# Fault Diagnosis and Prognosis Capabilities for Wind Turbine Hydraulic Pitch
Systems: An Overview

Alessio Dallabona11footnotemark: 1<EMAIL_ADDRESS>Mogens Blanke<EMAIL_ADDRESS>Henrik C. Pedersen<EMAIL_ADDRESS>Dimitrios Papageorgiou<EMAIL_ADDRESS>
###### Abstract

Wind energy is the leading non-hydro renewable technology. Increasing
reliability is a key factor in reducing the downtime of high-power wind
turbines installed in remote off-shore places, where maintenance is costly and
less reactive. Defects in the pitch system are responsible for up to $20\%$ of
a wind turbine downtime. Thus, prognosis and condition monitoring of such
defects are essential for avoiding downtime. This paper presents a generic
assessment of diagnosis capabilities in hydraulic pitch systems characterizing
high-power wind turbines. A mathematical model of the non-linear system
dynamics is presented along with a description of the most frequent faults
that can affect it. Structural analysis is employed to assess the diagnosis
and prognosis capabilities of defects in the pitch system. The structural
properties are furthermore explored to investigate possible sensor reduction
without compromising fault diagnosis capabilities.

###### keywords:

fault diagnosis , condition monitoring, wind turbine, pitch system, hydraulic
actuator, fluid power systems

††journal: Renewable Energy

[1]organization=Department of Electrical and Photonics Engineering, Technical
University of Denmark, addressline=Elektrovej 326, city=Lyngby, postcode=2800,
country=Denmark [2]organization=Department of Energy Technology, Aalborg
University, addressline=Pontoppidanstræde 111, city=Aalborg, postcode=9220,
country=Denmark

##  1 Introduction

Wind turbines production increased by a record of 273 TWh ($17\%$) in
2021222Data of 2022 is less meaningful because of the energy crisis, more
details at [27]., the highest among all renewable power technologies. The same
year the total production reads 1870 TWh, almost as much as all the other non-
hydro renewable technologies combined. The Net Zero Emissions target by 2050
is reflected in the tendency to increase the turbine’s size and power and to
move towards off-shore systems[26]. Minimizing the downtime for such systems
is a priority. In addition to the maintenance cost, one needs to consider the
missing revenue associated with the energy not being produced during the
repair. The offshore installation makes maintenance more challenging and,
thus, longer in time. Studies like [23, 8, 35] have shown that the main source
of failure in wind turbines is associated with the pitch regulation system.
The authors in [10], [20] and [33] have shown how failures in such systems may
have severe consequences. For high-power models, the pitch regulation system
is electro-hydraulic. Compared to purely electrical pitch systems, electro-
hydraulic systems offer higher power density, more robustness, and smoother
performances [59, 45, 40]. The application of fault detection and
accommodation schemes can be leveraged to reduce the required maintenance on
the hydraulic subsystem such that the up-time of the wind turbine
significantly increases.

A significant corpus of literature has been focusing on the design and
evaluation of methods for the detection and mitigation of individual faults
that can occur in wind turbines. A comprehensive review of the research
methods was presented in [3, 21]. Actuator faults have also been addressed in
the context of fault-tolerant control in [55, 44, 39, 42]. The authors in [2]
focused on the hydraulic pitch system and reviewed most of the results for
both fault diagnosis and fault-tolerant control. Other investigations related
to fault diagnosis and mitigation in the pitch system can be found in [19, 58,
31] and the references therein. The hydraulic circuit driving the pitch system
in wind turbines is similar to the ones used in several other applications in
hydraulics, such as mechanical presses, servo positioning, etc. Several
studies applied similar tools to detect and mitigate mainly leakage faults.
The most recent and relevant results for detection/estimation and mitigation
can be found in [24, 57, 1, 4, 52, 12, 63, 38, 25, 60, 53, 56, 61, 16, 13, 54]
and [41, 15, 48, 50, 49, 62], respectively. The references include results for
model-based, statistical-based, and learning-based methods.

The majority of the previously reported work pertained to the design of fault-
tolerant solutions in relation to specific faults without considering the
overall fault diagnosis capabilities of the system. To the best of the
authors’ knowledge, such a holistic investigation has not been carried out.
This study focuses on providing a means to systematically assess the potential
fault tolerance capabilities of hydraulic pitch systems. Specifically, the
contributions of this paper are:

  * 1.

Derivation of a benchmark model including explicit representations of the most
relevant faults.

  * 2.

Structural analysis of the benchmark model for assessing the fault diagnosis
capabilities of the system.

  * 3.

Investigation of sensor topology in connection to cost reduction while
retaining fault diagnosis features.

The remainder of the paper is structured as follows: Section 2 defines a
benchmark model that is used for investigating condition monitoring and fault
diagnosis in hydraulic pitch systems. The fault detection and isolation
capabilities of the system are analyzed in Section 3 by carrying out a
structural analysis on the benchmark model. Section 4 investigates topology
alterations that could improve fault diagnosis in the system. The results are
discussed in Section 5, and conclusions are drawn in Section 6.

##  2 Pitch System Topology and Modeling

The reference hydraulic pitch system for the article is presented in Figure 1
and represents a simplified schematics/topology of a pitch system under normal
operation, but excluding the safety features. A pump and an accumulator bank
(represented as one accumulator) are used to supply three equivalent circuits
composed of a proportional valve (PV) and a hydraulic cylinder. More
information about how such a system works is provided in [34].

Figure 1: Hydraulic pitch system components [47].

The benchmark model comprises the nominal dynamics detailed in [47] and all
major faults that could affect turbine availability and production. Although
modeling for fault-tolerance may require a multiplicative representation of
some defects [5], all faults in this study are expressed as additive, time-
varying terms (in blue color) since the effect of any generic fault can be
described in this way. A thorough description and models for diagnosis are
presented in Section 2.5. The sections 2.1 to 2.3 present the mathematical
model for the different elements comprised in the pitch system.

###  2.1 Hydraulic Cylinder

The main component allowing the pitching of the blades is the hydraulic
cylinder. Its dynamics is described by the force balance:

$M_{eq}\dot{v_{c}}=A_{p}p_{p}-A_{r}p_{r}-B_{v}v_{c}-F_{c}\,tanh(v_{c}/\gamma)\,{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Fr,c}}-F_{ext}$
(1)

where the notation generally refers to Figure 1 and $f_{Fr,c}$ is an incipient
fault due to increased friction.

Dynamical relations likewise give the pressure build-up in the piston-side and
the rod-side chambers:

$\dot{p_{p}}=\frac{\beta_{e,p}}{V_{0,p}+A_{p}x_{c}}(Q_{p}-A_{p}v_{c}-Q_{le,p}-Q_{li})$
(2)
$\dot{p_{r}}=\frac{\beta_{e,r}}{V_{0,r}+A_{r}(x_{c,max}-x_{c})}(-Q_{r}+A_{r}v_{c}-Q_{le,r}+Q_{li}),$
(3)

where $\beta_{e,i}$ is the effective bulk modulus of the oil for the
respective chamber. The bulk modulus of a fluid describes its ability to
resist compression. Such property is affected by the presence of air in the
fluid. The effective bulk modulus is introduced to account for this effect and
it is described by the following pressure-dependent equation:

$\beta_{e}=\frac{1}{\frac{1}{\beta_{oil}}+\varepsilon_{a}(p)\left(\frac{1}{c_{ad}p}-\frac{1}{\beta_{oil}}\right)}{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{B,e}}$
(4)
$\varepsilon_{a}(p)=\frac{1}{\frac{1-\varepsilon_{a,0}}{\varepsilon_{a,0}}\left(\frac{p_{atm}}{p}\right)^{\frac{-1}{c_{ad}}}+1}.$
(5)

Its value differs for different cylinder chambers and for the supply circuit.
The fault $f_{B,e}$ is related to the oil degradation, regardless of the part
of the plant where it first appears. For this reason, a unique value for
$\beta_{e}$ is used to describe the general effective bulk modulus, which
depends on the supply pressure $p_{s}$, introduced further down. An example of
the effective bulk modulus dependency on air content, pressure, and
temperature is described in [29]. Of the three, the air content is by far the
most significant, but as the system normally will be operating with pressures
well above 25 bar, changes in the effective bulk modulus will be very limited,
even for air content up to 10% volumetric air content (measured at atmospheric
pressure). Therefore, the model does not consider temperature as a state
variable. However, it is probably unlikely to detect a fault in the bulk
modulus in practice because of all the uncertainties associated with the
available models. Nevertheless, it is reported in the complete model to
highlight its importance.

The remaining terms in Equations 2 and 3 are the flow rates entering and
exiting from the chambers ($Q_{p}$ and $Q_{r}$), and the leakage flows. The
former are determined by the valve position and will be discussed later. The
latter include an external leakage from each chamber and an internal one
between the two of them:

$Q_{le,p}=C_{le,p}(p_{p}-p_{atm}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{le,p}}}$
(6)
$Q_{le,r}=C_{le,r}(p_{r}-p_{atm}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{le,r}}}$
(7)
$Q_{li}=C_{li}(p_{p}-p_{r}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{li}}}.$
(8)

Although cylinder leakage flows are negligible in the nominal plant, there may
be a minor cross-port leakage in the proportional valve (equivalent to
internal leakage in the cylinder). Therefore, modeling leakage in the above
three cases can be useful for separating the related faults $f_{Q_{le,p}}$,
$f_{Q_{le,r}}$ and $f_{Q_{li}}$ in three distinct equations.

###  2.2 Valves

The position of the cylinder is controlled by using a proportional valve (PV).
By varying the valve’s spool position, it is possible to regulate the flow
entering in the hydraulic cylinder chambers, performing the pitching action.
The equations describing the flows with respect to the valve’s spool position
are:

$\displaystyle Q_{p}=K_{v}(x_{v})$
$\displaystyle\left[\sqrt{|p_{s}-p_{p}|}sign(p_{s}-p_{p})H(x_{v})\right.$ (9)
$\displaystyle\left.-\sqrt{|p_{p}-p_{t}|}sign(p_{p}-p_{t})H(-x_{v})\right]{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{p}}}$
(10)
$Q_{rv}=-K_{v}(x_{v})\phi_{v}\sqrt{|p_{s}-p_{r}|}sign(p_{s}-p_{r})H(-x_{v}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{rv}}},$
(11)

where $H(\cdot)$ is the Heaviside step function for distinguishing the
different results for the different operating regions of the valve, i.e.,

$H(x)=\begin{cases}1,&x\geq 0\\\ 0,&x<0.\end{cases}$ (12)

Generally, the flow can be affected by a malfunctioning valve. Hence, the
possible faults $f_{Q_{p}}$ and $f_{Q_{rv}}$.

The valve is usually supplied by the manufacturer with an inner control loop
that sets the valve’s spool position to follow a reference, which is the
result of the upstream controller. The resulting valve closed-loop dynamics is

$\dot{v_{v}}+2\xi\omega_{0}\,{v_{v}}+\omega_{0}^{2}\,x_{v}{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Fr,v}}=\omega_{0}^{2}\,x_{v,ref}{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{wv,v}},\quad
x_{v,ref}=k_{u}u.$ (13)

Two possible faults can affect the valve: a mechanical fault similar to the
cylinder case, and an electrical one affecting the coils responsible for
moving the valve’s spool. The faults are kept separate to remark their
different nature.

Equation 11 describes the flow across the PV, which is generally different
than the flow to/from the rod-side chamber, given by

$Q_{r}=Q_{rv}+Q_{cv}.$ (14)

$Q_{cv}$ describes the flow through the check valve used for operating the
circuit in regenerative mode, for reducing the size of the supply circuit. The
equation for the flow in the check valve is given by

$Q_{cv}=K_{cv}(p_{r}-p_{s}-p_{cv,c})H(p_{r}+p_{cv,c}-p_{s}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{cv}}}.$
(15)

The valve can degrade or break. Thus, it introduces a possible fault
$f_{Q_{cv}}$ manifesting as flow perturbation.

###  2.3 Supply Circuit

Each cylinder-valve system is supplied by a common pressure source which is
located in the nacelle of the turbine. From a representation point of view,
the system is composed of a fixed displacement pump, an accumulator, and a
pressure relief valve ensuring that the system’s pressure is kept below a
certain limit. The pump charges the accumulator until the nominal system
pressure is reached, and its flow is then circulated through a filter back to
the tank. Hence, the pressure source during nominal operation is the
accumulator. As a consequence, the system’s pressure varies over time. The
equation describing the pressure dynamics at the accumulator is

$\dot{p_{s}}=\frac{1}{\frac{V_{oil}}{\beta_{eff,s}}+\frac{V_{gas}}{k\,p_{s}}}Q_{acc},$
(16)

where $Q_{acc}$ is the flow the accumulator exchanges with the rest of the
system, given by

$Q_{acc}=Q_{s}-Q_{rel}+\sum_{i=1}^{3}Q_{cv,i}-\sum_{i=1}^{3}Q_{v,i}\,{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{ru}}}.$
(17)

The flow $Q_{v}$ from the supply circuit to each of the proportional valves is

$Q_{v}=Q_{p}H(x_{v})-Q_{rv}H(-x_{v}).$ (18)

The flow $Q_{rel}$ through the relief valve, when the nominal pressure of the
plant is overtaken, is given by

$Q_{rel}=K_{rel}(p_{s}-p_{cr,r})H(p_{s}-p_{cr,r}){\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{Q_{rel}}}.$
(19)

Similarly to the other valves, the fault $f_{Q_{rel}}$ can be associated with
its rupture.

Finally, the volumes of oil and gas in the accumulator are given by

$V_{oil}=V_{acc}+V_{hose}-V_{gas}$ (20)
$V_{gas}=V_{acc}\left[\left(\frac{p_{gas,0}}{p_{s}}\right)^{1/k}H(p_{s}-p_{gas,0})\right]{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}+f_{acc}}.$
(21)

A faulty accumulator can lead to gas leaking into the oil. For a given
pressure, a reduction in the gas quantity is hence equivalent to a reduction
in the volume it occupies. Thus, the effect of this fault is modeled as a
volume perturbation $f_{acc}$.

###  2.4 Sensors

Generally, pressures in the chambers of each piston can be measured along with
the position of the rod.

Different sensors can be used for monitoring the plant. Generally, for each
piston, the position of the rod and pressures in the two chambers can be
measured. Each PV is provided with a closed-loop control circuit, which
leverages a position measurement for the control action to be established.
Potentially, such signals can be extracted and utilized for fault diagnosis
purposes. Finally, the pressure of the system can be measured. Other sensors,
such as e.g. flow rate sensors, exist and are possible to be installed.
However, they are not economically feasible. Hence, they are excluded from the
analysis.

The addition of each sensor implies the possibility that each of them can
fail, meaning that an equal number of faults need to be included in the model.

###  2.5 Fault Description

In the previous subsections, faults have been inserted as additive terms in
the equations describing the nominal plant operation. For setting up a
structural analysis, it is important to specify where the fault enters, as
that is the only relevant information for evaluating whether it is possible to
detect it or isolate it from other faults. In reality, since different faults
have different sources, they also have different properties as signals. This
information is only relevant in the design phase of the diagnostic tools.
Table 1 presents a basic description of all the faults according to [46, 2,
11, 37, 52, 28].

Table 1: Failure Modes. Please notice that the rating of the failures is based
on that a certain threshold is exceeded for each type of failure, where the
failure becomes significant.

Fault Name Fault Model Description Severity $f_{Fr,c}$
$\Delta_{B_{c}}v_{c}+\Delta_{F_{c}}\,tanh(v_{c}/\gamma)$ Increased friction in
the cylinder because of sludge formation. Not critical under a certain
threshold, but it can cause the cylinder to get stuck. In the initial phase it
appears as a variation of friction coefficients. High $f_{B,e}$ $\Delta_{B,e}$
Fault related to oil (i.e. gas) contamination, difficult to model differently
than a generic variation with respect to the nominal value. Medium
$f_{Q_{le,p}}\,f_{Q_{le,r}}$ $\Delta_{C_{le,i}}(p_{i}-p_{atm})$ Oil leakage
between a cylinder chamber and the outside. It can be slow or abrupt,
according to wear. Even with small values the turbine will be shut down. From
a control point of view, leakage do however act to increase the damping in the
system. High $f_{Q_{li}}$ $\Delta_{C_{li}}(p_{p}-p_{r})$ Oil leakage between
the two chambers in the cylinder. Same characteristics as the external one, it
just increases damping in the pitching. Low $f_{Q_{p}}\,f_{Q_{rv}}$
$\Delta_{K_{v}}[\cdot]$ Variation in the proportionality coefficient due to
mechanical wear of the valve, or by incorrect valve command. As long as the
valve is able to operate the severity is low. Low $f_{Fr,v}$
$2\Delta_{\xi}\Delta_{\omega_{0}}\,{v_{v}}+\Delta_{\omega_{0}}^{2}\,(x_{v}-x_{v,ref})$
Emergence of significant friction in the valve because of sludge formation or
wear. The effect is seen in the closed-loop dynamics parameters, and may lead
to the valve getting stuck with time. High $f_{wv,v}$
$\omega_{0}^{2}\Delta_{k_{u}}u$ Fault in the coil, leading to a wrong voltage
setting. It is modeled as a wrong position setting since the impact is
equivalent. High $f_{Q_{cv}}$ $\Delta_{Q_{cv}}$ It’s usually a discrete-time
nature fault leading to the valve getting stuck, more than leakages or a
variation in the proportional flow coefficient. High $f_{Q_{ru}}$
$\Delta_{Q_{ru}}$ Leakage flow in the rotary unit, i.e., the connection
between the pressure source and the three actuation circuits. Low
$f_{Q_{rel}}$ $\Delta_{Q_{rel}}$ It can be a variation in the proportional
coefficient, leakage, or a variation in the pressure at which it is triggered,
although these type of faults are rare. Low $f_{acc}$ $-V_{gas,l}$ Gas leakage
in the accumulator, with consequent reduction of the volume of gas, for a
given pressure. Generally slowly varying. Medium $f_{y,p_{s}}$ $f_{y,p_{p}}$
$f_{y,p_{r}}$ $\Delta_{y,p_{i}}$ Wrong measurement in the related pressure
sensor. Low $f_{y,x_{c}}$ $f_{y,x_{v}}$ $\Delta_{y,x_{i}}$ Wrong measurement
in the cylinder/valve position sensor. Position measurements are the only
signals used in the control loop. Hence, their importance. High

The fault description column provides information on how different faults are
related to each other. The severity of a given fault depends on how it
propagates in the system. Figure 2 illustrates such propagation properties of
the considered faults.

Figure 2: Diagram of most relevant fault modes and their causes.

The mathematical model and Table 1 do not include any description related to
the pump failure, as there is no dynamical relation associated with it. A
fault in the pump will, from an operational point of view, typically result in
reduced pump flow and ripples, leading to slower pressure build-up in the
system. One means of detecting such a fault is to monitor the pump pressure by
installing a pressure sensor in the vicinity of the pump.

##  3 Structural Analysis of the Benchmark Model

A mathematical model of a system can be translated into a set of constraints
for it. The violation of some of them is an indication that a fault occurred,
as the model is not able to describe the correct dynamics anymore. By
combining the information of the constraints with the knowledge of the
possible faults that may enter the plant, it is possible to understand which
of the latter are detectable and, eventually, isolable, with the given plant
configuration. It is worth remarking that these properties only depend on the
system’s structure and not on the design of the diagnostic system. Thus, a
structural analysis advises on possibilities for detectability and isolability
of faults in a system based on the knowledge of its structure, i.e., its
_structural detectability and isolability_ properties.

Structural analysis is a graph-based method to represent a system topology.
The basis is a graph consisting of: a) function blocks, each of which
represents constraints that describe behaviors of the function block; b)
variables in the system; c) paths that describe links between constraints and
variables. A system’s topology is described as a graph having constraints as
the set of vertices a), variables in the system, b), and edges c) that connect
the two types of vertices. The essence of structural analysis is to use tools
from the arsenal of graph theory to obtain causal matchings in the bi-
partitioned graph. A matching consists of a set of paths between unknown
variables and constraints [18]. When an unknown variable $x$ (e.g. a state or
a disturbance) is matched to a constraint $c$, the latter can be used for
calculating the unknown variable. When all unknown variables are matched to
constraints, any additional unmatched constraints can be used to describe
redundant information in a system and constitute so called residuals.
Residuals would be zero when there are no violations of normal behaviors and
some would be non-zero if one or more behaviors were violated. Structural
models were described at a tutorial level in [7] and references herein and
software tools are available for swift analysis of structural properties. The
SaTool [6] focuses on violation of constraints and residual generation,
including the computationally efficient method in [30].

Based on its graph-based representation, a system can be decomposed into three
subsystems, i.e., three sub-graphs. The _over-determined_ part contains
unknown variables that are all matched as well as unmatched constraints. The
_just-determined_ subsystem contains equal number of constraints and unknown
variables, which are matched to each other. Finally, the _under-determined_
part contains unmatched unknown variables. A necessary condition for fault
detection is that the over-constraint subsystem is nonempty and the under-
constraint subsystem is the empty set. The Dulmage-Mendelson (DM) algorithm
[17] is the original method for obtaining the structural decomposition of a
system. Constraints are divided into just-determined and over-determined
parts. If a fault appears in the just-determined part, no redundancy is
present, and it is not detectable. The redundant equations in the over-
determined part can be used for detecting faults that are affecting them. As a
result, faults in the over-determined part are structurally detectable.
Determining whether a fault is also isolable, requires a further analysis that
includes looking into generation of _residuals_. An efficient way of
determining the isolability properties was developed in [9].

###  3.1 Full Model Analysis

The analysis is carried out by referring to the equations stated in Section 2,
with the support of the ’Fault Diagnosis Toolbox’ from [22]. The standard
sensors present in a real system are utilized. The analysis hence delivers a
benchmark result for the capabilities of diagnosis in such a plant. Different
sensor configurations will be tested in Section 4 to obtain an equipment
topology that maintains the diagnostic features of the original one, but with
a reduced set of sensors. The Dulmage-Mendelson’s Decomposition for the
standardized hydraulic pitch system, together with the partition in equivalent
classes, is presented in Figure 3.

The faults related to friction in the three cylinders are the only faults that
appear in the just-determined part. Thus, they are not structurally
detectable. Such a result could be expected, as each term appears in the same
equations where the unknown variable $F_{ext}$ is present. When the friction
fault is active, there is insufficient information to distinguish between the
fault and a variation of the disturbance term. Furthermore, trying to estimate
the external force acting on the cylinder is not feasible from a practical
point of view, as reliable sensors aiming to measure it on an actual turbine
are characterized by excessive cost. Furthermore, assuming it is possible to
directly measure it, with a sensor that could get faulty, the DM decomposition
in Figure 4 shows that the friction faults become detectable but not
structurally isolable from the new faults introduced by the additional
sensors.

All the other faults are contained in constraints that belong to the over-
determined part of the system. Therefore, they are detectable. Furthermore,
most of the faults are located in different equivalent classes, making them
isolable. The two groups of faults for which this is not true are the valve
faults and the supply line faults.

Each couple of faults affecting the PV appear in the same equation (see
Equation 13), making it impossible to structurally isolate them. As mentioned
in Section 2.2, the two faults have been inserted separately to highlight
their different nature. The two faults are group-wise isolable with respect to
other faults, meaning that is structurally possible to isolate the valve as a
faulty component. Additionally, the model focuses on the description of the
hydraulic system and doesn’t account for the electrical dynamics of the
valve’s actuator, which is significantly faster and is considered as unmodeled
dynamics in an analysis of structural relations. Finally, the faults in
$Q_{p}$ and $Q_{rv}$ may also be affected by $f_{wv,v}$. This piece of
information can be leveraged during the diagnostic system design.

Figure 3: DM Decomposition for the full plant.

The other faults that are group-wise isolable are related to the supply line,
i.e., $f_{acc}$,$f_{Q_{ru}}$, and $f_{Q_{rel}}$. The oil leakages in the
rotary unit and in the relief valve are acting on the same part of the system,
i.e., the supply line. Thus, they are expected not to be distinguishable. The
gas leakage in the accumulator is affecting Equation 17, through 16 and 21, on
which both the other two faults are acting. The accumulator fault is a slow-
varying fault. In practice, it can be detected and isolated by estimating the
gas pre-charge pressure [36]. As a consequence, that fault could be removed
from the analysis and analyzed in this different framework. The other two
faults can be isolated in practice by placing two pressure sensors, for
example, before and after the rotary unit.

Figure 4: DM Decomposition for the full plant, measurement of $F_{ext}$.

###  3.2 Distinct Operation Regions

The hydraulic pitch system’s dynamics is characterized by different operating
regions, because of the presence of hydraulic valves and the accumulator. The
flow of each valve depends on the position of the related spool. The check
valve, the relief valve, and the volume of gas in the accumulator depend on
the relation between the system’s pressure and different pressure values
according to their characteristics. A table resuming the equations of interest
and the inequality conditions is stated in Table 2.

Table 2: Summary for distinct operation regions. Operation Regions | Equations | Variables | Condition
---|---|---|---
1,2 |  9, 11 | $x_{v}$ | $x_{v}\lessgtr 0$
3,4 | 15 |  $p_{r}$, $p_{s}$ | $p_{r}\lessgtr p_{s}-p_{cv,c}$
5,6 | 19 | $p_{s}$ | $p_{s}\lessgtr p_{cr,r}$
7,8 | 21 | $p_{s}$ | $p_{s}\lessgtr p_{gas,0}$

The different cases for each operating condition have been condensed into a
single equation by leveraging Heaviside functions. This way, structural
analysis was performed on the whole plant, and the result delivered the fault
detectability/isolability capabilities throughout all the operating regions.

In this section, each of them is analyzed to determine whether any of the
regions is limiting the performance of the system as a whole. The analysis is
carried out by considering a simplified setup in which only one valve-cylinder
pair is analyzed. In this way, the number of possible combinations is
drastically reduced from $4^{4}=256$ to $2^{4}=16$. In fact, each of the
additional subsystems is unrelated to each other, i.e., none of their
variables can be used to match any variables with another actuation subsystem.

Firstly, the DM decomposition is applied to the simplified system as a whole.
The result represents the benchmark for comparing the outcome of the different
cases. For a quick visual comparison between the different regions, the
toolbox provides an additional plot defined as ’isolability matrix’. If the
(i,j) element is not null, then fault j is diagnosed when fault i occurs. As a
consequence, the values only present on the diagonal are fully isolable, and
the ones grouped in squares around the diagonal element are groupwise
isolable.

Figure 5: Structural Analysis for plant with single cylinder: (a) DM
Decomposition. (b) Isolability Matrix: $f_{Fr,c}$ is not detectable, faults
$f_{Q_{rel}},f_{Q_{ru}},f_{acc}$ and $f_{F_{r,u}},f_{wv,v}$ are group-wise
isolable and all the other faults are isolable.

Non-isolable faults have non-zero elements on the related column. Non-
detectable faults are instead placed row-wise to distinguish them from the
non-isolable ones. Both the DM result and the related isolability matrix are
stated in Figure 5. As expected, the result follows the one in Section 3.1.
The two faults acting on the valve cannot be isolated, and the same applies to
the trio $f_{acc}$,$f_{Q_{ru}}$, and $f_{Q_{rel}}$. The cylinder friction
fault still can’t be detected. The same results are highlighted on the
isolability matrix.

The analysis of the separate operation regions follows the same procedure as
the previous one, where the equations containing a Heaviside function are
replaced with the one characterizing each specific case.

Figure 6: Isolability Matrices for all Operation Regions. Detectability and
isolability properties are independent of the operating regions.

The results are presented in the form of fault isolation matrices, as they
represent the most straightforward tool for comparison, in Figure 6. The
pattern of every plot coincides with every other and with the one in Figure 5.
The outcome is that the analysis performed in Section 2 is meaningful for all
the different conditions the plant is operating in. The full model can be
utilized for deriving conclusions about sensor placement for improved
diagnostic performance.

##  4 Sensor placement for topology improvement

The results presented in Section 2 constitute a benchmark for the
detectability and isolability properties of the system. Sensors have been
placed such that they measure all the variables that are measured in practice.
Each set of sensors measuring a different variable is defined as a sensor set,
which is present for each of the turbine blades.

Generally, by increasing a system’s redundancy thanks to the addition of more
sensors, it is possible to improve the detectability and isolability
properties of it. However, this is not the case for the topology under
analysis, where the impossibility of detecting or isolating certain faults
originates from the system structure and cannot be overcome by duplicating
existing sensors. Other quantities could, in principle, be measured. However,
placing such sensors is not feasible in real systems from an economic
standpoint. Thus, they are not included in the analysis. On the other hand, it
is possible that the performance presented in Section 2 can be obtained with a
lower degree of sensor redundancies.

In this section, different sensor combinations are investigated to determine
whether it is possible to achieve the same standard model performance, by
minimizing the number of sensors to be installed on the system. The tool that
has been applied is still the Structural Analysis Toolbox [22], by gradually
adding sensors and evaluating the performance.

The plant without any sensors is translated into a model containing an under-
determined part. No fault is neither detectable nor isolable, as expected.
Each sensor set is added and only the full sets
$\\{p_{p_{1}},p_{p_{2}},p_{p_{3}}\\}$, $\\{p_{r_{1}},p_{r_{2}},p_{r_{3}}\\}$
and $\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$ make the system just-determined.
Moreover, the combination of the two pressure measurements leads to the same
result, as long as one measurement per cylinder is provided. For example
$\\{p_{p_{1}},p_{p_{2}},p_{r_{3}}\\}$.

For each of the three just-determined models, each possible set of sensors is
added. The combination of $\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$ with either
$\\{p_{p_{1}},p_{p_{2}},p_{p_{3}}\\}$ or $\\{p_{r_{1}},p_{r_{2}},p_{r_{3}}\\}$
delivers isolability performances equivalent to the ones of the benchmark
model. The combination of each of $\\{p_{p_{1}},p_{p_{2}},p_{p_{3}}\\}$ and
$\\{p_{r_{1}},p_{r_{2}},p_{r_{3}}\\}$ with each other, or with any other set
between $p_{s}$ and $\\{x_{v_{1}},x_{v_{2}},x_{v_{3}}\\}$, does not lead to
any performance improvement. The same applies for the combination of
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$ with $p_{s}$ and/or
$\\{x_{v_{1}},x_{v_{2}},x_{v_{3}}\\}$.

The outcome of the analysis is that the maximum structural isolability
performance for such a plant is obtained by combining the measurement of the
position of each of the cylinders ($\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$),
with the pressure in one of the two chambers, for each piston
($\\{p_{p_{1}},p_{p_{2}},p_{p_{3}}\\}$, $\\{p_{r_{1}},p_{r_{2}},p_{r_{3}}\\}$,
or a correct combination of them). All the possible minimal sensor sets are
summarized in Table 3.

Table 3: Summary of minimal sensors set. Sensor Sets |  Description
---|---
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{1}},p_{p_{2}},p_{p_{3}}\\}$ |  Cylinder pistons positions, all piston-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{1}},p_{p_{2}}\\}$, $\\{p_{r_{3}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{1}}\\}$, $\\{p_{r_{2}},p_{r_{3}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{1}},p_{p_{3}}\\}$, $\\{p_{r_{2}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{2}}\\}$, $\\{p_{r_{1}},p_{r_{3}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{2}},p_{p_{3}}\\}$, $\\{p_{r_{1}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{p_{3}}\\}$, $\\{p_{r_{1}},p_{r_{2}}\\}$ |  Cylinder pistons positions, piston-side and rod-side pressures
$\\{x_{c_{1}},x_{c_{2}},x_{c_{3}}\\}$, $\\{p_{r_{1}},p_{r_{2}},p_{r_{3}}\\}$ |  Cylinder pistons positions, all rod-side pressures

The DM decomposition and the isolability matrix for both the original and
improved topology are stated for completion in Figure 7. In this particular
case, cylinder position and piston-chamber pressures are being measured.

Figure 7: Structural Analysis for plant with less sensors: (a) DM
Decomposition. (b) Isolability Matrix.

##  5 Discussion

Structural analysis was used to obtain an overview of the fault diagnosis
capabilities that can be achieved with the standard sensor configuration of
hydraulic pitch control systems. An initial analysis was carried out by
including all the possible sensors that such systems may include, i.e.,
pressure sensors for the supply circuit and both chambers of each cylinder,
position sensors for each cylinder, and position sensors for each valve.

In terms of isolability, two groups of violations of constraints were shown to
be group-wise isolable. The first group was represented by defects related to
the valve, i.e., changes in voltage or friction (Equation 13). The second
referred to leakages on the supply line, i.e., rotary unit leakage, relief
valve defect, or accumulator defect. All other defects that were inserted into
the system were shown to be isolable, which means that standard residual
generators will suffice to detect and isolate the root cause of the changes
they create in the pitch system signals.

The outcome of the detectability analysis was that the only fault that
couldn’t be detected from a structural perspective is an increased friction in
the cylinder. This was shown to be due to the presence of a disturbance term
in the same equation. This result from the structural analysis is very useful
indeed. It can be used to automatically generate residuals that achieve very
convincing coverage of detectability and isolability, and it points to the one
component in the system where supplemental effort is needed for condition
monitoring. The structural result does not imply that changes in cylinder
friction could not be detected. It just shows that the residuals auto-
generated by structural analysis would not suffice to capture changes in
cylinder friction separately from variations in load torques on the turbine
blades from wind. The estimation of cylinder friction is essential for pitch
system condition monitoring and will be subject for further scrutiny, [14].

The topology of a system may change in different operational modes, or
according to system excitation via different paths of control. This can be
utilized to enhance fault isolation over what is visible from the standard
structural isolability analysis. Active fault isolation is a set of techniques
where control inputs are excited and/or operational mode is changed, to
explore different input-to-output paths in topology. Structural results for
active fault isolation were presented in [7], and enhanced isolation by
shifting between operational modes, was shown for a water-hydraulic medical
”water for injection” plant in [32]. Methods for signal-based active isolation
enhance the structural results by using the time/frequency domain properties,
which structural analysis does not necessarily show. A generic setup for
active fault diagnosis was published in [51], with demonstration of active
diagnosis on a high fidelity wind turbine simulation in [43] where continuous-
time analysis and linear system assumptions were utilized.

##  6 Conclusions

This article provided an extended model that can be used for fault diagnosis
and fault tolerant control in hydraulic pitch systems of wind turbines. It
merged the dynamics during normal operation and all the major faults that
could occur in the system’s lifetime, together with a description of their
development and signal properties. The combination of these two pieces of
information was leveraged for deriving the structural detectability and
isolability properties achievable with the standard configuration presented,
by means of a Dulmage-Mendelson decomposition. Finally, different sensor
configurations were tested for reducing the level of redundancy while
maintaining the same isolability performances. The outcome was an indication
of the minimal sensor requirement for being able to maximize fault structural
isolability in the most generic scenario of wind turbine hydraulic pitching.

## CRediT autorship contribution statement

This paper is a collaboration between authors. A.D. is the main contributor
and is responsible for the conceptualization, formal analysis, investigation,
and most of the writing of the paper. M.B., H.C.P. and D.P. contributed to the
writing and with in-depth reviews throughout the process. All authors have
read and agreed to the published version of the manuscript.

## Declaration of competing interest

The authors declare no conflict of interest.

## Acknowledgements

This research was funded by The Danish Energy Technology Development and
Demonstration Programm (EUDP) through the project: “Decreased Cost of Energy
(CoE) from wind turbines by reducing pitch system faults”, grant number
64022-1058. The authors much appreciate this support.

## References

  * [1] Reza Mohammadi Asl, Yashar Shabbouei Hagh, Silvio Simani, and Heikki Handroos.  Adaptive square-root unscented Kalman filter: An experimental study of hydraulic actuator state estimation.  Mechanical Systems and Signal Processing, 132:670–691, October 2019\.
  * [2] Magnus F. Asmussen, Jesper Liniger, and Henrik C. Pedersen.  Fault Detection and Diagnosis Methods for Fluid Power Pitch System Components—A Review.  Energies, 14(5):1305, February 2021.
  * [3] Hamed Badihi, Youmin Zhang, Bin Jiang, Pragasen Pillay, and Subhash Rakheja.  A Comprehensive Review on Signal-Based and Model-Based Condition Monitoring of Wind Turbines: Fault Diagnosis and Lifetime Prognosis.  Proceedings of the IEEE, 110(6):754–806, June 2022.
  * [4] Mohamad Bahrami, Mahyar Naraghi, and Mohammad Zareinejad.  Adaptive super-twisting observer for fault reconstruction in electro-hydraulic systems.  Isa Transactions, 76:235–245, May 2018.
  * [5] Mogens Blanke, Michel Kinnaert, Jan Lunze, and Marcel Staroswiecki.  Diagnosis and Fault-Tolerant Control.  Springer, Berlin, Heidelberg, 2016.
  * [6] Mogens Blanke and Torsten Lorentzen.  SaTool - a Software Tool for Structural Analysis of Complex Automation Systems.  IFAC Proceedings Volumes, 39(13):629–634, 2006.
  * [7] Mogens Blanke and Marcel Staroswiecki.  Structural Design of Systems with Safe Behavior Under Single and Multiple Faults.  In Hong-Yue Zhang, editor, Fault Detection, Supervision and Safety of Technical Processes 2006, pages 474–479. Elsevier Science Ltd, Oxford, January 2007.
  * [8] James Carroll, Alasdair McDonald, and David McMillan.  Failure rate, repair time and unscheduled O&M cost analysis of offshore wind turbines: Reliability and maintenance of offshore wind turbines.  Wind Energy, 19(6):1107–1119, June 2016.
  * [9] Changxiong Chen, Liping Chen, and Xianjuan Cheng.  An efficient method for determining fault isolability properties based on an augmented system model.  European Journal of Control, 58:90–100, March 2021.
  * [10] Yusong Cheng, Jianze Wang, Kaoshan Dai, and Ashraf El Damatty.  Influence of mechanical faults in pitch, brake, controller systems on fragility of offshore wind turbine under aero-hydro loadings.  Ocean Engineering, 285:115386, October 2023.
  * [11] Seongpil Cho, Erin E. Bachynski, Amir R. Nejad, Zhen Gao, and Torgeir Moan.  Numerical modeling of the hydraulic blade pitch actuator in a spar-type floating wind turbine considering fault conditions and their effects on global dynamic responses.  Wind Energy, 23(2):370–390, February 2020.
  * [12] Seongpil Cho, Minjoo Choi, Zhen Gao, and Torgeir Moan.  Fault detection and diagnosis of a blade pitch system in a floating wind turbine based on Kalman filters and artificial neural networks.  Renewable Energy, 169:1–13, May 2021.
  * [13] Juying Dai, Jian Tang, Shuzhan Huang, and Yangyang Wang.  Signal-Based Intelligent Hydraulic Fault Diagnosis Methods: Review and Prospects.  Chinese Journal of Mechanical Engineering, 32(1):75, September 2019\.
  * [14] Alessio Dallabona, Mogens Blanke, and Dimitrios Papageorgiou.  Friction Estimation for Condition Monitoring of Wind Turbine Hydraulic Pitch System.  In Proc. IFAC SAFEPROCESS 2024 (Submitted), Ferrara, 2024\.
  * [15] Hoang Vu Dao, Duc Thien Tran, and Kyoung Kwan Ahn.  Active Fault Tolerant Control System Design for Hydraulic Manipulator With Internal Leakage Faults Based on Disturbance Observer and Online Adaptive Identification.  IEEE Access, 9:23850–23862, January 2021.
  * [16] Vladimir Djordjevic, Ljubisa Dubonjic, Marcelo Menezes Morato, Dragan Prsic, Vladimir Stojanovic, Vladimir Djordjevic, Ljubisa Dubonjic, Marcelo Menezes Morato, Dragan Prsic, and Vladimir Stojanovic.  Sensor fault estimation for hydraulic servo actuator based on sliding mode observer.  Mathematical Modelling and Control, 2(mmc-02-01-005):34–43, 2022\.
  * [17] A. L. Dulmage.  A structure theory of bipartite graphs of finite exterior dimension.  Trans. Roy. Soc. Canada, 3:1–13, 1959.
  * [18] A. L. Dulmage and N. S. Mendelsohn.  Coverings of Bipartite Graphs.  Canadian Journal of Mathematics, 10:517–534, 1958.
  * [19] Iker Elorza, Iker Arrizabalaga, Aritz Zubizarreta, Héctor Martín-Aguilar, Aron Pujana-Arrese, and Carlos Calleja.  A Sensor Data Processing Algorithm for Wind Turbine Hydraulic Pitch System Diagnosis.  Energies, 15(1):33, January 2022.
  * [20] Mahmoud Etemaddar, Mogens Blanke, Zhen Gao, and Torgeir Moan.  Response analysis and comparison of a spar-type floating offshore wind turbine and an onshore wind turbine under blade pitch controller faults: Response analysis of spar-type and onshore wind turbines under faults.  Wind Energy, 19(1):35–50, January 2016.
  * [21] Afef Fekih, Hamed Habibi, and Silvio Simani.  Fault Diagnosis and Fault Tolerant Control of Wind Turbines: An Overview.  Energies, 15(19):7186, September 2022.
  * [22] Erik Frisk, Mattias Krysander, and Daniel Jung.  A Toolbox for Analysis and Design of Model Based Diagnosis Systems for Large Scale Models.  IFAC-PapersOnLine, 50(1):3287–3293, July 2017.
  * [23] Juan Bueno Gayo.  Final Report Summary - RELIAWIND: Reliability focused research on optimizing Wind Energy systems design, operation and maintenance: Tools, proof of concepts, guidelines & methodologies for a new generation.  https://cordis.europa.eu/project/id/212966/reporting, 2011.
  * [24] Amin Yazdanpanah Goharrizi and Nariman Sepehri.  A Wavelet-Based Approach for External Leakage Detection and Isolation From Internal Leakage in Valve-Controlled Hydraulic Actuators.  Ieee Transactions on Industrial Electronics, 58(9):4374–4384, September 2011.
  * [25] Amin Yazdanpanah Goharrizi and Nariman Sepehri.  Internal Leakage Detection in Hydraulic Actuators Using Empirical Mode Decomposition and Hilbert Spectrum.  Ieee Transactions on Instrumentation and Measurement, 61(2):368–378, February 2012.
  * [26] IEA.  Wind Electricity – Analysis.  https://www.iea.org/reports/wind-electricity, 2022.
  * [27] IEA.  World Energy Outlook 2022.  https://www.iea.org/reports/world-energy-outlook-2022, 2022.
  * [28] H. Khan, S. Abou, and N. Sepehri.  Fault detection in electro-hydraulic servo-positioning systems using sequential test of Wald.  In IEEE CCECE2002. Canadian Conference on Electrical and Computer Engineering. Conference Proceedings (Cat. No.02CH37373), volume 3, pages 1628–1633, Winnipeg, Man., Canada, 2002\. IEEE.
  * [29] Darko Knežević, Aleksandar Milašinoviü, Zdravko Milovanovic, and Vladimir Saviü.  Analysis of Changes of Bulk Modulus of Mineral Oil - Effects on the Dynamic Behavior of Hydraulic Actuators.  In Proc. 12th 370 International Conference on Tribology, April 2011.
  * [30] M. Krysander, J. Aslund, and M. Nyberg.  An Efficient Algorithm for Finding Minimal Overconstrained Subsystems for Model-Based Diagnosis.  IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 38(1):197–206, January 2008.
  * [31] Jianyu Lan, Naichao Chen, Hongchuan Li, and Xudong Wang.  A review of fault diagnosis and prediction methods for wind turbine pitch systems.  International Journal of Green Energy, pages 1–28, September 2023\.
  * [32] Morten Laursen, Mogens Blanke, and Dilek Düştegör.  Fault Diagnosis Of A Water For Injection System Using Enhanced Structural Isolation.  International Journal of Applied Mathematics and Computer Science, 18(4):593–604, December 2008.
  * [33] Yong-bum Lee, Gi-chun Lee, Jong-dae Yang, Jong-won Park, and Dong-cheon Baek.  Failure analysis of a hydraulic power system in the wind turbine.  Engineering Failure Analysis, 107:104218, January 2020.
  * [34] Jesper Liniger.  Design of Reliable Fluid Power Pitch Systems for Wind Turbines.  The PhD Series of the Faculty of Engineering and Science, page Aalborg University, 2018.
  * [35] Jesper Liniger, Henrik C. Pedersen, and Mohsen Soltani.  Reliable Fluid Power Pitch Systems: A Review of State of the Art for Design and Reliability Evaluation of Fluid Power Systems.  In ASME/BATH 2015 Symposium on Fluid Power and Motion Control, page V001T01A026, Chicago, Illinois, USA, October 2015\. American Society of Mechanical Engineers.
  * [36] Jesper Liniger, Nariman Sepehri, Mohsen Soltani, and Henrik C. Pedersen.  Signal-Based Gas Leakage Detection for Fluid Power Accumulators in Wind Turbines.  Energies, 10(3):331, March 2017.
  * [37] Jesper Liniger, Mohsen Soltani, Henrik C. Pedersen, James Carroll, and Nariman Sepehri.  Reliability based design of fluid power pitch systems for wind turbines.  Wind Energy, 20(6):1097–1110, June 2017.
  * [38] Hongmei Liu, Dawei Liu, Chen Lu, and Xuan Wang.  Fault Diagnosis of Hydraulic Servo System Using the Unscented Kalman Filter.  Asian Journal of Control, 16(6):1713–1725, November 2014.
  * [39] Yanhua Liu, Ron J. Patton, and Shuo Shi.  Actuator fault tolerant offshore wind turbine load mitigation control.  Renewable Energy, 205:432–446, March 2023.
  * [40] Bin Lu, Yaoyu Li, Xin Wu, and Zhongzhou Yang.  A review of recent advances in wind turbine condition monitoring and fault diagnosis.  In 2009 IEEE Power Electronics and Machines in Wind Applications, pages 1–7, Lincoln, NE, USA, June 2009. IEEE.
  * [41] Ali Maddahi, Nariman Sepehri, and Witold Kinsner.  A Practical Approach for Designing Fault-Tolerant Position Controllers in Hydraulic Actuators: Methodology and Experimental Validation.  Journal of Dynamic Systems Measurement and Control-Transactions of the Asme, 142(8), August 2020.
  * [42] Yashar Mousavi, Geraint Bevan, and Ibrahim Beklan Kucukdemiral.  Fault-tolerant optimal pitch control of wind turbines using dynamic weighted parallel firefly algorithm.  ISA Transactions, 128:301–317, September 2022.
  * [43] Henrik Niemann, Niels Kjølstad Poulsen, Mahmood Mirzaei, and Lars Christian Henriksen.  Fault diagnosis and condition monitoring of wind turbines.  International Journal of Adaptive Control and Signal Processing, 32(4):586–613, April 2018.
  * [44] Kumarasamy Palanimuthu and Young Hoon Joo.  Reliability improvement of the large-scale wind turbines with actuator faults using a robust fault-tolerant synergetic pitch control.  Renewable Energy, 217:119164, November 2023.
  * [45] Pablo Castro Palavicino, Woongkul Lee, Bulent Sarlioglu, and Tatiana Minav.  On Faults and Diagnostics in Electrified Hydraulic Actuator Systems.  In 2018 20th European Conference on Power Electronics and Applications (Epe’18 Ecce Europe), New York, 2018. Ieee.
  * [46] Dimitrios Papageorgiou, Mogens Blanke, Hans Henrik Niemann, and Jan H. Richter.  Online friction parameter estimation for machine tools.  Advanced Control for Applications, 2(1):e28, 2020.
  * [47] Henrik C. Pedersen, Torben O. Andersen, and Jesper Liniger.  Investigation of Load Reduction Possibilities in Wind Turbines Using a Fluid Power Pitch System.  In Proceedings of the Asme/Bath Symposium on Fluid Power and Motion Control, 2015, page V001T01A051, New York, 2016. Amer Soc Mechanical Engineers.
  * [48] Van Du Phan and Kyoung Kwan Ahn.  Optimized-Based Fault-Tolerant Control of an Electro-Hydraulic System with Disturbance Rejection.  Applied Sciences-Basel, 12(18):9197, September 2022.
  * [49] Van Du Phan and Kyoung Kwan Ahn.  Fault-tolerant control for an electro-hydraulic servo system with sensor fault compensation and disturbance rejection.  Nonlinear Dynamics, 111(11):10131–10146, June 2023.
  * [50] Van Du Phan, Hoai Vu Anh Truong, and Kyoung Kwan Ahn.  Actuator failure compensation-based command filtered control of electro-hydraulic system with position constraint.  ISA Transactions, 134:561–572, March 2023.
  * [51] Niels Poulsen and Henrik Niemann.  Active Fault Diagnosis Based on Stochastic Tests.  International Journal of Applied Mathematics and Computer Science, 18(4):487–496, December 2008.
  * [52] Vignesh V. Shanbhag, Thomas J. J. Meyer, Leo W. Caspers, and Rune Schlanbusch.  Failure Monitoring and Predictive Maintenance of Hydraulic Cylinder—State-of-the-Art Review.  IEEE/ASME Transactions on Mechatronics, 26(6):3087–3103, December 2021.
  * [53] Siavash Sharifi, S. Mehdi Rezaei, Ali Tivay, Farzan Soleymani, and Mohammad Zareinejad.  Multi-class Fault Detection In Electro-hydraulic Servo Systems Using Support Vector Machines.  In 2016 4th Rsi International Conference on Robotics and Mechatronics (Icrom), pages 252–257, New York, 2016. Ieee.
  * [54] Kenan Shen and Dongbiao Zhao.  Fault Diagnosis for Aircraft Hydraulic Systems via One-Dimensional Multichannel Convolution Neural Network.  Actuators, 11(7):182, July 2022.
  * [55] Ziqiu Song, Jizhen Liu, Yajuan Liu, Yang Hu, and Fang Fang.  Fault-Tolerant Control of Floating Wind Turbine With Switched Adaptive Sliding Mode Controller.  IEEE Transactions on Automation Science and Engineering, pages 1–14, 2023.
  * [56] Xiaozhe Sun, Xingjian Wang, and Siru Lin.  Multi-Fault Diagnosis Approach Based on Updated Interacting Multiple Model for Aviation Hydraulic Actuator.  Information, 11(9):410, September 2020.
  * [57] Sandra Vasquez, Michel Kinnaert, and Rik Pintelon.  Active Fault Diagnosis on a Hydraulic Pitch System Based on Frequency-Domain Identification.  Ieee Transactions on Control Systems Technology, 27(2):663–678, March 2019.
  * [58] Paladugu Venkaiah, Bikash Kumar Sarkar, and Amitava Chaterjee.  Pitch control of electrohydraulic semi-rotary-actuated wind turbine with actuator and valve fault using generalized power-based exponential rate reaching law sliding mode controller.  Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 237(8):1423–1439, September 2023\.
  * [59] Julia Walgern, Katharina Fischer, Paul Hentschel, and Athanasios Kolios.  Reliability of electrical and hydraulic pitch systems in wind turbines based on field-data analysis.  Energy Reports, 9:3273–3281, December 2023.
  * [60] Qiao-Ning Xu, Kok-Meng Lee, Hua Zhou, and Hua-Yong Yang.  Model-Based Fault Detection and Isolation Scheme for a Rudder Servo System.  IEEE Transactions on Industrial Electronics, 62(4):2384–2396, April 2015.
  * [61] Yang Zhang, Shaoping Wang, Jian Shi, Xinyu Yang, Jiarui Zhang, and Xi Wang.  SAR performance-based fault diagnosis for electro-hydraulic control system: A novel FDI framework for closed-loop system.  Chinese Journal of Aeronautics, 35(10):381–392, October 2022.
  * [62] Z. H. a. O. Zhang, Z. H. O. N. G. Yang, S. H. U. C. H. a. N. G. Liu, S. H. U. a. N. G. Chen, and X. I. a. O. K. a. I. Zhang.  A Multi-Model Based Adaptive Reconfiguration Control Scheme for an Electro-Hydraulic Position Servo System.  International Journal of Applied Mathematics and Computer Science, 32(2):185–196, June 2022.
  * [63] Liwei Zhao, Shaoping Wang, Jian Shi, and Chao Zhang.  Fault diagnosis of hydraulic actuator based on improved convolutional neural network.  In 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM), pages 1–6, Vancouver, BC, Canada, August 2020. IEEE.