Intelligent Techniques for Control and Fault Diagnosis in Pressurized
Water Reactor: A Review
SWETHA R. KUMAR, JAYAPRASANTH DEVAKUMAR
Department of Instrumentation and Control Systems Engineering,
PSG College of Technology,
Coimbatore-641004, Tamil Nadu, INDIA
Abstract: Nuclear reactors serve approximately 10% of the world’s energy usage, and over 430 Nuclear Power
Plants (NPP) are currently built globally. They are safety-critical systems as neutron flux density in the nuclear
reactor core has to be critically controlled within limits. The parameters of a reactor core should be monitored
and optimally regulated to increase the performance of the system. Also, any fault in an NPP system may
potentially compromise plant safety. Thus, implementing early Fault Detection and Diagnosis (FDD) techniques
becomes crucial. With considerable advancements in computational speed and electronics becoming cost-
effective, Artificial Intelligence (AI) has grown implausible in recent times. This review article discusses on few
AI techniques to optimally control the neutron flux density and design an effective fault diagnosis algorithm to
detect sensor faults in the nuclear reactor core.
Keywords: Fault diagnosis; Neural Networks; Artificial Intelligence; Optimization Techniques; Nuclear reactor, Swarm
Inteligeence
Received: March 11, 2024. Revised: August 9, 2024. Accepted: September 13, 2024. Published: October 17, 2024.
1. Introduction
Power regulation and early fault detection are
crucial in a safety-critical process like a nuclear
reactor. Whether nuclear energy is produced
independently or in a combined cycle with other
renewables, artificial intelligence may play a critical
role in proceeding with innovation regardless of the
future guidelines enacted to satiate the world's
energy demand. Computational intelligence has long
been considered to have a variety of uses in the
nuclear sector. Artificial intelligence has progressed
tremendously in recent years due to computing
power and cheaper hardware developments.
Approximately 10% of the world's electricity is at
present produced by nuclear reactors, and more
nuclear power stations are enthusiastically being
built across the globe. However, the nuclear sector
was under pressure to innovate following a few
nuclear accidents like Fukushima, Three-mile Island
and Chernobyl, particularly in affluent nations.
The paper by Suman [1] briefly overviews the AI
techniques reported in the literature for application in
the nuclear power sector. The author highlights AI
algorithms like Neural Networks [2,3], Genetic
Algorithms [4,5,6], Particle Swarm Optimization
[7,8], Ant Colony Optimization [9,10], Artificial Bee
Colony Optimization [11,12], Simulated annealing
[13] and Support vector machine [14,15] which are
applied to the nuclear energy sector. The author also
mentions the following AI application areas:
Load following operation
Fuel management
Fault diagnosis in nuclear power plant
Identification of nuclear power plant
transients
Identification of accident scenario
The nuclear energy industry is driven to
innovate, and new reactor designs are marketed as
inherently safe, reliable, cost-effective, and versatile.
Current nuclear reactors aim to increase safety,
maintain availability, and lower operating and
maintenance costs. The studies focusing on
integrating the capabilities of artificial intelligence in
the nuclear industry have come a long way and the
time has come to teach this in upcoming advanced
nuclear power plants [90]f
. The objective of this paper is to investigate two
such areas in NPP where AI techniques can be
implemented. They are as follows:
Utilization of Swarm Intelligence
algorithms for the design of optimal PID
controller that regulates neutron density.
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Utilization of Neural Networks for state
estimation and fault detection in Pressurized
Water Reactor core.
An extensive literature survey is carried out to
gain insights into the above two technologies.
Abbreviations used in this article are listed in Table
1.
Table 1: Abbreviations
AI
Artificial Intelligence
ACO
Ant Colony Optimization
AGR
Advanced gas-cooled reactor
ART1
binary Adaptive Resonance
Network
AVR
Automatic Voltage Regulator
BRNN
Bayesian Recurrent Neural
Network
BWR
Boiling water reactor
CAN
Controller Area Network
EKF
Extended Kalman filter
FDD
Fault Detection and Diagnosis
FDI
Fault Detection and Isolation
FEM
Finite Element Method
FNR
Fast neutron reactor
GM
Gain Margin
HTGR
High temperature gas-cooled reactor
IAE
Integral Absolute Error
IAEA
International Atomic Energy
Agency
IMC
Internal Model Control
ISE
Integral Square Error
ITAE
Integral Time Absolute Error
KNN
K-Nearest Neighbors
LRNN
Locally Recurrent Neural Network
LWGR
Light water graphite reactor
MSE
Mean Square Error
NARX
NPP
PCA
PID
PHWR
PM
PSO
PWR
RBF-
NN
RNN
SISO
SVM
TEP
UKF
2. System Description
2.1 Nuclear reactor
In a nuclear reactor, energy is released by
splitting atoms of radioactive elements. This energy
is captured as heat in either a gas or water and is
utilised to generate steam. It is released from the
regular fission of the fuel's atoms. The steam powers
the electricity-generating turbines (as in most fossil
fuel plants). Among the several nuclear reactor types,
Pressurized Water Reactors (PWR) are the most
prevalent, as depicted in Table 1.1 (Source:
www.iaea.org). According to the International
Atomic Energy Agency's (IAEA) nuclear power
status report [16] approximately 308 PWR-type
nuclear reactors are providing 294.8 GW of power
worldwide.
Table 2 Operable Nuclear Power Plants
Reactor Type
Number
Power
(GWe)
Fuel
Coolant
Moderator
Pressurized water reactor (PWR)
308
294.8
Enriched UO2
Water
Water
Boiling water reactor (BWR)
61
61.9
Enriched UO2
Water
Water
Pressurized heavy water reactor
(PHWR)
47
24.3
Natural UO2
Heavy water
Heavy
water
Light water graphite reactor (LWGR)
11
7.4
Enriched UO2
Water
Graphite
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Advanced gas-cooled reactor (AGR)
8
4.7
Natural U,
Enriched UO2
CO2
Graphite
Fast neutron reactor (FNR)
2
1.4
PuO2 and
UO2
Liquid
sodium
None
High temperature gas-cooled reactor
(HTGR)
1
0.2
Enriched UO2
Helium
Graphite
Pressurized Water Reactors utilizes water as
both moderator and coolant. The design is eminent
by a primary cooling unit which flows water via the
core of the reactor with very high pressure, and a
secondary unit which produces steam to drive the
turbine [17]. This PWR is also known as water-water
energetic reactors (VVER) in Russia. A PWR has
vertically arranged fuel assemblies with 200-300
enriched uranium filled fuel rods.
Since the water in the reactor core attains a
temperature of around 325°C, it must be reserved
under a pressure of nearly 150 times that of the
atmosphere to avoid boiling. In a pressurizer as seen
in Figure 1.5 [18], steam preserves the pressure.
Water serves as a moderator in the primary cooling
circuit. If any of it went to steam, the fission reaction
would be slowed. This is the negative feedback
effect. The fission reaction can be controlled or shut
down by the use of control rods. Control rods are the
chief control element of the reactor core. Water boils
in the heat exchangers, which acts as steam
generators, in the secondary unit due there is less
pressure there. The steam condenses and returns to
the heat exchangers in contact with the primary
circuit after powering the turbine to generate
electricity [88].
2.2 Pressurized water reactor model
The reactor power model is built on point kinetic
equations with three groups of delayed neutrons
 ; and reactivity feedback is affected by
changes in fuel and coolant temperatures [19, 89].
There are seven state variables in this SISO model.
The following are the equations for a Pressurized
water nuclear reactor core:
The three groups' delayed neutrons-based point
kinetic equations are

 

 (1)

   (2)
Figure 1 Layout of Pressurized Water Reactors [18]
Where is normalized neutron density, 
is ith group normalized delayed neutron precursor
density. Delayed neutrons are neutrons produced
during the radioactive decay of certain neutron-rich
fission fragments. They are produced within a few
milliseconds to seconds after the fission reaction.
These delayed neutrons are grouped into three or six
groups.
The reactor’s thermal-hydraulic model is given by,



out (3)

 
󰇛󰇜
out 󰇛󰇜
in (4)
Where is Fuel average temperature and
is Coolant average temperature. , out are
coolant inlet and outlet temperatures respectively.
Nuclear reactors use the essential term
"reactivity" to describe when a reactor system
deviates from criticality. A shift toward
supercriticality is indicated by addition of small
positive value. A shift toward subcriticality is
indicated by addition of small negative value. This
reactivity changes as the speed of the control rod
variations, as does the total reactivity is
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rod
 (5)
  󰇛 󰇜 (6)
rod is the reactivity induced due to control
rods and is the reactivity induced due to fuel and
coolant temperatures. is total reactivity. Also
,and are related to initial equilibrium
neutron density 󰇛󰇜. The following equations
demonstrate the dependency.
󰇡
󰇢 (7)
󰇡
󰇢  (8)
󰇛 󰇜 (9)
󰇛 󰇜 (10)
The reactor power is expressed as,
󰇛󰇜 (11)
The reactor model's parameters and values are listed
in Table 2 and Table 3.
Table 2. Parameters in PWR model
P0
Full core power, MW
nr
Normalized neutron density (relative to neutron density at rated power
P0)
cri
ith Group normalized precursor density (relative to density at rated
power)
Tf
Fuel average temperature, oC
Tf0
Fuel average temperature at the initial condition, oC
Tc
Coolant average temperature, oC
Tc0
Coolant average temperature at the initial condition, oC
Tin
Coolant inlet temperature, oC
Tout
Coolant outlet temperature, oC
Total reactivity, K/K

Reactivity due to control rod movement, K/K
Temperature reactivity feedback, K/K
Zr
Control rod speed, fraction of core, length/s
Gr
Control rod total reactivity, K/K
Effective delayed neutron fraction
ith group effective delayed neutron fraction
Coolant temperature coefficient, 󰇛K/K) / oC
Fuel temperature coefficient, 󰇛K/K) / oC
Neutron generation time, s
ith Delayed neutron group decay constant, s-1
Macroscopic thermal neutron fission cross-section, cm-1
Average number of neutrons produced per fission of 235U
G
Useful thermal energy liberated per fission of 235U, MW-s
V
Core volume, cm3
ff
Fraction of reactor power deposited in the fuel
Fuel total heat capacity, MW.s/ oC
Coolant total heat capacity, MW.s/ oC
M
Mass flow rate time heat capacity of water, MW/ oC
Coefficient of heat transfer between fuel and coolant, MW/ oC”
Table 3 Values of parameters used in reactor model
Parameters
Values
Thermal power
3000 MW
Core height
400 cm
Core radius
200 cm
 cm-1
 
 
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










0.632 s-1
3. Review of swarm intelligence
algorithms for control
Swarm Intelligence is one of the progressive
research areas in the domain of Artificial
Intelligence, which has become prevalent in solving
various optimization problems and thus has a wide
range of applications. Specifically in the control
domain, it has become one of the useful methods for
optimally tuning the controller parameters to
achieve efficient control [12]. Swarm Intelligence is
driven by the cohesive nature of the social insect
territories or other animal communities [104].
Optimization is the procedure of finding the best
inputs u* in obtaining the optimal output y* with
minimum cost J*. Optimization problem is solved
by choosing the design parameter, then formulating
the constraints and defining a cost function. The aim
of the cost function is to determine a value for
chosen design parameter satisfying the given
constraint that delivers the optimum response. With
respect to controller tuning, optimization algorithms
will provide optimal controller tuning parameters
that minimize the error and control effort [23].
Around 90% of control loops in the process
industries use the PID control algorithm. This wide
application is because of its simple structure that
could be effortlessly understood by process
operators. A typical structure for a regular PID
controller comprises three components namely:
proportional gain kp, integral gain ki and derivative
gain kd. The derivative gain develops the
control action according to the rate of change of
error, the integral gain develops the control action in
response to the sum of all past errors, and the
proportional gain produces the control action for
present error. PID controller tuning is done either by
trial and error using the operator’s process
knowledge or by conventional tuning methods.
The frequently used traditional PID tuning
techniques, like Cohen-Coon and Ziegler-Nichols,
may not provide effective tuning parameters due to
changing process dynamics and inaccurate process
models [82]. The optimal controller gains for good
performance can be attained via swarm intelligence
which is measured in terms of fitness functions such
as integral square error, absolute error, mean square
error, etc. These optimization algorithms are simple,
flexible to search randomly and also avoid local
optima [24].
3.1 Framework
Essentially, swarm intelligence algorithms are
iterative stochastic search procedures, where
heuristic data is shared to perform the search. Figure
2 shows a general framework for swarm intelligence
algorithms. It is compulsory to define the parameter
values prior to the initialization process.
Initialization and the ensuing strategies set off the
evolutionary process. A termination condition is set
to stop the iteration process which may be a single
condition or a combination of two criteria. The
fitness function, which can be either one basic
metric or a combination, is responsible for
evaluating the search agents. Agents are updated by
the algorithm until the preceding termination
condition is met. The best search result is then
obtained. The execution of each step may occur in a
varied order for a given swarm intelligence
algorithm, and some processes may be repeated
multiple times inside a single iteration.
3.1.1 Classification
Swarm Intelligence algorithms mimic the
collective behaviour of birds or fish or insects that
are prevalent throughout the ecosystem. As these
algorithms are widely applied in various engineering
domains, classifications by various collective
behaviour were proposed by researchers [25]. The
rough classification of such algorithms is illustrated
in Figure 3. A detailed literature study is carried out
for PSO and ACO algorithms in this article.
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Figure 2 General Framework of Swarm Intelligence
Algorithm
Figure 3 Classification of Swarm Intelligence
Algorithms
3.1.2 Particle Swarm Optimization
Particle Swarm Optimization (PSO) is a
popular metaheuristic optimization technique
inspired by the social behaviour of bird flocking or
fish schooling [92]. Introduced by Dr. James
Kennedy and Dr. Russell Eberhart, PSO is widely
used for solving various optimization problems in
diverse domains, including engineering, economics,
medicine, and machine learning (Kennedy 2006).
PSO has been used in various applications of
automatic control systems that heavily rely on PID
controllers.
Particle swarm optimization simulates the
behavioural patterns of swarming birds or schooling
fish. The flowchart of PSO is as shown in Figure 4
[26]. Each particle/bird has its own position and
velocity. These particles adjust their velocities to
alter their position in order to seek meal, avoid
danger, or identify best possible environmental
parameters. Furthermore, each particle remembers
the best location that it has identified. Each particle
conveys this information about the best location to
the other particles. The velocity of such particles is
then updated based on the particle's or the group's
flying experience.
Figure 4 Flow diagram for Particle Swarm
Optimization
Gaing provided a thorough explanation of
how to use the PSO method to quickly find the ideal
PID controller parameters for an Automatic Voltage
Regulator (AVR) system [27]. The suggested
method exhibited excellent characteristics, such as
simple implementation, consistent convergence
behaviour, and good computational efficiency. The
proposed method proved effective and reliable in
increasing the step response of an AVR system when
compared to the Genetic Algorithm (GA).
Moreover, the PSO algorithm is also employed to
design a fractional order PID controller for an AVR
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system [29]. In this work, a novel cost which is a
function of Overshoot, rising time, settling time,
steady state error, Gain Margin (GM) and Phase
Margin (PM) is used.
To execute the optimisation of the
controller gains and enhance the performance of a
single-shaft Combined Cycle Power Plant, a
fractional order fuzzy-PID (fuzzy-FoPID) controller
based on the PSO algorithm is presented [23]. In
order to increase the response during frequency
drops or changes in loading, the proposed controller
is employed in speed control loops. The simulation
results demonstrate the performance and efficacy of
the suggested strategy for frequency decrease or
loading modification.
Using PSO, Zeng et al optimized an IMC
PID controller to stabilise the core power of the
Molten Salt Breeder Reactor [29]. A control
technique based on a process mathematical model
for controller design is known as Internal Model
Control (IMC). IMC's principle of design is to add
the inverse of the minimum phase component of the
model for a single variable system to the system,
approximate the dynamic inversion of the model by
the controller, and parallelize the object model with
the actual object.
The tuning problem of digital Proportional-
Integral-Derivative (PID) variables for a dc motor
controlled via the Controller Area Network (CAN)
was examined by (Qi et al. 2020) [30]. PSO
technique was introduced to optimally tune the PID
controller's parameters for systems susceptible to
stochastic delays. To deal with the stochastic
characteristics, the optimisation method includes a
stability requirement for time-delayed systems and
proposes an objective function with an average
value for the PSO algorithm. Similarly, much
research in PSO for tuning controller gains is
reported in the literature [7,31,32,33]
3.1.3 Ant Colony Optimization
An algorithm known as Ant Colony
Optimisation (ACO) was inspired by how ants
forage. It was initially proposed by Marco Dorigo to
address the Travelling Salesman Problem and other
combinatorial optimisation problems. Ants in nature
interact with one another and build pathways
between their nests and food sources via
pheromones. The pheromone trail gets stronger the
more ants move along a particular path. The quickest
routes between the nest and the food supply are
formed by ants generally following the routes with
higher pheromone levels. This idea is used by the
ACO algorithm to locate efficient solutions to
optimisation issues [34, 83]. This principle can be
used to tune PID controllers.
Ant colony optimization is a probability based
technique in which the optimal route in a plot is
sought observing the behaviour of ants looking to
find a path between their colony and a food source.
The ants find the best route to any distanced food
source. Refer to Figure 5 to understand the
mechanisms behind this [26]. First, an ant leaves the
hives in looking for food and finds it in a particular
location; the leftover ants will follow the
pheromones left by the first ant. If there are different
routes to the same source, the pheromones on the
quickest route will last longer than the pheromones
from the other paths, causing the quickest route more
rewarding for new ants emerging from the nest, The
pheromone intensity on that path will rise, while the
pheromone intensity on the longest path will drop.
Figure 5 Flow diagram for Ant Colony
Optimization
Hsiao et al. (2004) obtained good load
disturbance response by minimizing the integral
absolute control error [35]. At the same time, a good
transient response is guaranteed by minimizing the
time domain specifications. This study proposes a
solution algorithm based on the ant colony
optimization technique to determine the parameters
of the PID controller for getting good performance
for a given plant. The proposed method was
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implemented and tested on several plants with
promising results that compare with known methods.
Multiobjective ant colony optimisation was
utilised by Chiha et al. to fine-tune PID controllers
[36]. To find the Pareto-optimal solution,
multiobjective ant algorithms are required. Results
from simulations show that the new tuning method
employing multiobjective ant colony optimisation
outperforms both the traditional "Ziegler-Nichols"
approach and genetic algorithms in terms of control
system performance. Youssef Dhieb et al. employed
an ACO-tuned PID to eliminate the induction motor's
harmonics and speed ripple [37]. Using the finite
element method (FEM), the parameters of this motor
were determined. Two distinct tuning methods based
on manual and ACO tuning of PID-controller
parameters have been presented.
The control of a levitating object in a magnetic
levitation plant using a fractional order PID (FoPID)
controller is presented in [9]. The parameters of this
FoPID controller have been updated using the
Ziegler Nichols method and the Ant Colony
Optimisation (ACO) algorithm. For comparison
study, the output results of the FoPID controller are
compared to those of the conventional PID
controller. In comparison to the conventional PID
controller, the FoPID controller has demonstrated
incredibly effective outcomes due to its additional
parameters.
Arun & Manigandan constructed an Ant colony
Optimization-based PID controller for a zeta
converter [38]. The higher-order zeta converter
system is reduced to second order using three distinct
reduction techniques. Then, the ACO-based PID
controller is designed for a reduced-order process
and is matched with the full-order zeta converter.
The results show that the designed controller for the
zeta converter gives a good response for both
models, the controller gives good performance
indices based on ISE, IAE, and ITAE. Similarly,
Karami used ACO-tuned PID to Micro-Robot
Equipped with a Vibratory Actuator [39] and
Rahman used it for vibration control of a wind
turbine tower [40]
4. Fault Detection and Diagnosis
Techniques
Faults are unpermitted deviations from the
typical behaviour of the process or its
instrumentation. It is classified as process faults,
sensor faults and actuator faults conditional on the
site it arises. Identifying the location of the fault and
determining its magnitude is called fault diagnosis.
With the huge demand for complex processes and
automation, innumerable procedures were proposed
to detect and locate the fault [41, 82]. An unobserved
fault in the process may have catastrophic effects
such as environmental hazards or safety risks. The
primary stage in treating a failure is determining its
location, which is vital for conserving the plant's
ideal conditions [80].
The fault detection and isolation (FDI)
methods are broadly classified into Model-free and
Model-based approaches [85]. The subcategories
are shown in Figure 6.
Figure 6 Methods in Fault Detection and Isolation
4.1 Model-free Approaches
Model-free approaches are FDD techniques that
do not depend on explicit mathematical models of
the problem under consideration. Few such model-
free approaches are discussed here [42].
In physical redundancy, many measuring
devices are mounted to read the same
physical entity. Any inconsistencies
amongst the sensor readings will show a
sensor fault. At least three sensors are
needed to detect a fault in the sensor using
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this method.
The limit-checking technique compares
process measurements with a threshold
value. Surpassing this threshold specifies a
fault. Thresholds must be clearly defined as
measurements will fluctuate even during
normal load variations.
Under ordinary operating circumstances,
the majority of process measurements
display a conventional frequency spectrum.
Every departure from this is a sign of
abnormality.
In the logical reasoning technique, process
information is analyzed qualitatively using
tools such as if-then rules. These qualitative
approaches can process inaccurate and
inadequate information to reach a fault
decision. Two prevalent techniques are
expert systems and fuzzy logic.
Data-driven approaches practice
multivariate statistical techniques and
machine learning algorithms to find a fault.
They also count on associations amongst
correlated measurements in a process but
utilize them subtly by examining fault-free
training data attained during standard
operations. Thus, these methods are also
denoted as process history-based
approaches. Principal Component Analysis,
Artificial neural networks are extensively
utilized for Fault diagnosis [93, 96, 97].
4.2 Model-based Approaches
Analytical redundancy is the main idea behind
model-based fault diagnosis methods. In model-
based FDD, the standard behaviour of a process is
characterized by a mathematical model which can be
an input-output model or a state space model. Sensor
outputs are predicted analytically by means of the
model that defines their associations. The concept
can be extended to predict new quantities
analytically, such as model parameters and system
states. Residuals are the variations between the
analytically predicted values and the
true measurements. Faults lead to violations of the
normal relationships represented by the model,
which causes the residuals to fluctuate abnormally.
Therefore, faults can be found by statistically
examining these residuals. The processes of model-
based FDD can be separated into the succeeding
subsystems: residual generation, residual evaluation
and decision making. The model-based FDD
scheme is shown in Figure 7.
Figure 7 Model-based FDD scheme
An approximate mathematical model of the
monitored process is obtained by first principle
modelling or state and parameter estimation
methods. Residuals produced are then evaluated to
provide fault isolation decisions. Even when there is
no fault, residuals are not zero because of the noise
and modelling mistakes. Threshold margins are set
in no-fault circumstances [42]. A structural
framework's residual analysis can be utilized to
regulate the fault's nature and position. The methods
of residue generation are as follows:
Kalman Filter: This filter's prediction error can
be applied as a residual for fault detection. If
there is any fault, the residuals violate the
threshold value. This technique is useful for
finding additive errors. It can handle stochastic
disturbances in the system. The filter equations
are as follows:
󰇛 󰇜 󰇛 󰇜 󰇛󰇜 (12)
󰇛 󰇜 󰇛 󰇜 󰆒󰇛󰇜󰇛󰇜 (13)
󰇛󰇜 󰇛󰇜
(14)
where 󰆒󰇛󰇜 is Kalman gain
Nonlinear Filters: Filters like Extended Kalman
filter, Unscented Kalman filter, Particle filter
can be used to generate residues for a highly
nonlinear process [91,98,102].
Neural Networks: Neural network models can
be built using input-output data of the process.
These models are then utilized for state
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estimation. Different architectures of neural
networks are available and they can be chosen
based on the process data [86, 95]. A multilayer
Feedforward NN includes one input layer, one
or more hidden layers, and one output layer.
Each component of the input vector
󰇟󰇠 is weighted by its weight matrix
. The neuron bias is summated to give the
net input

 (15)
Then, an activation function f is utilized to
produce the neuron output o. Similarly, many
topologies of neural networks are available.
Parameter Estimation: It is used to detect and
isolate multiplicative faults that arise due to the
plant’s underlying parameters. Physical
coefficients shall be estimated for diagnosis. It
requires significant online computations and
high input excitation. The least-square
parameter estimator equation is
 󰇟󰇠 (16)
where is an estimation of  is a matrix
consisting of 󰇛󰇜. is a vector consisting of
󰇛󰇜.
Diagnostic Observers: Similar to state and
parameter estimators, the observer innovations
can also be utilized for fault detection. Observer
equation is
󰇛 󰇜 󰇛󰇜 󰇛󰇜 󰇛󰇛󰇜 󰇛󰇜󰇜 (17)
󰇛󰇜 󰇛󰇜 󰇛󰇜 (18)
where is an estimate of , and is is the
observer feedback matrix.
Parity Equations: They are reorganized direct
input-output model equivalences subjected to
linear dynamic transformation. The residuals
from the transformed model aid for fault
detection.
󰇛󰇜 󰇛󰇜󰇛󰇜 󰇛󰇜󰇛󰇜 (19)
where 󰇛󰇜 is residual.
4.3 Review of FDD Techniques
Hardware or analytical redundancies are used
to monitor and isolate the fault. The magnitude of
the fault can also be found. Though hardware
redundancy is reliable, it increases cost, space and
weight of the process. Analytical redundancy is a
model-based fault detection method wherein states
are estimated analytically from other correlated
measurements using the model or plant data [43].
The residuals are the differences between the
analytically estimated quantities and the actual
measurements. When the residual signal crosses the
threshold, a fault is indicated. Upon assessing the
residual trend, faults can be classified as additive or
multiplicative. Instant fault isolation can be
achieved via structured or directional residuals.
The survey papers [44, 45] on model-based,
signal-based and knowledge-based fault diagnosis
give a complete overview of the fault diagnosis
methods and their applications. The merits and
limitations of each technique were discussed.
Model-based FDD techniques are reviewed for
deterministic, stochastic systems. Signal-based FDD
techniques are classified based on time and
frequency domain. Knowledge-based FDD methods
are on extracted quantitative or qualitative data. The
books by Janos Gertler in 1998 [42] and Rolf
Isermann in 2006 [43] features the model-based
approach to fault detection and diagnosis in process
industries and systems.
Safarinejadian & Kowsari used an Extended
Kalman Filter (EKF) and Unscented Kalman Filter
(UKF) with Gaussian processes to detect faults in
highly non-linear dynamical aviation tracking
systems [47]. For 2-D systems defined by the
Fornasini & Marchesini (F-M) model, a 2-D Kalman
filter based fault detection was proposed by (Wang
& Shan [48]. A residual is produced using a
recursive 2-D Kalman filter. The residual is
explicitly tied to faults inside the evaluation window
based on the residual model across a 2-D evaluation
window. An intelligent particle filter for real-time
fault detection on a three-tank system was proposed
by Yin & Zhu [49]. A genetic operators-based
approach is used to overcome particle
impoverishment problems in general PF. Kumar et
al tries to estimate and identify the types of faults in
centrifugal pumps using a system identification
approach [50]. These papers are examples of where
model-based FDD techniques are used.
Based on the acoustic measurement of current
amplitude, [51] presented a new Fault Detection and
Diagnostics (FDD) control approach for current
sensors of permanent magnet synchronous machine
drives in field-oriented control mode. The suggested
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Volume 4, 2024
scheme does not require an exact system model with
specific parameters, unlike the traditional observer-
/model-based fault detection methods for current
sensors. Instead, it simply needs data on three-phase
currents and the location of the motor rotor. The goal
of [52] is to detect faults in belt conveyor idlers
using an acoustic signal-based approach. Mel
Frequency Cepstrum Coefficients and Gradient
Boost Decision Tree are used to extract and classify
features in a novel manner. These two publications
serve as illustrations of the application of signal-
based FDD approaches.
A fault detection method based on the
calculation of sets of parameters for a photovoltaic
module under various operating conditions, using a
neuro-fuzzy methodology, was proposed by [53].
The evaluation and comparison of norms based on
the aforementioned criteria, along with threshold
values, determine the condition of the PV system.
The Support Vector Machines (SVMs) classification
approach described by [54, 87] is used for fault
detection in wireless sensor networks, which are
vulnerable to a variety of problems, including
hardware, software, and communication faults. [55]
use supervised algorithms like support vector
machines and the K-Nearest Neighbour method to
anticipate boiler problems in power plants. These
papers serve as illustrations of the application of
knowledge-based FDD methodologies.
FDD methods are also demanded in nuclear
power sectors to improve their safety and reliability.
Ma & Jiang presented the various FDD that can be
utilized for the following applications in NPPs:
Monitoring of device calibration, dynamic
performance, equipment, reactor core, loose parts
and transient recognition [56]. Neural networks can
be applied to all the above-mentioned applications
[57, 3, 58]. This article focuses on the review of
Neural networks for nonlinear state estimation.
4.3.1 Neural Networks for Nonlinear State
Estimation
Robotics, control systems, and signal
processing are just a few of the areas where neural
networks have been successfully used to solve state
estimation challenges. The neural network
architecture and training method must be specifically
designed for state estimation purposes. Additionally,
gathering enough pertinent training data is essential
for neural network applications in state estimation
tasks.
Rumelhart et al. (1986) presented the
backpropagation algorithm for training neural
networks [59]. While not directly focused on state
estimation, it laid the basis for applying neural
networks to various nonlinear tasks, including state
estimation. Nielsen in 1996 explored the use of
neural networks for modelling and predicting
nonlinear dynamic systems [60]. It delivers insights
into how neural networks can be used for state
estimation in such systems. The Radial Basis
Function Neural Network (RBF-NN) is applied to
match an Extended Kalman filter (EKF) in a data
assimilation scenario.
By constraining the state estimator to adopt the
topology of a multilayer feedforward network,
Parisini & Zoppoli developed a novel method for
solving the optimal state estimation problem using
neural networks [61, 84]. It is possible to convert the
original functional problem into a nonlinear
programming problem by using non-recursive and
recursive estimating strategies, which are both taken
into consideration. Quantitative findings on the
accuracy of such approximations are presented.
The use of artificial neural networks to estimate
and predict bioprocess variables was examined by
Karim & Rivera [62]. Two case studies were carried
out on ethanol generation by Zymomonas mobilis.
Results for various training sets and training
strategies are shown. It is demonstrated that the
neural network estimator offers accurate online
estimations of the bioprocess state. The design of an
artificial neural network-based model for centrifugal
pumping system fault detection was described by
Rajakarunakaran et al [63]. The binary Adaptive
Resonance Network (ART1) and feed-forward
network with a backpropagation algorithm are the
two artificial neural network approaches used for
developing the fault detection model. Seven different
categories of centrifugal pumping system anomalies
were examined to determine the effectiveness of the
designed backpropagation and ART1 models.
Using 1-D convolutional neural networks with
an inherent adaptive design, Turker Ince proposed a
quick and precise motor condition monitoring and
early fault-detection system to combine the feature
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Volume 4, 2024
extraction and classification phases of motor fault
detection into a single learning body [64]. The
suggested method instantly applies to the raw data
(signal), which eliminates the need for a separate
feature extraction algorithm and leads to faster and
more hardware-efficient systems. The usefulness of
the suggested strategy for real-time motor condition
monitoring has been demonstrated by experimental
findings acquired utilising actual motor data.
Sun et al suggested a unique deep learning
methodology that uses Bayesian Recurrent Neural
Networks (BRNNs) with variational dropout to
discover and identify probabilistic faults [2].
Complex nonlinear dynamics can be modelled using
the BRNN. In addition to producing uncertainty
estimates, the suggested BRNN-based technology
enables simultaneous fault detection of chemical
processes, direct fault diagnosis, and fault
propagation analysis. With reference to the industry
standard Tennessee Eastman Process (TEP) and an
actual dataset from the chemical production sector,
the method's performance is shown and compared to
that of (dynamic) principal component analysis.
4.3.2 State Estimation for Fault Diagnosis in
PWR
One of the most popular analytical redundant
methods for fault detection is state estimation. To
estimate the state of a nonlinear Pressurized water
reactor, several conventional nonlinear state
estimators, namely the Ensemble Kalman filter,
Unscented Kalman filter, and Particle filter, have
been proposed in the literature. They do, however,
require prior knowledge of the system's
nonlinearities. Neural network estimators, on the
other hand, are data-driven and rely solely on the
input-output measurement of the process. The
capabilities of neural networks for nonlinear state
estimation have been investigated in various
literatures [65] both in offline and online
environments.
A pressurized water reactor is a safety-critical
system that requires early fault detection, which can
be accomplished via the use of analytical redundancy
components. In analytical redundancy, the states are
estimated analytically from other correlated
measurements using the model or plant data [41] .
The residuals are the differences between the
analytically estimated quantities and the actual
measurements. When the residual signal crosses the
threshold, a fault is indicated. Upon assessing the
residual trend, faults can be classified as additive or
multiplicative. Instant fault isolation can be achieved
via structured or directional residuals.
The dynamics of the PWR are stated in [66].
Among the state variables, Neutron flux, Fuel
average temperature, Coolant average temperature
are measurable via sensors. These sensor
measurements can be compared with the analytical
redundant component output value to identify faults.
Due to the lack of suitable sensors, variables like
reactivity and delayed neutron precursor
concentrations can only be measured inferentially.
Thus, state estimation becomes critical for control
and fault detection in NPPs.
Racz recommended the Kalman filtering
method to estimate reactivity for minor changes in
reactivity [67]. Dong presented a Robust Kalman
filter to estimate various state variables of a reactor,
with the performance of the designed robust Kalman
filter outperforming the Ensemble Kalman filter
[68]. Shimazu & van Rooijen compared the
qualitative performance of IPK and EKF techniques
[69]. Zahedi & Ansarifar speculated using the EKF
technique to estimate poison concentrations in PWR
nuclear reactors based on reactor power
measurements [70]. Mishra et al explored Adaptive
Unscented Kalman Filtering for NPP Reactivity
Estimation [71]. EKF and Kullback–Leibler
divergence were observed by Gautam et al for sensor
incipient fault detection and isolation of NPP [72].
The main limitation of the methods described above
is the requirement for a precise mathematical model
whose underlying parameters do not vary
significantly and whose initial states are known. This
cannot be guaranteed for a large reactor core.
The use of neural networks for nonlinear state
estimation is impressive in this AI era [1]. Mehrdad
Boroushaki et al. proposed a multi-NARX structure
for estimating the core of a nuclear reactor [73].
Hatice Akkurt described a neural network estimator
for predicting pressurized water reactor system
parameters during transients [74]. Cadini et al.
suggested a Locally Recurrent Neural Network
(LRNN) for approximating a simplified nuclear
reactor's nonlinear dynamic system model [75].
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Aside from that, several artificial intelligence
techniques such as SVM, PCA [76], and neural
networks [77,2] are used in NPP fault detection and
condition monitoring.
Kumar et al. compared different AI techniques
for system identification and state estimation which
outworths the promising nature of NN for dynamic
estimation [78]. Though the neural network is
claimed as a good nonlinear state estimator that
works on input-output data [79], the comparative
study on different topologies of NN to analyze the
suitable network for state estimation in water
reactors is not presented in the literature.
5. Conclusion
The prime motive of this review article is to
investigate the uses of intelligent techniques to
enhance safety in Pressurized water reactor core. The
major contributions of this article are twofold:
Utilization of Swarm Intelligence algorithms for the
design of optimal PID controller that regulates
neutron density and Utilization of Neural Networks
for state estimation and fault detection in PWR core.
Moreover, Intelligent techniques can also be applied
to Fuel management, accident scenario, digital twin,
fault tolerant schemes and nuclear power plant
transients.
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.
Conflicts of Interest: “The authors declare no
conflict of interest.”
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Contribution of Individual Authors to the
Creation of a Scientific Article
Swetha R. Kumar: Conceptualization,
Methodology, Writing – original draft.
D. Jayaprasanth: Supervision, Correction.
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.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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