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Citation: Qi, B.; Liang, J.; Tong, J.
Fault Diagnosis Techniques for
Nuclear Power Plants: A Review
from the Artificial Intelligence
Perspective. Energies 2023,16, 1850.
https://doi.org/10.3390/en16041850
Academic Editor: Dino Musmarra
Received: 2 January 2023
Revised: 20 January 2023
Accepted: 10 February 2023
Published: 13 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Review
Fault Diagnosis Techniques for Nuclear Power Plants: A
Review from the Artificial Intelligence Perspective
Ben Qi , Jingang Liang * and Jiejuan Tong
Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
*Correspondence: jingang@tsinghua.edu.cn
Abstract:
Fault diagnosis plays an important role in complex and safety-critical systems such as
nuclear power plants (NPPs). With the development of artificial intelligence (AI), extensive research
has been carried out for fast and efficient fault diagnosis based on intelligent methods. This paper
presents a review of various AI-based system-level fault diagnosis methods for NPPs. We first discuss
the development history of AI. Based on this exposition, AI-based fault diagnosis techniques are
classified into knowledge-driven and data-driven approaches. For knowledge-driven methods, we
discuss both the early if–then-based fault diagnosis techniques and the current new theory-based ones.
The principles, application, and comparative analysis of the representative methods are systematically
described. For data-driven strategies, we discuss single-algorithm-based techniques such as ANN,
SVM, PCA, DT, and clustering, as well as hybrid techniques that combine algorithms together. The
advantages and disadvantages of both knowledge-driven and data-driven methods are compared,
illustrating the tendency to combine the two approaches. Finally, we provide some possible future
research directions and suggestions.
Keywords: fault diagnosis; artificial intelligence; knowledge-driven; data-driven; nuclear power plants
1. Introduction
Advances in technology have increased the level of automation in industry, but they
have made systems increasingly complex, placing higher demands on system safety and
reliability. One way to improve system safety and reliability is to improve the quality, relia-
bility, and robustness of system components, but this still cannot eliminate the occurrence
of faults [
1
,
2
]. Therefore, fault diagnosis has become an important technique to ensure the
safety and reliability of industrial systems. For complex nuclear power plant systems, fault
diagnosis techniques are designed to monitor whether the system and its components are
functioning properly, detect the type of fault at an early stage, and determine the location
and severity of the fault to avoid further damage [3].
Fault diagnosis includes fault monitoring, fault location, and fault analysis [
4
,
5
]. Fault
monitoring determines whether there is a fault in the system and components. Fault
location determines the location of the fault. Fault analysis performs the function of deter-
mining the type, severity, and cause of the fault. Traditional fault diagnosis techniques are
generally divided into hardware-redundancy-based, model-based, and signal-processing-
based methods [
6
–
8
]. The hardware-redundancy-based method is to use a redundant
component design idea to detect component faults when the component outputs are dif-
ferent from those of the redundant components [
9
–
12
]. The model-based method requires
a more accurate mathematical model of the system, similar to the concept of hardware
redundancy, which is diagnosed by comparing the output of the mathematical model with
that of the actual system [
13
–
16
]. The signal-processing-based method requires mathe-
matical or statistical processing of the measured data to extract information related to the
fault [17–20].
Energies 2023,16, 1850. https://doi.org/10.3390/en16041850 https://www.mdpi.com/journal/energies
Energies 2023,16, 1850 2 of 27
More than two-thirds of the nuclear reactors in service by the end of 2021 worldwide
were pressurized water reactors (PWRs), and the typical pressurized water reactor system
composition is shown in Figure 1. PWR nuclear power plants use light water as a coolant
and moderator [
21
], which mainly consists of a nuclear steam supply system [
21
,
22
], a
turbine generator system [
23
], and other auxiliary systems [
24
]. After the coolant absorbs
the heat energy released from nuclear fuel fission, the heat is then transferred through the
steam generator to the second circuit to generate steam, which then enters the turbine to
do work and generate electricity [
25
]. Nuclear power plant systems contain hundreds of
subsystems with potential radiological hazards. If a fault occurs during operation, the
operator is required to accurately determine the fault type. Therefore, fault diagnosis is an
important support technology to assist operators in making fault identification. Traditional
fault diagnosis techniques for nuclear power plants rely mainly on expert experience,
which is somewhat uncertain and subjective. With the advancement of instrumentation
and control systems, nuclear power plants generate a large amount of data. Artificial
intelligence can process the large amount of data, and the research on fault diagnosis
technology based on AI is increasing.
Energies 2023, 16, x FOR PEER REVIEW 2 of 28
requires mathematical or statistical processing of the measured data to extract information
related to the fault [17–20].
More than two-thirds of the nuclear reactors in service by the end of 2021 worldwide
were pressurized water reactors (PWRs), and the typical pressurized water reactor system
composition is shown in Figure 1. PWR nuclear power plants use light water as a coolant
and moderator [21], which mainly consists of a nuclear steam supply system [21,22], a
turbine generator system [23], and other auxiliary systems [24]. After the coolant absorbs
the heat energy released from nuclear fuel fission, the heat is then transferred through the
steam generator to the second circuit to generate steam, which then enters the turbine to
do work and generate electricity [25]. Nuclear power plant systems contain hundreds of
subsystems with potential radiological hazards. If a fault occurs during operation, the op-
erator is required to accurately determine the fault type. Therefore, fault diagnosis is an
important support technology to assist operators in making fault identification. Tradi-
tional fault diagnosis techniques for nuclear power plants rely mainly on expert experi-
ence, which is somewhat uncertain and subjective. With the advancement of instrumen-
tation and control systems, nuclear power plants generate a large amount of data. Artifi-
cial intelligence can process the large amount of data, and the research on fault diagnosis
technology based on AI is increasing.
Figure 1. Main structure of the pressurized water reactor [26].
System-level faults are one of the major causes of accidents in nuclear power plants.
In the event of a fault, trained operators are faced with hundreds of subsystems and a
large number of monitoring and control parameters, and the immense psychological
stress can easily lead them to misjudgments, which can lead to serious radiological con-
sequences. With the rise of AI, numerous studies on fault diagnosis based on AI have
emerged. AI is a technology that resembles human intelligence through some pro-
grammed language of computers. AI has shown great advantages in some aspects. First,
AI can process huge sources of information in a short period, helping operators extract
critical information quickly after a fault occurs. Second, AI can also eliminate human error.
Even the best experts in the nuclear field have the potential to make mistakes, while AI
systems built on specific tasks do not suffer from such errors. Third, AI can work contin-
uously, and continuous condition monitoring is essential for nuclear power plants. AI
Figure 1. Main structure of the pressurized water reactor [26].
System-level faults are one of the major causes of accidents in nuclear power plants.
In the event of a fault, trained operators are faced with hundreds of subsystems and a large
number of monitoring and control parameters, and the immense psychological stress can
easily lead them to misjudgments, which can lead to serious radiological consequences.
With the rise of AI, numerous studies on fault diagnosis based on AI have emerged. AI
is a technology that resembles human intelligence through some programmed language
of computers. AI has shown great advantages in some aspects. First, AI can process huge
sources of information in a short period, helping operators extract critical information
quickly after a fault occurs. Second, AI can also eliminate human error. Even the best
experts in the nuclear field have the potential to make mistakes, while AI systems built
on specific tasks do not suffer from such errors. Third, AI can work continuously, and
continuous condition monitoring is essential for nuclear power plants. AI does not always
work, e.g., some AI technologies that rely on training are unreliable if they encounter
situations other than training.
Energies 2023,16, 1850 3 of 27
With the development of AI technology, more and more scholars have focused on the
application of AI in nuclear power plant fault diagnosis [
3
,
27
–
29
]. However, there is no
systematic compendium of AI-based fault diagnosis methods for nuclear power plants.
This paper aims to comprehensively review the progress of fault diagnosis techniques
from an AI perspective and establish a new framework for fault diagnosis classification.
Fault diagnosis technology is divided into two types: knowledge-driven and data-driven.
The existing research is described and analyzed in detail under this framework. One of
the purposes of this paper is to introduce existing nuclear power plant fault diagnosis
problems to the research group of AI and to introduce AI concepts and techniques to the
nuclear power industry, to make the combination of AI and fault diagnosis better. This
paper also tries to identify the problems to be solved and the direction of future research.
Note that this paper will not discuss all the techniques in the field of fault diagnoses, such
as traditional signal-processing-based fault diagnosis techniques and component-level fault
diagnosis. The reader may refer to [
16
,
30
] for more information on the history and methods
of diagnosis techniques.
This paper is organized as follows: Section 2is a fault diagnosis classification frame-
work from the AI perspective. Section 3introduces knowledge-driven fault diagnosis
techniques and representative methods. Section 4introduces data-driven fault diagno-
sis techniques and representative methods. Section 5is the comparative analysis of the
two methods. Section 6provides the conclusions of this paper and the directions for
future research.
2. Fault Diagnosis Classification from the AI Perspective
It is important to identify the history of AI development, which helps to establish a
framework for AI-based fault diagnosis technology for nuclear power plants.
2.1. Development History of AI
Artificial intelligence (AI) was born in 1956, and there are two competing lines of devel-
opment, namely, symbolism and connectionism [
31
]. As shown in Figure 2, connectionism,
also known as data-driven methods, predates symbolism and originates in early computers
and cybernetics [
32
]. The concept of neural networks was introduced by neuroscientist
Warren McCulloch and logician Walter Pitts in 1943 [
33
]. The development trend in Figure 2
shows the dominance of connectionism in the early stages, and connectionism saw a major
development in the late 1950s [
34
]. Frank Rosenblatt, inspired by the work of many parties,
proposed a true connectionism system [
35
]. In the 1960s and 1970s, a variety of connec-
tionist techniques were developed [
36
–
38
], such as statistical learning techniques based on
decision theory [
38
] and reinforcement learning techniques [
39
], with representative works
such as Samuel’s checkers program [40] and Nilsson’s “learning machines” [41].
In the late 1970s, limited by the computing power of the time, the development
of connectionism reached a low point, and the school of symbolism gradually emerged.
Symbolism, also known as knowledge-driven methods, was defined as artificial intelligence
at the Dartmouth Conference in 1956, and connectionism in cybernetics was introduced into
AI years later [
42
]. Symbolism dominated the field of AI from the 1960s to the early 1990s.
At the request of National Aeronautics and Space Administration (NASA) in 1965, Stanford
University successfully developed the Dendritic Algorithm (DENRAL) expert system,
which has a very rich knowledge of chemistry and can help chemists infer molecular
structures from mass spectrometry data. The completion of this system marked the birth of
expert systems [
43
]. By the mid-1970s, expert systems had gradually matured, the most
representative of which was the Daptomycin (MYCIN) system by Sholtev et al., which was
used to diagnose and treat bloodstream infections and encephalitis infections and could
provide prescription recommendations [
44
]. Another highly successful expert system is
the Prosecutor (PROSPECTOR) system, which was used to assist geologists in detecting
mineral deposits and was the first to achieve significant economic benefits [
45
]. After
the mid-1980s, expert systems have been widely put into commercial operation. One
Energies 2023,16, 1850 4 of 27
famous example is the eXpert CONfigurer (XCON)/R1 expert system developed by the
Department of Environmental Conservation (DEC) in collaboration with Carnegie Mellon
University, which saves millions of dollars per year [
46
]. Subsequently, symbolism went
downhill due to its complex construction process and limited performance [
47
]. Since the
1990s, there has been a strong tendency for connectionism to replace symbolism due to
improved algorithms, increased computing power, and improved data resources [
48
–
50
].
Geoffrey Hinton, the father of neural networks, and his student Ruslan proposed a solution
to the problem of gradient disappearance in deep network training, starting the wave
of deep learning in industry and academia [
51
]. However, in 2012, Google launched the
Knowledge Graph project, which is essentially an improvement on the semantic web of
the 1960s symbolism school and to some extent represents progress in the development of
symbolism [52].
Energies 2023, 16, x FOR PEER REVIEW 4 of 28
Figure 2. History of AI, two lines of development, and the dominant situation in each period.
In the late 1970s, limited by the computing power of the time, the development of
connectionism reached a low point, and the school of symbolism gradually emerged.
Symbolism, also known as knowledge-driven methods, was defined as artificial intelli-
gence at the Dartmouth Conference in 1956, and connectionism in cybernetics was intro-
duced into AI years later [42]. Symbolism dominated the field of AI from the 1960s to the
early 1990s. At the request of National Aeronautics and Space Administration (NASA) in
1965, Stanford University successfully developed the Dendritic Algorithm (DENRAL) ex-
pert system, which has a very rich knowledge of chemistry and can help chemists infer
molecular structures from mass spectrometry data. The completion of this system marked
the birth of expert systems [43]. By the mid-1970s, expert systems had gradually matured,
the most representative of which was the Daptomycin (MYCIN) system by Sholtev et al.,
which was used to diagnose and treat bloodstream infections and encephalitis infections
and could provide prescription recommendations [44]. Another highly successful expert
system is the Prosecutor (PROSPECTOR) system, which was used to assist geologists in
detecting mineral deposits and was the first to achieve significant economic benefits [45].
After the mid-1980s, expert systems have been widely put into commercial operation. One
famous example is the eXpert CONfigurer (XCON)/R1 expert system developed by the
Department of Environmental Conservation (DEC) in collaboration with Carnegie Mellon
University, which saves millions of dollars per year [46]. Subsequently, symbolism went
downhill due to its complex construction process and limited performance [47]. Since the
1990s, there has been a strong tendency for connectionism to replace symbolism due to
improved algorithms, increased computing power, and improved data resources [48–50].
Geoffrey Hinton, the father of neural networks, and his student Ruslan proposed a solu-
tion to the problem of gradient disappearance in deep network training, starting the wave
of deep learning in industry and academia [51]. However, in 2012, Google launched the
Knowledge Graph project, which is essentially an improvement on the semantic web of
the 1960s symbolism school and to some extent represents progress in the development
of symbolism [52].
In conclusion, connectionism is dominant in the current development process of AI
while symbolism is in a slow development stage. However, both AI routes have their one-
sidedness. Connectionism lacks robustness and interpretability, while symbolism lacks
data mining and relies excessively on expert subjective opinions and complex
Figure 2. History of AI, two lines of development, and the dominant situation in each period.
In conclusion, connectionism is dominant in the current development process of AI
while symbolism is in a slow development stage. However, both AI routes have their
one-sidedness. Connectionism lacks robustness and interpretability, while symbolism lacks
data mining and relies excessively on expert subjective opinions and complex combinatorial
rules. Therefore, the two schools have a strong complementarity, and the integration of the
two schools will certainly become a major trend in the future development of AI. For the
convenience of description, this paper refers to symbolism as the first-generation AI and
connectionism as the second-generation AI.
2.2. AI-Based Fault Diagnosis Classification
Since the 1980s, AI-based fault diagnosis techniques have been applied in nuclear
power plants [
53
], and subsequent developments have been closely linked to AI techniques.
The nuclear accident diagnosis expert system [
54
] is a typical representative of the first-
generation AI-based techniques, which consists of a fault diagnosis knowledge base, a
comprehensive knowledge base, and a fault diagnosis inference machine. The system
obtains fault types by importing the monitored physical symptoms into the inference
Energies 2023,16, 1850 5 of 27
machine and interacting with the diagnostic knowledge base. Early expert systems were
mainly based on simple if–then rules in the computer domain [
55
], and new theories
such as signed directed graphs (SDGs) [
56
], Bayesian networks (BNs) [
57
], and dynamic
uncertain causality graphs (DUCGs) [
58
] were gradually introduced subsequently. Neural-
network-based fault diagnosis technology is a typical application of second-generation AI,
which uses historical data to train neural networks to obtain a diagnostic model capable
of identifying faults [
59
]. In addition, scholars have conducted in-depth research on the
applications of single and hybrid algorithms. Scholars applied a single algorithm including
artificial neural networks, principal component analysis, support vector machine, decision
tree, and unsupervised clustering to fault diagnosis and preliminarily verified the feasibility
of these methods [
60
–
64
]. Subsequently, hybrid algorithms such as fuzzy logic–neural
network, laminar model–neural network, principal component analysis–neural network,
laminar model–support vector machine, and principal component analysis–convolution
neural network are proposed, and these hybrid algorithms have been proven to have better
diagnostic performances than single algorithms [65–73].
VOSviewer 1.6.17 is a software tool for constructing and visualizing bibliometric
networks. In this paper, we use VOSviewer software to conduct statistical and cluster
analyses of the literature to obtain the hot topics and frontier trends in the field of “nuclear
power plant fault diagnosis”. A subject search was conducted by the keyword “fault
diagnosis”, and the research direction was set to “nuclear science technology” based on
all the databases subscribed to the Web of Science. The clustering view shown in Figure 3
was obtained by performing text analysis on 647 relevant papers. The brighter the node
color in the graph, the more relevant papers are. Being closer to the center indicates that
the research object receives more attention. The fault diagnosis methods related to AI can
be divided into part A and part B as shown in Figure 3. In part A, “knowledge base”,
“expert system”, “fuzzy logic”, and “fuzzy logic” can be seen, and they belong to the
first generation of AI technology. Part A is located at the edge of the clustering diagram,
which indicates that the current attention to the application of the first generation of AI
technology is not high. In part B, “artificial neural network” and “training” can be seen,
and they belong to the second generation of AI technology. It can be seen that part B has
brighter color and higher centrality, which indicates that the fault diagnosis method based
on second-generation AI is the current research hot spot.
Energies 2023, 16, x FOR PEER REVIEW 6 of 28
Figure 3. Cluster diagram for fault diagnosis of nuclear power plants.
As shown in Figure 4, this paper establishes a new fault diagnosis classification
framework from the AI perspective, that is, knowledge-driven and data-driven fault di-
agnosis methods. Knowledge-driven methods correspond to first-generation AI technol-
ogy, and data-driven methods correspond to second-generation AI technology. Then, the
development of the two methods is systematically combed to help readers understand the
progress of fault diagnosis technology from the AI perspective.
Figure 4. Fault diagnosis classification framework.
3. Knowledge-Driven Fault Diagnosis Methods
Knowledge-driven fault diagnosis methods for nuclear power plants, also known as
expert systems, can be regarded as a combination of the knowledge base and the inference
machine. They mainly use the experience accumulated by domain experts in long-term
practice. As shown in Figure 5, the knowledge-driven fault diagnosis methods can be di-
vided into two types, the early if–then (Section 3.1) and the current new theories (Section
3.2). These new theories include signed directed graphs, Bayesian networks and dynamic
uncertain causality graphs, etc. The inference mechanism is the main difference between
them. Finally, we summarize the characteristics of these knowledge-driven methods (Sec-
tion 3.3).
Figure 3. Cluster diagram for fault diagnosis of nuclear power plants.
Energies 2023,16, 1850 6 of 27
As shown in Figure 4, this paper establishes a new fault diagnosis classification frame-
work from the AI perspective, that is, knowledge-driven and data-driven fault diagnosis
methods. Knowledge-driven methods correspond to first-generation AI technology, and
data-driven methods correspond to second-generation AI technology. Then, the develop-
ment of the two methods is systematically combed to help readers understand the progress
of fault diagnosis technology from the AI perspective.
Energies 2023, 16, x FOR PEER REVIEW 6 of 28
Figure 3. Cluster diagram for fault diagnosis of nuclear power plants.
As shown in Figure 4, this paper establishes a new fault diagnosis classification
framework from the AI perspective, that is, knowledge-driven and data-driven fault di-
agnosis methods. Knowledge-driven methods correspond to first-generation AI technol-
ogy, and data-driven methods correspond to second-generation AI technology. Then, the
development of the two methods is systematically combed to help readers understand the
progress of fault diagnosis technology from the AI perspective.
Figure 4. Fault diagnosis classification framework.
3. Knowledge-Driven Fault Diagnosis Methods
Knowledge-driven fault diagnosis methods for nuclear power plants, also known as
expert systems, can be regarded as a combination of the knowledge base and the inference
machine. They mainly use the experience accumulated by domain experts in long-term
practice. As shown in Figure 5, the knowledge-driven fault diagnosis methods can be di-
vided into two types, the early if–then (Section 3.1) and the current new theories (Section
3.2). These new theories include signed directed graphs, Bayesian networks and dynamic
uncertain causality graphs, etc. The inference mechanism is the main difference between
them. Finally, we summarize the characteristics of these knowledge-driven methods (Sec-
tion 3.3).
Figure 4. Fault diagnosis classification framework.
3. Knowledge-Driven Fault Diagnosis Methods
Knowledge-driven fault diagnosis methods for nuclear power plants, also known
as expert systems, can be regarded as a combination of the knowledge base and the
inference machine. They mainly use the experience accumulated by domain experts in
long-term practice. As shown in Figure 5, the knowledge-driven fault diagnosis methods
can be divided into two types, the early if–then (Section 3.1) and the current new theories
(Section 3.2). These new theories include signed directed graphs, Bayesian networks and
dynamic uncertain causality graphs, etc. The inference mechanism is the main difference
between them. Finally, we summarize the characteristics of these knowledge-driven
methods (Section 3.3).
Energies 2023, 16, x FOR PEER REVIEW 7 of 28
Figure 5. History of knowledge-driven fault diagnosis methods and their application in the nuclear
field.
3.1. Fault Diagnosis Methods Based on If–Then
The fault diagnosis technology based on if–then rules mainly includes the establish-
ment of the knowledge base and the inference engine. William et al. built a fault diagnosis
expert system by taking four types of typical accidents (LOFW, SGTR, LOCA, and MSLB)
in nuclear power plants as the diagnosis objects [55]. They first established nine if–then
rules (Table 1) based on domain knowledge and then constructed an expert system based
on these rules. As shown in Figure 6, the system infers from known facts until the type of
accident is obtained. If there is not enough information to conclude, the system infers
backward to determine what information it needs to know. The system will then query
the nuclear plant instrumentation or use the operator to fill in the knowledge gaps. Berg-
man et al. first used expert systems to diagnose faults in boiling water reactors [74]. Since
expert knowledge has uncertainty, some scholars have introduced the concept of fuzzy
membership in the representation of expert knowledge and used fuzzy logic for inference
as a way to deal with the uncertainty of expert knowledge [75,76]. Suon et al. developed
a fuzzy expert system for the early detection of steam leakage faults in nuclear power
plants [77]. Fuzzy theory is good at describing the uncertainty caused by imprecision,
while evidence theory can describe the uncertainty caused by ignorance. Yang et al. pro-
posed an expert system based on a confidence rule base based on fuzzy theory, evidence
theory, and decision theory [78,79]. The confidence rule base adds the concept of confi-
dence to the if–then rule, which can represent the complex causal relationship between
various types of data with uncertainty. The above shows that the early expert systems in
the nuclear field focused on the application and improvement under if–then rules.
Table 1. If–then rules.
Rule Num-
ber If Then
1 (PCS pressure decreasing)
(HPIS on) PCS integrity challenged
2 PCS temperature increasing
PCS–SCS heat transfer inade-
quate
3 PCS temperature increasing SG inventory inadequate
4 (High containment radiation)
(High containment pressure)
Containment integrity chal-
lenged
5 (PCS–SCS heat transfer inadequate) Accident is LOFW
Figure 5.
History of knowledge-driven fault diagnosis methods and their application in the
nuclear field.
3.1. Fault Diagnosis Methods Based on If–Then
The fault diagnosis technology based on if–then rules mainly includes the establish-
ment of the knowledge base and the inference engine. William et al. built a fault diagnosis
expert system by taking four types of typical accidents (LOFW, SGTR, LOCA, and MSLB) in
nuclear power plants as the diagnosis objects [
55
]. They first established nine if–then rules
(Table 1) based on domain knowledge and then constructed an expert system based on these
rules. As shown in Figure 6, the system infers from known facts until the type of accident
Energies 2023,16, 1850 7 of 27
is obtained. If there is not enough information to conclude, the system infers backward to
determine what information it needs to know. The system will then query the nuclear plant
instrumentation or use the operator to fill in the knowledge gaps.
Bergman et al
. first used
expert systems to diagnose faults in boiling water reactors [
74
]. Since expert knowledge
has uncertainty, some scholars have introduced the concept of fuzzy membership in the
representation of expert knowledge and used fuzzy logic for inference as a way to deal
with the uncertainty of expert knowledge [
75
,
76
]. Sutton et al. developed a fuzzy expert
system for the early detection of steam leakage faults in nuclear power plants [
77
]. Fuzzy
theory is good at describing the uncertainty caused by imprecision, while evidence theory
can describe the uncertainty caused by ignorance. Yang et al. proposed an expert system
based on a confidence rule base based on fuzzy theory, evidence theory, and decision
theory [
78
,
79
]. The confidence rule base adds the concept of confidence to the if–then rule,
which can represent the complex causal relationship between various types of data with
uncertainty. The above shows that the early expert systems in the nuclear field focused on
the application and improvement under if–then rules.
Table 1. If–then rules.
Rule Number If Then
1(PCS pressure decreasing)
(HPIS on) PCS integrity challenged
2 PCS temperature increasing PCS–SCS heat transfer inadequate
3 PCS temperature increasing SG inventory inadequate
4(High containment radiation)
(High containment pressure) Containment integrity challenged
5(PCS–SCS heat transfer inadequate)
(Low feedwater flow) Accident is LOFW
6(SG inventory inadequate)
(Low feedwater flow) Accident is LOFW
7(PCS integrity challenged)
(Low feedwater flow) Accident is LOCA
8(PCS integrity challenged)
(SG level increasing) Accident is SGTR
9(SG inventory inadequate)
(High steam flow) Accident is MSLB
Abbreviations: PCS: primary coolant system; HPIS: high pressure injection system; SCS: secondary coolant system;
SG: steam generator; LOFW: loss of feedwater; LOCA: loss of coolant accident; SGTR: steam generator tube
rupture; MSLB: main steam line break.
Energies 2023, 16, x FOR PEER REVIEW 8 of 28
(Low feedwater flow)
6 (SG inventory inadequate)
(Low feedwater flow) Accident is LOFW
7 (PCS integrity challenged)
(Low feedwater flow) Accident is LOCA
8 (PCS integrity challenged)
(SG level increasing) Accident is SGTR
9 (SG inventory inadequate)
(High steam flow) Accident is MSLB
Abbreviations: PCS: primary coolant system; HPIS: high pressure injection system; SCS: secondary
coolant system; SG: steam generator; LOFW: loss of feedwater; LOCA: loss of coolant accident;
SGTR: steam generator tube rupture; MSLB: main steam line break.
Figure 6. Schematic diagram of an expert system based on if–then rules [55].
3.2. Fault Diagnosis Methods Based on New Theories
3.2.1. Signed Directed Graphs
Signed directed graphs (SDGs) are also knowledge-driven methods, which do not
require an exact mathematical model. SDGs first originated in the chemical industry and
wer e propos ed by Iri e t al. [80] . SDGs co nsis t of nodes and directed arrows between nodes,
which can effectively represent the relationships between elements within a system. As
shown in Figure 7, the node representation in SDG is flexible. Nodes a, b, and c can rep-
resent not only physical variables, such as pressure and temperature, but also some parts
of the system, such as switches and valves. Nodes R1 and R2 can represent an event, such
as a specific fault cause or adverse consequence [10]. The relationships between nodes in
SDG are expressed qualitatively, and it is not necessary to provide the exact quantitative
relationships between system nodes. Therefore, it is easier to establish the model. For fault
diagnosis of the SDG model, the means of combining reverse inference and forward infer-
ence are generally adopted. Assume that nodes a and b are abnormal and c is normal.
According to the reverse inference, two compatible paths can be obtained: b → a → R1
and b → a → R2. R1 and R2 are the candidate fault sources. Then the forward inference is
verified. If R1 is the fault source, node c should be large or small, but the state of node c is
normal, which is not consistent with the observation. Therefore, the candidate fault source
R1 is a false solution and should be discarded. Similarly, the forward inference for R2 is
verified, and R2 is consistent with the actual observed value when R2 is the fault source,
Figure 6. Schematic diagram of an expert system based on if–then rules [55].
Energies 2023,16, 1850 8 of 27
3.2. Fault Diagnosis Methods Based on New Theories
3.2.1. Signed Directed Graphs
Signed directed graphs (SDGs) are also knowledge-driven methods, which do not
require an exact mathematical model. SDGs first originated in the chemical industry and
were proposed by Iri et al. [
80
]. SDGs consist of nodes and directed arrows between nodes,
which can effectively represent the relationships between elements within a system. As
shown in Figure 7, the node representation in SDG is flexible. Nodes a, b, and c can
represent not only physical variables, such as pressure and temperature, but also some
parts of the system, such as switches and valves. Nodes R1 and R2 can represent an event,
such as a specific fault cause or adverse consequence [
10
]. The relationships between nodes
in SDG are expressed qualitatively, and it is not necessary to provide the exact quantitative
relationships between system nodes. Therefore, it is easier to establish the model. For
fault diagnosis of the SDG model, the means of combining reverse inference and forward
inference are generally adopted. Assume that nodes a and b are abnormal and c is normal.
According to the reverse inference, two compatible paths can be obtained: b
→
a
→
R1
and b
→
a
→
R2. R1 and R2 are the candidate fault sources. Then the forward inference is
verified. If R1 is the fault source, node c should be large or small, but the state of node c is
normal, which is not consistent with the observation. Therefore, the candidate fault source
R1 is a false solution and should be discarded. Similarly, the forward inference for R2 is
verified, and R2 is consistent with the actual observed value when R2 is the fault source,
which means that R2 is a plausible fault source. More detailed information on the signed
directed graph can be found in [81–83].
Energies 2023, 16, x FOR PEER REVIEW 9 of 28
which means that R2 is a plausible fault source. More detailed information on the signed
directed graph can be found in [81–83].
Figure 7. Schematic representation of the structure of a symbolic directed graph. Nodes a and b
are abnormal and c is normal. R1 and R2 are the candidate fault sources.
To improve SDGs’ accuracy and sensitivity, SDGs have been successively combined
with other methods, such as SDGs–expert system [84], SDGs–principal component analy-
sis [85], SDGs–qualitative trend analysis [86], SDGs–hazard and operability [87], SDGs–
fuzzy logic [88,89], and SDGs–Bayesian networks [90].
In the nuclear field, Wu et al. thoroughly studied the application of SDGs methods
for fault diagnosis and successively combined SDGs with fuzzy theory and correlation
analysis for online monitoring and diagnosis of nuclear power plants [91–93]. The fault
diagnosis technology based on SDGs can reveal the fault propagation path and compre-
hensively explain the fault cause, which is its remarkable feature. However, when the sys-
tem is complex, the rule combination explosion problem will appear in accordance with
the directed graph, which is one of the reasons why this method is not widely used at
present.
3.2.2. Bayesian Networks
A Bayesian network is a directed acyclic network, which consists of nodes and di-
rected edges. Nodes include parameter nodes and fault nodes, and the relationship be-
tween nodes is connected by directed edges. The uncertainty of the relationship between
nodes is expressed by a conditional probability table [94]. Figure 8 shows a simple Bayes-
ian network model in which 1
X is the fault nodes and has two states (“0” and “1”), and
25
XX− are parameter nodes, each of which has i, j, k, l states. Assuming that the pa-
rameter nodes have two states, their conditional probability tables are shown in Tables 2
and 3. The directed edges between the nodes indicate the dependencies between the par-
ent and child nodes, such as 1
X with 2
X. More detailed information on Bayesian net-
works can be found in [95,96].
Figure 8. Schematic representation of the structure of a Bayesian network.
Figure 7.
Schematic representation of the structure of a symbolic directed graph. Nodes a and b are
abnormal and c is normal. R1 and R2 are the candidate fault sources.
To improve SDGs’ accuracy and sensitivity, SDGs have been successively combined
with other methods, such as SDGs–expert system [
84
], SDGs–principal component anal-
ysis [
85
], SDGs–qualitative trend analysis [
86
], SDGs–hazard and operability [
87
], SDGs–
fuzzy logic [88,89], and SDGs–Bayesian networks [90].
In the nuclear field, Wu et al. thoroughly studied the application of SDGs methods for
fault diagnosis and successively combined SDGs with fuzzy theory and correlation analysis
for online monitoring and diagnosis of nuclear power plants [
91
–
93
]. The fault diagnosis
technology based on SDGs can reveal the fault propagation path and comprehensively
explain the fault cause, which is its remarkable feature. However, when the system is
complex, the rule combination explosion problem will appear in accordance with the
directed graph, which is one of the reasons why this method is not widely used at present.
3.2.2. Bayesian Networks
A Bayesian network is a directed acyclic network, which consists of nodes and directed
edges. Nodes include parameter nodes and fault nodes, and the relationship between
nodes is connected by directed edges. The uncertainty of the relationship between nodes
Energies 2023,16, 1850 9 of 27
is expressed by a conditional probability table [
94
]. Figure 8shows a simple Bayesian
network model in which
X1
is the fault nodes and has two states (“0” and “1”), and
X2−X5
are parameter nodes, each of which has i,j, k,l states. Assuming that the parameter nodes
have two states, their conditional probability tables are shown in Tables 2and 3. The
directed edges between the nodes indicate the dependencies between the parent and child
nodes, such as
X1
with
X2
. More detailed information on Bayesian networks can be found
in [95,96].
Energies 2023, 16, x FOR PEER REVIEW 9 of 28
which means that R2 is a plausible fault source. More detailed information on the signed
directed graph can be found in [81–83].
Figure 7. Schematic representation of the structure of a symbolic directed graph. Nodes a and b
are abnormal and c is normal. R1 and R2 are the candidate fault sources.
To improve SDGs’ accuracy and sensitivity, SDGs have been successively combined
with other methods, such as SDGs–expert system [84], SDGs–principal component analy-
sis [85], SDGs–qualitative trend analysis [86], SDGs–hazard and operability [87], SDGs–
fuzzy logic [88,89], and SDGs–Bayesian networks [90].
In the nuclear field, Wu et al. thoroughly studied the application of SDGs methods
for fault diagnosis and successively combined SDGs with fuzzy theory and correlation
analysis for online monitoring and diagnosis of nuclear power plants [91–93]. The fault
diagnosis technology based on SDGs can reveal the fault propagation path and compre-
hensively explain the fault cause, which is its remarkable feature. However, when the sys-
tem is complex, the rule combination explosion problem will appear in accordance with
the directed graph, which is one of the reasons why this method is not widely used at
present.
3.2.2. Bayesian Networks
A Bayesian network is a directed acyclic network, which consists of nodes and di-
rected edges. Nodes include parameter nodes and fault nodes, and the relationship be-
tween nodes is connected by directed edges. The uncertainty of the relationship between
nodes is expressed by a conditional probability table [94]. Figure 8 shows a simple Bayes-
ian network model in which 1
X is the fault nodes and has two states (“0” and “1”), and
25
XX− are parameter nodes, each of which has i, j, k , l states. Assuming that the pa-
rameter nodes have two states, their conditional probability tables are shown in Tables 2
and 3. The directed edges between the nodes indicate the dependencies between the par-
ent and child nodes, such as 1
X with 2
X. More detailed information on Bayesian net-
works can be found in [95,96].
Figure 8. Schematic representation of the structure of a Bayesian network.
Figure 8. Schematic representation of the structure of a Bayesian network.
Table 2. CPT of parameters X2, X3, and X4.
P(X1)P(X2|X1)X1=1 X1=0 P(X3|X1)X1=1 X1=0 P(X4|X1)X1=1 X1=0
X1=1 0.5 X2=1 0.90 0.05 X3=1 0.95 0.05 X4=1 0.90 0.05
X1=0 0.5 X2=0 0.10 0.95 X3=0 0.05 0.95 X3=0 0.10 0.95
Table 3. CPT of parameter X5.
P(X5|X3,X4)X3=1 X3=0
X4=1X4=0X4=1X4=0
X5=1 0.90 0.05 0.95 0.10
X5=1 0.10 0.95 0.05 0.90
Assuming that the state information of the parameter node
X5
is currently obtained
as
l1
, the probability that the faulty node
X1
is in state 1 (faulty state) is inferred from
Equation (1).
P(X1=1|X5=l1) = P(X1=1,X5=l1)
P(X5=l1)=∑i,j,k P(X1=1,X2=i,X3=j,X4=k,X5=l1)
P(X5=l1)
=∑i,j,k P(X5=l1|X3=j,X4=k)P(X3=j|X1=1)P(X4=k|X1=1)P(X2=i|X1=1)P(X1=1)
P(X5=l1)
(1)
Bayesian networks were first used to build regulatory systems and have been used in
industrial systems since the 21st century, especially in the area of reliability.
Lerner et al
.
proposed a dynamic Bayesian network (DBN) for tracking and diagnosing complex sys-
tems [
97
]. Przytula et al. proposed an efficient BN generation procedure for diagnosis
and applied it to internal combustion locomotives, satellite communication systems, and
Energies 2023,16, 1850 10 of 27
satellite test equipment [
98
], which can handle continuous variables representing parameter
states and discrete variables representing fault situations. Mahadevan et al. applied the BN
concept to a new method for reassessing the reliability of structural systems [99].
In the nuclear field, Wu proposed a fault diagnosis framework for NPPs with BNs
as the core, which combines PCA, data fusion, and fuzzy theory to achieve an online
diagnosis of NPPs with multi-sensor information [
100
]. Jones et al. proposed a DBN system
for diagnosing the state of nuclear power plants, which can predict the progress of an
accident [
101
]. Oh et al. focused on the diagnostic performance under normal operating
conditions and LOCA system states based on a dynamic Bayesian network and adopted
the step-by-step diagnostic idea for system states and accident types [
102
]. Yi Ren et al.
proposed a method of uncertainty reliability evaluation combining GO-FLOW and dynamic
Bayesian network. This method uses sensitivity analysis to provide input information
that contributes most to uncertainty. The uncertainty is then quantified using the DBN
algorithm and Monte Carlo simulation to appropriately estimate the analysis results [
103
].
Zhao et al. combined Bayesian networks with a probabilistic risk assessment to achieve fast
prediction of accident source terms. They used Bayesian networks for online fault diagnosis
and matched the fault diagnosis results with the accident sequences in probabilistic risk
assessment to obtain the source term release class [
104
–
106
]. Bayesian networks have
advantages over if–then and SDG in accommodating missing information and uncertainty
inference and quantifying diagnostic results.
3.2.3. Dynamic Uncertain Causality Graphs
In the 1990s, Zhang proposed a knowledge expression and inference model based on
probability, the Dynamic Causality Diagram (DCD) [
107
]. Based on the DCD, Zhang further
proposed the dynamic uncertain causality graphs (DUCGs), which added conditional action
events and default events. It expressed the uncertain causality by independent random
events and graphically. When predicting, the qualitative inference results are obtained first,
and then the probability is calculated numerically [
108
]. Compared with BNs, the DUCG
model is greatly simplified by removing unrelated independent events, and inference
becomes very easy when evidence of independent connecting events or action events is
introduced. In addition, DUCG overcomes the shortcomings that the concise expression
of knowledge and inference methods of the BN applicable in the single-assignment case
are not applicable in the multi-assignment case. The reason for describing the state of a
variable is called an assignment. A single-assignment variable means that there is only one
assignment for a variable, and a multiple-assignment variable means that there is more
than one assignment for a variable. For detailed principles of DUCG theory, readers can
refer to [58,109–112].
In the nuclear field, Deng was the first to establish a DUCG model for fault diagnosis
in NPPs and validated the performance of the model with a second-loop feeder pipe
leakage fault [
113
]. Zhang et al. proposed a DUCG method with fault diagnosis and fault
process deduction [
114
]. Zhao et al. proposed a DUCG diagnosis system for CPR1000
reactor type and compared the method with other diagnosis methods, which promoted
the development of an intelligent diagnosis system for the CPR1000 [
115
–
118
]. Dong et al.
studied the new inference algorithm and industrial fault diagnostic system for nuclear
power plants [119,120].
According to our literature study, the application of DUCG in the nuclear field is
still in its infancy. There is a lack of specialized books on this theory, which hinders
the promotion of DUCG technology to a certain extent. However, DUCG-based medical
diagnosis technology is developing more rapidly, and Zhang’s team is also conducting
related research and promotion [121–126].
3.3. Summary of Knowledge-Driven Fault Diagnosis Methods
This section focuses on knowledge-driven fault diagnosis methods for NPPs and
classifies the existing methods into two types: if–then rule (Section 4.1) and new theories
Energies 2023,16, 1850 11 of 27
(Section 4.2). Expert systems (if–then), signed directed graphs, Bayesian networks, and dy-
namic uncertainty causal graphs are introduced in detail. The development characteristics
of these four methods are shown in Figure 9. The earliest expert systems are based on if–
then rules and rely on the rules stored in the expert knowledge base. The symbolic-directed
graph method incorporates qualitative knowledge representation between nodes, which
greatly improves the inference ability. The Bayesian network introduces uncertain inference
technology, which can accommodate information loss and improve system robustness.
Dynamic uncertainty causal graphs develop multi-assignment inference techniques based
on Bayesian networks, which possess higher inference efficiency. These knowledge-driven
methods share common drawbacks. They all need to establish a complete knowledge base
first. Therefore, it is necessary to improve the efficiency of knowledge acquisition and the
completeness of the knowledge base. In addition, the complex cause–effect relationships
within nuclear power plants make the knowledge base complex and large, which requires
improved reasoning efficiency.
Energies 2023, 16, x FOR PEER REVIEW 11 of 28
obtained first, and then the probability is calculated numerically [108]. Compared with
BNs, the DUCG model is greatly simplified by removing unrelated independent events,
and inference becomes very easy when evidence of independent connecting events or ac-
tion events is introduced. In addition, DUCG overcomes the shortcomings that the concise
expression of knowledge and inference methods of the BN applicable in the single-assign-
ment case are not applicable in the multi-assignment case. The reason for describing the
state of a variable is called an assignment. A single-assignment variable means that there
is only one assignment for a variable, and a multiple-assignment variable means that there
is more than one assignment for a variable. For detailed principles of DUCG theory, read-
ers can refer to [58,109–112].
In the nuclear field, Deng was the first to establish a DUCG model for fault diagnosis
in NPPs and validated the performance of the model with a second-loop feeder pipe leak-
age fault [113]. Zhang et al. proposed a DUCG method with fault diagnosis and fault pro-
cess deduction [114]. Zhao et al. proposed a DUCG diagnosis system for CPR1000 reactor
type and compared the method with other diagnosis methods, which promoted the de-
velopment of an intelligent diagnosis system for the CPR1000 [115–118]. Dong et al. stud-
ied the new inference algorithm and industrial fault diagnostic system for nuclear power
plants [119,120].
According to our literature study, the application of DUCG in the nuclear field is still
in its infancy. There is a lack of specialized books on this theory, which hinders the pro-
motion of DUCG technology to a certain extent. However, DUCG-based medical diagno-
sis technology is developing more rapidly, and Zhang’s team is also conducting related
research and promotion [121–126].
3.3. Summary of Knowledge-Driven Fault Diagnosis Methods
This section focuses on knowledge-driven fault diagnosis methods for NPPs and clas-
sifies the existing methods into two types: if–then rule (Section 4.1) and new theories (Sec-
tion 4.2). Expert systems (if–then), signed directed graphs, Bayesian networks, and dy-
namic uncertainty causal graphs are introduced in detail. The development characteristics
of these four methods are shown in Figure 9. The earliest expert systems are based on if–
then rules and rely on the rules stored in the expert knowledge base. The symbolic-di-
rected graph method incorporates qualitative knowledge representation between nodes,
which greatly improves the inference ability. The Bayesian network introduces uncertain
inference technology, which can accommodate information loss and improve system ro-
bustness. Dynamic uncertainty causal graphs develop multi-assignment inference tech-
niques based on Bayesian networks, which possess higher inference efficiency. These
knowledge-driven methods share common drawbacks. They all need to establish a com-
plete knowledge base first. Therefore, it is necessary to improve the efficiency of
knowledge acquisition and the completeness of the knowledge base. In addition, the com-
plex cause–effect relationships within nuclear power plants make the knowledge base
complex and large, which requires improved reasoning efficiency.
Figure 9. Development characteristics of the four methods.
Figure 9. Development characteristics of the four methods.
4. Data-Driven Fault Diagnosis Methods
The data-driven fault diagnosis method for nuclear power plants can be regarded as
a combination of a “data base” and an “inference machine”. The “data base” is defined
as the massive data resources required by the method, which should be distinguished
from the concept of the database in the computer field. Additionally, the “inference
machine” refers to a trained model based on large amounts of data, which is different from
knowledge-driven “inference machines” (Section 3). As shown in Figure 10, the application
of data-driven fault diagnosis methods in the nuclear field can be divided into two types:
single algorithms (Section 4.1) and hybrid algorithms (Section 4.2). Most hybrid algorithms
are improved based on single algorithms and have stronger diagnostic performance. To
enable readers to understand the data-driven methods and their research progress in detail,
the principles of several representative methods and their application progress in NPP fault
diagnosis are introduced in Section 4.1. The research progress of fault diagnosis based on
hybrid algorithms is introduced in Section 4.2. Finally, we summarize the characteristics of
data-driven methods (Section 4.3).
4.1. Fault Diagnosis Methods Based on Single Algorithms
In this section, we present several representative single algorithms and their research
progress in the nuclear field and conclude with a brief comparison of these methods.
Energies 2023,16, 1850 12 of 27
Energies 2023, 16, x FOR PEER REVIEW 12 of 28
4. Data-Driven Fault Diagnosis Methods
The data-driven fault diagnosis method for nuclear power plants can be regarded as
a combination of a “data base” and an “inference machine”. The “data base” is defined as
the massive data resources required by the method, which should be distinguished from
the concept of the database in the computer field. Additionally, the “inference machine”
refers to a trained model based on large amounts of data, which is different from
knowledge-driven “inference machines” (Section 3). As shown in Figure 10, the applica-
tion of data-driven fault diagnosis methods in the nuclear field can be divided into two
types: single algorithms (Section 4.1) and hybrid algorithms (Section 4.2). Most hybrid
algorithms are improved based on single algorithms and have stronger diagnostic perfor-
mance. To enable readers to understand the data-driven methods and their research pro-
gress in detail, the principles of several representative methods and their application pro-
gress in NPP fault diagnosis are introduced in Section 4.1. The research progress of fault
diagnosis based on hybrid algorithms is introduced in Section 4.2. Finally, we summarize
the characteristics of data-driven methods (Section 4.3).
Figure 10. History of data-driven development and its application in the nuclear field.
4.1. Fault Diagnosis Methods Based on Single Algorithms
In this section, we present several representative single algorithms and their research
progress in the nuclear field and conclude with a brief comparison of these methods.
4.1.1. Artificial Neural Network
Artificial neural networks (ANNs) are mathematical models that mimic the structure
and function of biological neural networks. They are used to approximate or evaluate
functions [127]. An ANN is a system that can learn and summarize existing data to pro-
duce a system that can be automatically identified. The most common artificial neural
network is a back propagation neural network (BPNN), as shown in Figure 11, which con-
sists of an input layer, one or more hidden layers, and an output layer in which neurons
are connected by weights. Each neuron contains two transformation steps internally [128–
130]. First, the weighted sum of all input values connected to that neuron is calculated.
Second, the weighted sum is nonlinearly transformed using an activation function.
Figure 10. History of data-driven development and its application in the nuclear field.
4.1.1. Artificial Neural Network
Artificial neural networks (ANNs) are mathematical models that mimic the structure
and function of biological neural networks. They are used to approximate or evaluate
functions [
127
]. An ANN is a system that can learn and summarize existing data to produce
a system that can be automatically identified. The most common artificial neural network
is a back propagation neural network (BPNN), as shown in Figure 11, which consists of an
input layer, one or more hidden layers, and an output layer in which neurons are connected
by weights. Each neuron contains two transformation steps internally [
128
–
130
]. First,
the weighted sum of all input values connected to that neuron is calculated. Second, the
weighted sum is nonlinearly transformed using an activation function.
Energies 2023, 16, x FOR PEER REVIEW 13 of 28
Figure 11. BP neural network.
The training process of a BPNN is as follows: when a BPNN obtains a learning sam-
ple, the sample is transmied from the input layer through the hidden layer to the output
layer, which is the input response of the network. If the network fails to obtain the ex-
pected target output in the output layer, the error signal will enter the back-propagation
phase and return to the input layer along the original connection path. The error signal
can be reduced by modifying the weights of each layer. When errors are propagated re-
peatedly, the correct prediction of the output layer increases. The back-propagation pro-
cess is stopped until the error is sufficiently small, and then a mapping is created between
the input and output to obtain a model with predictive or diagnostic capabilities. With the
development of technology, artificial neural networks have developed in various forms.
The network architecture can be divided into three types: feed-forward neural networks
[131], recurrent neural networks [132], and reinforcement networks [133].
Since artificial neural networks can handle complex multimodal, associative, inferen-
tial, and memory functions, this matches the fault diagnosis of complex nuclear power
systems. The fault diagnosis method based on a neural network is to establish a mapping
of the fault diagnosis based on the training data. The trained network is then used for new
observations to judge anomalies. Zwingelstein et al. first applied the BPNN to the fault
diagnosis of NPPs and preliminarily verified the feasibility [60,134,135]. In addition to
BPNNs, such as recurrent neural networks (RNNs) [136], improved BPNNs [137], self-
organizing neural networks [138], and Hopfield neural networks [139] have all been stud-
ied in applications. In general, research based on neural networks is mostly in the prelim-
inary validation phase. The combination of neural networks with other algorithms for di-
agnosis is the mainstream trend. The related content will be presented in Section 4.2.
4.1.2. Support Vector Machine
The basic idea of support vector machines (SVMs) is to divide data into different cat-
egories using a hyperplane formed by formulas. Taking the simplest two classifications as
an example, as shown in Figure 12, the formula represents different hyperplanes. For a
linearly separable dataset, 1wx b+= and 1wx b+=− denote the two boundaries of
the hyperplane. All hyperplanes that can divide the dataset into two classes are within
these two boundaries. Among all hyperplanes, the goal of SVM is to find an optimal deci-
sion boundary that is farthest from the nearest samples of different classes, that is, to ob-
tain the most robust classification hyperplane. Since the nuclear power plant operation
data are nonlinear, it is not possible to establish the hyperplane by the same method. The
solution is to map the data from the low-dimensional space to the high-dimensional space
and find the optimal hyperplane in the high-dimensional space, and the kernel function
is the core of the method. More detailed principles about SVM can be found in [133–135].
Figure 11. BP neural network.
The training process of a BPNN is as follows: when a BPNN obtains a learning sample,
the sample is transmitted from the input layer through the hidden layer to the output layer,
which is the input response of the network. If the network fails to obtain the expected
target output in the output layer, the error signal will enter the back-propagation phase and
return to the input layer along the original connection path. The error signal can be reduced
Energies 2023,16, 1850 13 of 27
by modifying the weights of each layer. When errors are propagated repeatedly, the correct
prediction of the output layer increases. The back-propagation process is stopped until the
error is sufficiently small, and then a mapping is created between the input and output
to obtain a model with predictive or diagnostic capabilities. With the development of
technology, artificial neural networks have developed in various forms. The network
architecture can be divided into three types: feed-forward neural networks [
131
], recurrent
neural networks [132], and reinforcement networks [133].
Since artificial neural networks can handle complex multimodal, associative, infer-
ential, and memory functions, this matches the fault diagnosis of complex nuclear power
systems. The fault diagnosis method based on a neural network is to establish a mapping
of the fault diagnosis based on the training data. The trained network is then used for
new observations to judge anomalies. Zwingelstein et al. first applied the BPNN to the
fault diagnosis of NPPs and preliminarily verified the feasibility [
60
,
134
,
135
]. In addi-
tion to BPNNs, such as recurrent neural networks (RNNs) [
136
], improved BPNNs [
137
],
self-organizing neural networks [
138
], and Hopfield neural networks [
139
] have all been
studied in applications. In general, research based on neural networks is mostly in the
preliminary validation phase. The combination of neural networks with other algorithms
for diagnosis is the mainstream trend. The related content will be presented in Section 4.2.
4.1.2. Support Vector Machine
The basic idea of support vector machines (SVMs) is to divide data into different
categories using a hyperplane formed by formulas. Taking the simplest two classifications
as an example, as shown in Figure 12, the formula represents different hyperplanes. For a
linearly separable dataset,
w·x+b=
1 and
w·x+b=−
1 denote the two boundaries of the
hyperplane. All hyperplanes that can divide the dataset into two classes are within these
two boundaries. Among all hyperplanes, the goal of SVM is to find an optimal decision
boundary that is farthest from the nearest samples of different classes, that is, to obtain the
most robust classification hyperplane. Since the nuclear power plant operation data are
nonlinear, it is not possible to establish the hyperplane by the same method. The solution is
to map the data from the low-dimensional space to the high-dimensional space and find
the optimal hyperplane in the high-dimensional space, and the kernel function is the core
of the method. More detailed principles about SVM can be found in [133–135].
Energies 2023, 16, x FOR PEER REVIEW 14 of 28
Figure 12. Support vector machine.
Golieb et al. first used support vector machines for the diagnosis of NPP accidents
and verified the feasibility of SVM for data classification [135]. Zio et al. used support
vector machines in the diagnosis of subsystems such as feed water system [136], first-loop
system [137], and other components of abnormal monitoring [138,139]. Kim et al. used
support vector machines to predict the times of serious accidents to help operators beer
manage accidents [140]. Abiodun et al. established diagnostic models for different com-
ponents of NPPs in the form of a support vector set for early fault diagnosis [141]. As with
neural network methods, NPP fault diagnosis relying on SVM alone has been less studied.
As a fundamental method, the current research involving SVMs is more in the area of
hybrid algorithms, which will be presented in subsequent sections.
4.1.3. Decision Tree
The decision tree is a tree structure learned from data. The decision tree is based on
a tree structure to make decisions. It selects one of several aributes of the training sam-
ples for determination each time and assigns the samples to different sets according to
their values on that aribute, after which the next round of decisions is made until all the