor O&M.

Application Method Findings References
Transient detection, classification, and prediction Dynamic neural network aggregation model A two-level classifier architecture was adopted, to obtain the type, severity, and location of transients individually [79]
OLM and verification AANN The input and output of AANN are the same set of nuclear power plant operating parameters with certain interrelationships, thus it can be used for nuclear reactor online sensor verification [80]
OLM and verification AANN Developed model can be used for simultaneous failures of multiple measuring instruments [82]
Online sensor calibration and fault classification AANN Developed model can be used to distinguish fault components and intensity, and to reconstruct unmeasured signals [83]
Online sensor calibration and fault classification AANN sensor error verification of the UTSG [84]
OLM and FD RNN High performance of the developed model was shown by means of two different applications: OLM and diagnosis in a high-temperature gas cooled nuclear reactor and rotating machinery [85]
Control rod position monitoring RBFNN, GMDH and LM All methods can be utilized separately to unfold the control rod position from the in-core neutron flux measurements [86]
Trend prediction of operating parameters Neuro-fuzzy technique Possible to detect the failure of the equipment or the corresponding measurement sensor when the prediction results deviate from the actual measurement results [87]
OLM Probabilistic SVM A single-step interval prediction was performed to show the feasibility of the model [88]
Trend prediction of operating parameters Dynamic BPNN Developed model has achieved more accurate and stable prediction results. However, since the online BPNN still relies on time-consuming gradient descent iterative training, in order to ensure the computation speed, the number of training steps is greatly limited. [89]
Online sequential condition prediction EOS-ELM Fast learning speeding without obvious overfitting problems [90]
Water level prediction DNN-GA DNN model has better performance than cascaded fuzzy neural network [91]
Operating parameters prediction during LOCA DNN/LSTM Proposed methods are 100,000 times faster than the original simulation tool with satisfying accuracy [92]
Prediction of neutron flux and power distributions ROM-ML Able to predict high-dimensional outputs with physics-informed digital twins framework [94]
Compensation for low-precision model deviation K-means and ANN A digital twin model consisting of offline and online stages is proposed, and its calibration results are shown to have good agreement with the ground truth [95]
System-level FD ANN 8 operating conditions can be accurately diagnosed and classified [98]
System-level FD ANN A dynamic architecture was proposed, in which the first network is used to judge whether the system is in an abnormal state, and the second network is used for classification of abnormal conditions [99]
System-level FD PCA PCA enables fast compression of multiple dimensions for transient identification [100]
System-level FD RBFNN Able to recognize the three accidents, even with a noise level up to 10% [101]
System-level FD CNN Developed model outperforms other classification models in terms of accuracy robustness, and reliability [102]
System-level FD DL Identification of NPP accidents with 99.82% accuracy and unknown situations with 100% [103]
System-level FD KPCA and similarity clustering Able to detect both the type and the degree of faults [104]
FD of the pressurizer Unsupervised clustering Efficient fault classification on unlabeled datasets [111]
FD of the RCP AAKR A strategy that can balance false and missed alarms [112]
FD of the rotating machinery LSTM A novel weakly supervised training method was proposed to detect, identify, and localize anomalies from time-series data automatically [113]
FD of CEDM Digital twin technology Feasibility of using digital twin technology for CEDM health monitoring and FD is demonstrated [114]
FD of screen cleaners XGB Robustness of ensemble learning methods to uninformative features is more advantageous than other ML methods [115]
FD of rotating machines DL CRNN shows better small sample learning capability and anti-noise robustness compared to other models [116]
Identification of an accidental drop of control rods RBFNN Impact of the lack of experimental data on the model performance is highlighted [117]
FD of sensors RNN A robust system based on RNN that can tolerate sensor failures is developed [118]
FD of sensors PCA Improving the ability of data reconstruction and detection of multiple sensor failures [120]
FD of sensors PCA Moving average filtering method is adopted to reduce false alarms [119]
FD of a steam generator Neuro-fuzzy network Methodology is applied successfully for FD and isolation [122]
FD of a steam generator PCA Different fault directions are obtained using singular value decomposition of the prediction errors, and used for fault isolation from new projections [123]
Incipient SGTR diagnosis SVM Able to estimate uncertain parameters that are sensitive to certain faults [124]
FD of a steam generator ANFIS Highly capable of diagnosing SGTR transient [125]
RUL prediction of IGBT ANN, ANFIS Capable of predicting RUL of the IGBT device under varying loads [132]
RUL estimation of electric gate valves TCN Developed model has impressive performance and generalization ability, and the computation efficiency is enhanced by incorporating a convolution auto-encoder as a preprocessing layer [133]

3.1. Online condition monitoring

Online condition monitoring (OLM) is a comprehensive technology with multi-disciplinary cross-penetration [78]. OLM technology is adopted in NPPs to achieve three objectives:

  • (1)

    real-time and accurate monitoring of important safety parameters, such as the three-dimensional power distribution during the operation of the reactor, to ensure that they do not exceed the design limit, and to provide a reference that allows operators to efficiently implement the corrective measures;

  • (2)

    to eliminate the excessive conservatism in the operating procedures of the reactor, reduce the operating margin, and improve the economy while ensuring the safety of the reactor.

  • (3)

    to obtain the burnup distribution at the end of the reactor cycle life and provide a reliable basis for planning a more economical refueling scheme, thereby extending the refueling interval and enhancing the economic benefits of the NPP.

Mo and Lee [79] proposed dynamic neural network aggregation to determine the type of transients, severity, and location individually, and they achieved satisfactory performance compared with a conventional ANN. Hines and Uhrig [80] were the first researchers to propose online monitoring and online sensor calibration for NPPs on the basis of an auto-associative neural network (AANN). AANN [81] was designed to satisfy the same dimensions of the input and output. Under normal operating conditions, the output values of the trained auto-associative neural network should be consistent with the actual measured values. When the measurement sensor fails or the system is disturbed, the predicted values may deviate. Researchers have applied AANN to the simultaneous occurrence of multiple instrument faults [82]; online sensor calibration and fault classification of BWR [83]; and sensor error verification of a U-tube steam generator (UTSG) [84]. RNN has also been used for OLM and has been validated on the data generated by a high-temperature gas-cooled reactor simulator [85]. Three methods (radial basis function neural network (RBFNN), group method of data handling (GMDH), and the Levenberg–Marquardt (LM) algorithm) have been adopted for control rod position monitoring [86].

Using monitoring data for the short-term prediction of the systematic operating conditions in NPPs is a common strategy for OLM. Marseguerra and Zio [87] used the neuro-fuzzy technique to predict the time-series signal of the water level change of the steam generator under the transient condition and under the condition of steam turbine load change for the timely detection of device malfunctions. Liu and Seraoui [88] proposed an online prediction method of the nuclear reactor equipment operating state on the basis of the probabilistic support vector regression model. Liu and Xie [89] established an NPP operating parameter prediction model based on the online training BPNN, and verified the effectiveness of the model by predicting the fluctuating system operating parameters such as the coolant void fraction and the water level of the steam generator and the pressurizer. Chen and Gao [90] proposed an online-condition approach for flow oscillation pattern recognition and trend forecasting of a natural circulation system based on the ensemble of online sequential extreme learning machine (EOS–ELM), which achieves a significantly high training speed and good accuracy. There are few existing short-term prediction studies on various complex thermal-hydraulic conditions (e.g., severe accidents) in NPP systems, even though such prediction models have great significance from the viewpoint of practical application. Koo and An [91] employed the DNN-GA algorithm to predict the water level changes in the event of a severe accident of the NPP. Furthermore, DNN/LSTM were leveraged to predict the outputs (e.g. temperature, pressure, break flow rate, water level)) during the loss-of-coolant accident (LOCA), with a minimum accuracy of 92% and a maximum accuracy of 99%, and this method was 100,000 times faster than the original simulation tool [92].

The recent emergence of digital twin technology has provided a new perspective for OLM. The digital twin of an NPP refers to the mirrored entity of the NPP projected from the physical space to cyberspace. When a real NPP is running, its digital twin can obtain data that cannot be measured using sensors via soft measurement, and ultra-real-time high-precision simulations are conducted to study the consequences of different operations in order to facilitate the decision-making process. Fig. 2 shows how this study interprets the operation mechanism of the digital twin of an NPP.

Fig. 2.

Fig. 2

Interaction operation mechanism of a real-world NPP and its digital twin. DI: data interaction.

Kochunas and Huan [93] discussed the availability, modeling approaches, and challenges of the digital twin technology application in the field of nuclear engineering, and they further explored the impact of the challenges brought about by the uncertainty quantification and propagation. Gong and Cheng [94] presented a digital-twin-based approach to predict the high-dimensional output quantities of interest, such as the neutron flux and power distributions, by combining ML and ROM. Song and Song [95] proposed an autonomous calibration method for NPP digital twins to compensate for the computational bias of low-precision models. An initial calibration model was established at the offline end using the error database and ML methods, and the model was dynamically and continuously updated at the online end using real-time measurement data.

3.2. Fault diagnosis

Numerous faults may occur in the systems and equipment of NPPs during operation, which may adversely affect the reliability of the NPPs. Since the Three Mile Island accident [96], studies on fault diagnosis (FD) methods for NPPs gradually intensified. As a representative model-free method, data-driven-based fault diagnosis does not rely on relevant explicit mathematical models, and it can effectively avoid the difficulty of accurately modeling complex nonlinear systems in NPPs through physics-based methods. Thus far, FD may be the most active application of AI techniques in various fields of nuclear reactors, and significant progress has been achieved. Macroscopically, the FD of NPPs can be classified into two categories: system level and component level [97].

From the system-level FD perspective, Bartlett and Uhrig [98] proposed a fault transient diagnosis method for NPPs using a self-optimizing ANN with a dynamic node architecture. The proposed model uses 27 monitoring parameters as the input and 8 operating conditions (7 fault conditions and a full-power normal operating condition) as the output. Basu and Bartlett [99] proposed a fault transient diagnosis method for NPPs on the basis of two BPNNs with a dynamic node structure. One neural network is used to judge whether the nuclear power plant is operating normally, and the other neural network is used to judge the type of fault transient that has occurred. Park and Park [100] used principal component analysis (PCA) to map hundreds of variables into a low-dimensional space for typical FD in the secondary loop system of an NPP. Gomes and Medeiros [101] used a Gaussian RBFNN to identify PWR accidents. Lee and Lee [102] conducted real-time abnormality diagnosis by employing a dual-channel CNN and found that it outperforms other classification models in terms of accuracy and reliability. Santos and Pereira [103] developed a modular structured DL-based NPP accident identification system that allows rapid detection of anomalous events and can respond to “don't know” events. Furthermore, a framework based on kernel principal component analysis (KPCA) and similarity clustering that can be utilized to detect the type and assess the severity of malfunctions was developed for the FD of NPP system [104], and both real and simulated datasets used in this paper are provided [105]. In addition, system-level FD in NPPs has attracted attention and been deeply explored because of its practical importance, and some public datasets are provided, which can be used for algorithm verification and improvement [[106], [107], [108], [109], [110]].

Existing research on the FD of NPP components is more abundant and diverse. Baraldi and Di Maio [111] proposed an unsupervised clustering-based method to discriminate the transients caused by different faults of the pressurizer. Di Maio and Baraldi [112] explored the feasibility of FD for the reactor coolant pump (RCP) of the PWR using auto-associative kernel regression (AAKR). Miki and Demachi [113] developed a weakly supervised LSTM algorithm for the automatic extraction of potential anomalous features in time-series data, which was effectively used for the FD of rotating bearings. Oluwasegun and Jung [114] extracted features from coil current profiles and adopted multiple machine learning approaches for the fault diagnosis and classification of the control element drive mechanism (CEDM). Deleplace and Atamuradov [115] proposed an ensemble learning FD method using extreme gradient boosting (XGBoosting), and showed that its fault classification ability exceeded that of SVM and K-nearest neighbors (KNN) by applying it to the screen cleaners of NPPs. Four DL methods were adopted for the FD of rotating machines of NPPs, among which the convolutional recurrent neural network (CRNN) showed the best performance [116]. Souza and Medeiros [117] carried out identification of the accidental drop of the control rods in PWR reactors using RBFNN. Furthermore, RNN [118] and PCA [119,120] were adopted for sensor FD in NPPs, to enhance fault tolerance against false alarms and detection capability against multiple sensor failures.

For a steam generator, Lu and Upadhyaya [121] adopted GMDH to model the multivariate process of UTSG and PCA to generate the representative fault signatures. Razavi-Far and Davilu [122] attempted to perform fault detection and isolation for UTSG using two types of neuro-fuzzy networks. Li and Upadhyaya [123] used PCA for the FD of a helical coil steam generator. Ayodeji and Liu [124] proposed a rapid method for detecting both incipient and large leakages in steam generators using an optimized SVM model. Mwaura and Liu [125] adopted the adaptive neuro-fuzzy inference system (ANFIS) approach for the FD of a steam generator, which is not only sensitive to incipient faults but also strongly capable of time-series prediction. To evaluate the accuracy and robustness of the present model, steam generator tube rupture (SGTR) scenarios were simulated using the Qinshan I NPP (CNP300 PWR) reactor coolant system with thermal-hydraulic code. The results showed that the error is less than 1%.

3.3. Predictive maintenance

In general, the nuclear industry presently adopts a maintenance program based on a regular preventive strategy to maintain and repair the main equipment of an NPP. However, the basis for determining the maintenance time in regular preventive maintenance is the average service life of similar equipment, and the actual operating status of specific equipment is not considered. Thus, owing to conservative considerations, the issue of excessive maintenance inevitably occurs in engineering practice. On the one hand, excessive maintenance will cause wastage of resources and increase the costs. On the other hand, it will increase the system risks introduced by human errors in the maintenance process. To improve the overall safety and economy of NPP O&M, the prognostics and health management (PHM) framework, which is shown in Fig. 3, aims to transform the “on-time maintenance strategy” into an “on-demand maintenance strategy” via residual useful life (RUL) prediction of the key equipment [126]. RUL prediction is mainly defined as employing suitable algorithms to mine the monitoring data for the equipment with signs of performance degradation or failure, and predicting the future development trend of the performance status and the RUL of the equipment [127].

Fig. 3.

Fig. 3

Snapshot of the PHM architecture.

In general, AI-based RUL prediction methods can be classified into two categories:

  • (1)

    Direct mapping: ML models are used to directly establish the mapping relationship between the monitoring data of the sensors and the RUL of the equipment. An ensemble of a neural network model [128], an RNN-based model [129], and a hybrid PCA classification and regression trees (CARTs)–multivariate adaptive regression splines (MARS)-based approach [130] was adopted to establish the mapping relationship between the measurement data of the sensors and the RUL of the engine. Patil, Tagade [131] proposed a method for training the SVM model on the basis of the features extracted from the voltage and temperature of a lithium battery, which can be used to directly predict the life stage of the battery.

  • (2)

    Degenerate trajectory modeling: The degradation process of the equipment is described using the degradation trajectory metrics, and ML methods are adopted to fit the trajectory profile. Finally, the failure time point of the equipment is determined by setting the failure threshold. Ahsan, Stoyanov [132] adopted BPNN and ANFIS to forecast the RUL of an insulated-gate bipolar transistor (IGBT), which is a critical component of the low-frequency power control system of NPPs. Wang, Peng [133] proposed an improved temporal convolution network (TCN) model for the RUL estimation of electric gate valves in NPPs, and they integrated a high-performance convolutional autoencoder layer to improve the model feature extraction performance. The external cracks of the valve were selected as the typical failure mode, and signals such as differential pressure, flow, and acoustic waves were selected as features representing the aging state of the valve. The results showed that the model has good performance and generalization ability, and it can address the high computational requirements of models such as LSTM and RNN.

4. Open issues

4.1. Data issues

A nuclear reactor is essentially a complex system involving numerous nonlinear, dynamic, and time-varying parameters as well as multidisciplinary coupling. As a de facto non-novel field, AI has played an indispensable role in promoting the development of nuclear reactors in recent decades. In particular, in the last decade, the considerable success of ML applications in various fields worldwide has raised many researchers’ expectations for using ML-/DL-based methods to explore future possibilities in nuclear reactor research. From the core design optimization to the PHM of an NPP, many existing studies have demonstrated their availability through multiple metrics such as computational accuracy.

However, concerns persist as to whether AI techniques can be scaled to real-world issues of NPPs. First, in terms of data, a high proportion of the data used to train and test models in the reviewed studies is derived from simulation calculations owing to the high-cost investment from the acquisition of experimental data of NPPs, as well as the risk of reproducing some complex operating conditions (such as severe accident scenarios). Therefore, for the AI model, the information characteristics represented by the data used for training in the implicit space are likely to differ significantly from the real-world data, and there is a high possibility of data distribution drift caused by non-stationary environments. Souza, Medeiros [117] indicated that a lack of real experimental adversely affects the performance of the model while establishing an AI-based model for the identification of accidental falls of the control rod. Meanwhile, Suman [134] also raised concerns about the inconsistency caused by different data sets selected by laboratory studies, because some algorithms will only show the best performance on confined data sets. Standard datasets for specific targets in the nuclear reactor field should be developed in order to provide a path for determining the best AI model. In addition, a common and noteworthy cognitive bias is that the vast amount of data accumulated by NPPs over decades can be effectively exploited to develop models. A typical example is the common sample imbalance in FD, i.e., the difference between normal samples and fault samples is massive, resulting in the weak classification ability of the supervised model for a small number of samples. Although some methods have been developed for data augmentation (e.g., synthetic minority over-sampling technique (SMOTE) [135]) to address this problem, it should be emphasized that the development of a high-performance AI model requires high-value-density/high-quality data rather than just a large amount of data.

4.2. Black box dilemma

Another concern is that the AI system represented by DL algorithms is essentially a black box. Between the input and the output of a DL model, there are invisible hidden layers, where the neural network encodes features through multiple layers of neuron clusters, which makes the process obscure for humans. Fig. 4 shows the AI explainability versus performance paradox. Models with better performance usually have a more complex internal mechanism and are therefore difficult to explain, whereas models with a clearer mechanism, such as linear models and rule-based models, lack the ability to deal with some complex nonlinear problems. An ideal model has both good performance and high explainability.

Fig. 4.

Fig. 4

Trade-off between performance and explainability of widely used AI models, adopted from the study by Ref. [136]. HBN: hierarchical Bayesian networks SLR: simple linear regression; CRF: conditional random fields; MLN: Markov logic network; AOG: stochastic and–or graphs; XGB: extreme gradient boosting; GAN: generative adversarial network.

In addition, Szegedy and Zaremba [137] showed that by slightly perturbing the sample set, an otherwise advanced neural network can be significantly misled on a specific task. Through image classification tasks, Nguyen and Yosinski [138] confirmed that DNNs are easily fooled by misleading images to make false judgments with high confidence, such as recognizing red and white lines as a baseball. This problem has raised questions about the robustness of AI technology: can existing AI models withstand adversarial attacks such as escape attacks [139]?

The high requirement in terms of the safety performance is one of the most important fundamental criteria for the design and O&M of nuclear reactors. Therefore, to further promote the fusion of AI and nuclear technologies, researchers must continue to improve the transparency, robustness, and accountability of AI models, rather than confining themselves to accuracy-only measurements.

5. Future directions

5.1. AI in scientific computing

To effectively address the problem of the dependence of AI algorithms on a large amount of labeled training data in engineering practice, a novel field known as scientific machine learning (SciML) is evolving rapidly. SciML aims to use physical principles as prior knowledge in order to deeply integrate with ML models so as to improve the accuracy, representation ability, and robustness of the models in specific scientific problems [[140], [141], [142]].

Chen and Zhang [143] suggested that existing SciML methods can be roughly classified into two categories in terms of the research purpose: knowledge embedding and knowledge discovery.

5.1.1. Knowledge embedding

The objective of knowledge embedding is to fully exploit the physical mechanism and project it from the symbolic semantic space to the vector feature space of the data-driven model to further improve the performance of the model and reduce the high demand for data. In fact, the concept of knowledge embedding has the potential to optimize the entire life cycle modeling process of ML, including data preprocessing, model structure design, model parameter optimization, model convergence, and model performance evaluation.

The present mainstream research is relatively focused on using prior physical knowledge to constrain the model convergence mechanism, especially the loss function. Daw and Karpatne [144] proposed physical-guided neural networks (PgNNs), which constrain the convergence direction of the model by introducing the difference between the model prediction result and the physical mechanism into the loss function. Raissi and Perdikaris [145] proposed physics-informed neural networks (PINNs), which add partial differential governing equations, initial conditions, and boundary conditions as soft constraints into the loss function. PINN has been validated as an excellent meshless method for data-driven solutions of partial differential equations (PDE), and it can also be used to solve some inverse problems such as the parameter determination of equations. Additional models such as theory-guided neural networks (TgNNs) [146] and theory-guided hard constraint projection (HCP) [147] have been proposed to achieve the optimization of PINN-like methods in practical applications. Furthermore, Willard and Jia [141] emphasized the importance of the ML-enhanced physical models, which carry out mechanistic computing and ML computing simultaneously, such as residual modeling [148].

In nuclear engineering and related fields, knowledge embedding methods have been gradually assimilated into the novel paradigm of ML. Jin and Cai [149] established the PINN models of the Navier–Stokes equations in the form of velocity–pressure and velocity–vorticity, and subsequently employed them to solve laminar flow and channel turbulence problems. Wang and Huang [150] used the PINN method to quantify and reconstruct the natural convection flow field on the basis of temperature and velocity measurements. Mishra and Molinaro [151] employed PINNs to obtain approximating solutions of forward and inverse problems for radiative transfer. Zhao and Shirvan [152] proposed an architecture called the physics-informed machine learning-aided framework (PIMLAF) for CHF prediction based on residual modeling methodology; they considered the residual by subtracting the experimental results and mechanistic model results as the target of the ML prediction model. It has been verified that PIMLAF has higher accuracy than the original mechanistic model and a stronger generalization ability than the independent ML model under various flow conditions with high flexibility and simplicity and wide applicability. Presently, the development of the knowledge embedding domain is in a vigorous early stage. How to better integrate prior knowledge and data-driven models while ensuring accuracy and efficiency involves many uncertainties, which can provide many opportunities and challenges for researchers.

5.1.2. Knowledge discovery

Knowledge discovery refers to the complete discovery of the laws governing physical and chemical phenomena from data. Specifically, the input consists of various observation data, and the output often consists of the governing equations dominated by PDEs. Compared with knowledge embedding, which aims to enhance the model performance, knowledge discovery focuses on seeking explicit knowledge as an explanation for ML models. Xu and Zhang [153] designed an architecture that combines neural networks and GA to mine PDE governing equations from sparse noisy data, and proved its effectiveness and robustness in applications such as the Burgers equation. Lejarza and Baldea [154] proposed an ML-based architecture via moving horizon nonlinear optimization, which can extract the underlying governing equations of dynamical systems from noisy datasets. While key governing equations such as the neutron transport equation are well established for nuclear reactor science, domains such as radiation-material interactions remain problematic. Hence, they have the potential for the application of knowledge discovery approaches in the future. However, the field of knowledge discovery presently involves several problems, such as over-fitting of the resulting PDE, insufficient robustness of the method, and difficulty in ensuring the balance between the accuracy and the simplicity of the equations [143].

5.2. From XAI to causal learning

Many researchers have recently devoted themselves to exploring and seeking effective methods for elucidating the logic underlying the AI model, and they have developed a novel academic domain known as explainable artificial intelligence (XAI). XAI research is committed to promoting the construction of more transparent and reliable AI systems so that humans can not only acquire decision support from AI but also understand how AI systems make decisions. XAI methodologies can be categorized along multiple dimensions. The existing literature generally classifies the XAI taxonomy as follows [[155], [156], [157]]:

  • Stage: ante-hoc [158,159] and post-hoc, where post-hoc methods are further classified into model-agnostic and model-specific.

  • Scope: local [160,161] and global [162,163].

  • Output format: numeric [164], visualization [165], etc.

Note that a particular method often has multiple properties, such as the well-known local interpretable model-agnostic explanations (LIME) [166] and Shapley additive explanations (SHAP) [167], which are both global and local in terms of the scope of explainability. In the field of nuclear engineering, few researchers have shown sufficient interest in XAI. For example, Ayodeji and Amidu [52] adopted LIME and SHAP to calculate the importance of the input features in predicting the turbulent eddy viscosity in RANS simulations and their influence on the results. At present, the XAI methodology is yet to be widely embraced by nuclear engineering researchers, which would provide additional opportunities for the fusion of nuclear engineering and AI and introduce additional XAI methodologies to explore more robust, transparent, and accountable data-driven models for nuclear reactors.

By contrast, the existing XAI methodology with post-hoc methods as the mainstream standard cannot address the out-of-distribution generalization (OODG) problem, i.e., there are spurious correlations in the training set or unexpected changes in the model deployment environment. In other words, XAI methods can help determine whether the original model is reliable to some extent; however, they cannot make the original model reliable. A key reason for this generalization problem is that most existing AI algorithms are driven by association, and these models usually only know the “how” (i.e., “correlation”) but do not know the “why” (i.e., “causality”). Hence, to extend the idea of causal inference to the field of ML, removing false associations and using causal associations to guide model learning are critical fundamental ways to improve the stability of models in unknown environments.

Some reviews have pointed out that causal learning can provide effective theoretical support for ML in the estimation of feature importance and the measurement of model fairness. However, for transferability and robustness, most existing causal inference methods require further improvement. For ML, especially DL, the main difficulty of this task lies in the high-dimensional complexity caused by the high coupling of the explicit features of the data, making it difficult to extract effective causal variables [[168], [169], [170], [171], [172]]. In the future, the fusion of AI and nuclear reactor technologies is anticipated, where essential issues will be addressed, such as bridging the gap between causal learning and ML, developing consensus to match more complex real-world scenarios, and making AI models more reliable without compromising their predictive capabilities.

6. Conclusion

Existing studies on the application of AI to nuclear reactor design optimization and O&M were reviewed. Most of these studies have achieved excellent results on limited datasets. However, to further promote AI technologies so that they can be scaled to real-world nuclear reactor problems, such as improving the safety, future industrial-grade AI models must have stronger interpretability and generalization capabilities. Therefore, the mechanism–data dual paradigm should be widely employed, as many studies have proved that it can address the high data demand of AI models in scientific computing problems. Moreover, XAI and causal learning warrant further exploration owing to their potential to uncover the black box.

Author contribution statement

All authors listed have significantly contributed to the development and the writing of this article.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

No data was used for the research described in the article.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Contributor Information

Qingyu Huang, Email: huangqingyu_npic@126.com.

Jian Deng, Email: dengjian_npic@163.com.

Abbreviation

AI

artificial intelligence

AAKR

auto-associative kernel regression

AANN

auto-associative neural network

ANFIS

adaptive neuro-fuzzy inference system

ANN

artificial neural network

BPNN

back-propagation neural network

BWR

boiling water reactor

CART

classification and regression tree

CEDM

control element drive mechanism

CFD

computational fluid dynamics

CHF

critical heat flux

CNN

convolutional neural network

CRNN

convolutional recurrent neural network

DI

data interaction

DL

deep learning

DNN

deep neural network

DOM

discrete ordinate method

EA

evolutionary algorithm

EOS-ELM

ensemble of online sequential extreme learning machines

FD

fault diagnosis

FVM

finite volume method

GA

genetic algorithm

GMDH

group method of data handling

HANN

Hopfield artificial neural network

HCP

theory-guided hard constraint projection

IGBT

insulated-gate bipolar transistor

KNN

k-nearest neighbors

KPCA

kernel principal component analysis

LIME

local interpretable model-agnostic explanations

LM

Levenberg–Marquardt

LOCA

loss-of-coolant accident

MARS

multivariate adaptive regression splines

MCM

Monte Carlo method

ML

machine learning

NPP

nuclear power plant

OLM

online condition monitoring

O&M

operation & maintenance

OODG

out-of-distribution generalization

PCA

principal component analysis

PDE

partial differential equation

PgNN

physics-guided neural network

PHM

prognostics and health management

PIMLAF

physics-informed machine learning-aided framework

PINN

physics-informed neural network

PSO

particle swarm optimization

RANS

Reynolds-averaged Navier–Stokes

RBFNN

radial basis function neural network

RCP

reactor coolant pump

RF

random forest

RL

reinforcement learning

ROM

reduced order model

RUL

residual useful life

SciML

scientific machine learning

SGTR

steam generator tube rupture

SHAP

Shapley additive explanations

SVM

support vector machine

TCN

temporal convolution network

TgNN

theory-guided neural network

UTSG

U-tube steam generator

XAI

explainable artificial intelligence

XGB/XGBoosting

extreme gradient boosting

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