DETECTION OF HYDRAULIC CYLINDER LEAKAGE...Kalman Filter (EKF) is applied in a form of State...

DETECTION OF HYDRAULICCYLINDER LEAKAGE

OES10-4-F19

Aalborg UniversitySustainable Energy Engineering

Offshore Energy Systems

Aalborg Universityhttp://www.aau.dk

Title:Detection of HydraulicCylinder Leakage

Theme:Long Thesis:Advanced Controlof Offshore Energy Systems

Project Period:Fall Semester 2018 /Spring Semester 2019

Project Group:OES10-4-F19

Participant(s):Dominik Marija Rebic

Supervisor(s):Jesper Liniger

Copies: 1

Page Numbers: 31

Date of Completion:May 31, 2019

Abstract:

This Thesis investigates the applica-tion of Fault Detection and Diagnosis(FDD). Experiments were performedon the hydraulic crane setup at the Hy-draulics Laboratory at the AAU Esb-jerg Campus.Hydraulic and mechanical models ofthe system in question were ob-tained. Simulated and experimentaldata were compared and mathemati-cal non-linear model was validated.System modeling and validation isdone for the non-faulty system, laterintroduced with the faults, i.e. internaland external leakage.Since the main objective of the The-sis is to detect said faults, ExtendedKalman Filter (EKF) is applied in aform of State Augmented ExtendedKalman Filter (SAEKF). Leakage co-efficients are chosen for augmentedstates. Performance of the chosenmethod is investigated and discussed.

The content of this report is freely available, but publication (with reference) may only be pursued due to

agreement with the author.

http://www.aau.dk

Copyright c© Aalborg University 2019

Contents

List of Figures v

Preface vi

1 Introduction 11.1 Initiating problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 System Modeling 42.1 Hydraulic crane setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Hydraulic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Directional Control Valve (DCV) . . . . . . . . . . . . . . . . . 62.2.2 Hydraulic circuit decomposition . . . . . . . . . . . . . . . . . 62.2.3 Continuity equation . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 Flow equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Mechanical modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Force equation: Newton’s second law . . . . . . . . . . . . . . 112.3.2 Friction force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.3 System equation . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.4 Equivalent Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Open-loop Model Validation 153.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Simulink model . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.2 System noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Fault Detection and Diagnosis 194.1 Introduction to FDD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2.1 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

iii

Contents iv

4.2.2 EKF equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2.3 State-space model . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3 EKF results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Conclusion 295.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Bibliography 31

List of Figures

1.1 FTA of the hydraulic system . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Hydraulic crane setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Pantograph [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Schematic drawings of DCV in different working positions [4] . . . . 62.4 Hydraulic circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.5 Forces acting on the cylinder . . . . . . . . . . . . . . . . . . . . . . . 112.6 Friction forces [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.7 Trigonometric representation of the hydraulic crane . . . . . . . . . . 14

3.1 Simulink model of the hydraulic crane setup . . . . . . . . . . . . . . 163.2 Multiple step input ±10% and ±30% . . . . . . . . . . . . . . . . . . 173.3 Multiple step input ±30% and ±60% . . . . . . . . . . . . . . . . . . 18

4.1 Block diagram of a process in a model-based FDD [2] . . . . . . . . . 204.2 EKF Simulink model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Estimated and measured output comparison . . . . . . . . . . . . . . 254.4 Estimated leakage coefficients . . . . . . . . . . . . . . . . . . . . . . . 254.5 Estimated and measured output comparison . . . . . . . . . . . . . . 264.6 Estimated leakage coefficients . . . . . . . . . . . . . . . . . . . . . . . 274.7 Estimated and measured output comparison . . . . . . . . . . . . . . 274.8 Estimated leakage coefficients . . . . . . . . . . . . . . . . . . . . . . . 28

v

Preface

This Long Thesis was made by the Offshore Energy Systems Master programmestudent at the Aalborg University, Esbjerg as a 9th Semester Project and 10th SemesterThesis in one.

I would like to thank my supervisor Jesper Liniger for his supervision throughoutthe entire process and for always having patience and time to help.

I would also like to thank my beautiful family for constant support and encour-agement.

Lastly, to Irena, for all the love.

Aalborg University, May 31, 2019

Dominik Marija Rebic<[email protected]>

vi

Chapter 1

Introduction

1.1 Initiating problem

Wind turbines are currently designed for a 25-year service life with the possibil-ity of operational extension. Extending their efficient operation can significantlyincrease the return on investment and decrease the cost of electricity [1].

Hydraulic systems play a great role in modern industry, such as offshore wind en-ergy systems design. Recent years yielded in rapid growth of large wind turbinesdevelopment, thus increasing the impact on both safety and cost. Need for reliablesystems is therefore essential.

Reliability is described as the probability of a component or system to functioncorrectly over a certain period of time and for certain operating conditions [2]. Toensure the system is reliable and to minimize the possibility of a fault occurrence,systematic approach needs to be taken during the system design process. This isdone by identification procedures such as Failure Mode Effect Analysis (FMEA) orFault Tree Analysis (FTA) [1].

Fault Tree Analysis (FTA) uses a top-down approach where the system is brokendown into subsystems and components and connected using logic gates in orderto cover entire range of scenarios where a fault can occur and paths of the faultpropagation.

1

1.2. Problem decomposition 2

HYDRAULICSYSTEM

HOSES CYLINDER VALVES ACCUMULATOR

PISTONRING

PISTONSEAL

RUPTURE/DAMAGE

POORCONNECTION

WORNOUT

DAMAGE

PISTONROD

INTERNALLEAKAGE

INTERNALLEAKAGE

EXTERNALLEAKAGE

EXTERNALLEAKAGE

Figure 1.1: FTA of the hydraulic system

Figure above is showing certain causes and consequences of a cylinder leakage.Except possible component damage, leakage can also lead to hydraulic systemmalfunction and even emergency shut down. This means longer down-time andincrease in maintenance cost and time. More serious scenarios implicate healthand safety issues or even fatalities. Early leakage fault detection decreases saidevents while increases system reliability.

1.2 Problem decomposition

The goal of this project is to perform a Fault Detection and Diagnosis methodcalled Extended Kalman Filter on an experimental hydraulic crane setup in orderto detect level of cylinder leakage. This is done by augmenting the state-spacemodel with leakage coefficients as new states.

In order to achieve set goal, the initiating problem needs to be decomposed intothe following segments:

• Obtaining the hydraulic and mechanical model and building the simulationof the hydraulic crane process

• Validating model accuracy by comparing experiment and simulation data

1.2. Problem decomposition 3

• Extended Kalman Filter application on the hydraulic crane model and aug-menting the state-space model

• Validating the method used

As detecting cylinder leakage being the main focus of the project, three differentleakages are regarded:

• Internal cylinder leakage

• External leakage from piston side control volume

• External leakage from rod side control volume

Chapter 2

System Modeling

2.1 Hydraulic crane setup

Figure 2.1: Hydraulic crane setup

System in question is a hydraulic crane, an experimental setup located in the FluidPower Laboratory at the Aalborg University Esbjerg. The crane works on the pan-tograph principle with a hydraulic cylinder as the force actuator.

A pantograph is a mechanical device originally made for scaled drawing. Useris drawing while simultaneously copying the image in a larger or a smaller scale

4

2.2. Hydraulic modeling 5

(Figure 2.2). Based on the principle of two pairs of parallel lines intersecting, cor-responding angles and length ratios are preserved. Therefore, as the piston in thecylinder is extended/compressed, the crane end movement trajectory is propor-tionately enlarged.

Figure 2.2: Pantograph [3]

In the sections below it will be described how the mathematical model is obtainedby deriving and combining mechanical and hydraulic modeling.

2.2 Hydraulic modeling

Most of the hydraulic machines in use today operate hydrostatically – that isthrough pressure. In a hydrostatic device, power is transmitted by pushing ona confined liquid. A transfer of energy takes place because a quantity of liquid issubject to pressure [4].

The main components of the hydraulic crane system are:

• fluid (hydraulic oil) acting as a power transmitter, lubrication for the movingparts and protection against corrosion.

• crane accumulator which contains oil and enables the circular flow (both startand end point in the circuit); also regulates the fluid temperature since notalways the same fluid is in motion.

• hydraulic pump sets the fluid in motion from the tank.

• piston inside of the hydraulic cylinder which is displaced based on the fluidinflow in a certain chamber.

• filters needed to purify the oil from potential debris and fragments. Filtersmay be inserted in suction lines (to protect the pump), delivery lines (toprotect valves and actuators) and return lines (to remove picked up contami-nation) [4].


• Directional Control Valve controls the amount and direction of the fluid inthe system which indirectly controls the crane movement velocity.

2.2.1 Directional Control Valve (DCV)

Directional control valves belong to the group of valves controlling flow direction.Their purpose is to direct pump flow to an actuator as well as allow return flowfrom the same actuator to the reservoir. They are classified according to the numberof service ports and number of possible configurations (positions).

Figure 2.3: Schematic drawings of DCV in different working positions [4]

Valve employed on the system is a 4/3-way spool (type of the moving body gen-erating the different flow paths) directional control valve (four ports and threepossible positions: a, 0, and b, respectively) [4]. Figure 2.3 shows three differentworking regimes:

• regime a when xs > 0.

• regime 0 when xs = 0.

• regime b when xs < 0.

2.2.2 Hydraulic circuit decomposition

The circuit is decomposed in two control volumes: control volume A (volumeof the fluid between DCV and the piston in the cylinder), denoted as CVa and


control volume B (volume of the fluid between piston in the cylinder and DCV)CVb. Corresponding pressures pa and pb and fluid flow rates Qa and Qb are alsodenoted (Figure 2.4).

Figure 2.4: Hydraulic circuit

To obtain the hydraulic model, continuity and flow equations are derived for thesystem at hand.


2.2.3 Continuity equation

The basic principle behind the continuity equation is conservation of mass. Forthe control volumes in the regarded system, the mass flow rate Qa present in thecontrol volume CVa is not equivalent to the Qb present in CVb. This results with thecylinder displacement (crane movement) due to pressure build up in the system(Eq. 2.1).

Qin −Qout = V +Vβ· p (2.1)

Since the hydraulic circuit is divided into two control volumes, equation for eachis derived separately. Also, while building the equations, cylinder extension (up-wards motion) is considered.

CVa → Qa −Qi −Qea = Ap · xc +Ap · xc + Vh

β· pa (2.2)

CVb → −Qb + Qi −Qeb = −Ar · xc +Ar · (xc,max − xc) + Vh

β· pb (2.3)

Variable Value [Unit] DescriptionQa − [m3/s] Flow rate in the CVa

Qb − [m3/s] Flow rate out of the rod chamberQi − [m3/s] Flow rate of the internal leakage (piston to rode chamber)Qea − [m3/s] Flow rate of the external leakage (out of the CVa)

Qeb − [m3/s] Flow rate of the external leakage (out of the CVb)

Ap 3.117 · 10−3 [m2] Cross sectional area of the pistonAr 2.41 · 10−3 [m2] Cross sectional area of the piston rodxc − [m] Piston position in the cylinderxc − [m/s2] Piston velocity

xc,max 0.18 [m] Maximum piston position in the cylinderpa − [pa] Pressure in the CVa

pb − [pa] Pressure in the CVb

Vh 1.7671 · 104 [m3] Volume of the hoseβ 7000 · 105 [Pa] Bulk modulus

Table 2.1: Variables used in continuity equations


Bulk modulus

When pressurized a hydraulic fluid is compressed causing an increase in density.This is described by means of the compressibility. Reciprocal of the compressibilityis stiffness or bulk modulus of the fluid β. In real systems air will be present inthe fluid. The volume percentage at atmospheric pressure will go as high as 20 %.As air is much more compressible than the pure fluid, it has, potentially, a stronginfluence on the effective stiffness of the air containing fluid. The fluid stiffnessmay be calculated for any temperature and pressure combination regardless of thespecific type of mineral oil. For fixed temperature the stiffness is proportional tothe pressure rise caused by a compression of the fluid [4].

The ideal bulk modulus (no air in the fluid) is 16000 · 105 Pa (when the referencevolumetric ratio of free air in the fluid at atmospheric pressure ε0 = 0). As a rule ofthumb, the stiffness under working conditions used for modelling a system shouldnot be set above 10000 bars (10000 · 105 Pa) [4]. Hence, bulk modulus is chosen tobe 7000 · 105 Pa.

2.2.4 Flow equation

The flow restrictions or orifices are a basic means for the control of fluid power.An orifice is a sudden restriction of short length in a flow passage and may have afixed or variable area (variable for a valve) [4].

Most industrial hydraulic systems involve high-pressure flow through valve open-ings and the resulting flow is turbulent. A discharge coefficient Cd = 0.62 is typi-cally used for the high-pressure valve flow found in industrial hydraulic systems[5].

Substituting turbulent flow coefficient KT (Eq. 2.3) in general flow equation (Eq.2.4)

KT = Cd · Ad ·√

2ρ

(2.4)

Q = Cd · Ad ·√

2ρ· ∆p (2.5)

flow equation is then derived

Q = KT ·√

∆p (2.6)


and adjusted for the crane system:

Qa =

Kv1 · xs ·

√|ps − pa| · sign(ps − pa) for xs > 0

0 for xs = 0

Kv2 · xs ·√|pa − pt| · sign(pa − pt) for xs < 0

(2.7)

Qb =

Kv2 · xs ·

√|pt − pb| · sign(pt − pb) for xs > 0

0 for xs = 0

Kv1 · xs ·√|pb − ps| · sign(pb − ps) for xs < 0

(2.8)

Initially, the valve coefficient was assumed Kv = 4 · 10−7, but since upward anddownward motion yield in different pressures for the same (absolute) value of thevalve opening (i.e. xs = ±0.2 ), it needs to be tuned further. By the trial and errorapproach, valve coefficients are chosen:

• Kv1 = 4.16 · 10−7

• Kv2 = 3.87 · 10−7

Tuning the valve coefficient shows to be leading to the more accurate model.

Internal and external leakage flows are stated as well, even though for the non-faulty system, leakage coefficients are assumed zero and, therefore, leakage flowsare also assumed zero:

Qi = KLi · (pa − pb) (2.9)

Qea = KLea · pa (2.10)

Qeb = KLeb · pb (2.11)

Variable Value [Unit] Descriptionxs [−1, 1][%] Valve spool position

Kv1, Kv2 − [−] Valve coefficientKLi, KLea, KLeb − [−] Leakage coefficientQi, Qea, Qeb − [−] Internal and external leakage

Cd 0.62 [−] Discharge coefficientAd − [m2] Discharge areaρ − [kg/m3] Fluid density

Table 2.2: Variables used in flow equations

2.3. Mechanical modeling 11

2.3 Mechanical modeling

2.3.1 Force equation: Newton’s second law

Newton’s Second Law states that the sum of all forces ∑ F acting on the object isequal to its mass m multiplied by the acceleration of the object a. Adjusted for thecylinder in question, the equation is given:

∑ Fcylinder = Meq · xc (2.12)

Sum of the forces acting in the cylinder are represented on the free body diagramshown in Figure xx.

∑ Fcylinder = Fa − Fb − Ff − Fg (2.13)

Force Fa is acting on the piston upwards from the piston chamber in the cylinderand Fb downwards from the rod chamber side. Ff represents friction force and Fg

is a gravitational force of the cylinder.

Figure 2.5: Forces acting on the cylinder

2.3.2 Friction force

Friction is a force phenomenon which opposes relative movement between to sur-faces in contact [6]. Friction force vector is reverse-proportional to the piston move-ment direction: while cylinder is retracting, Ff acts upwards, and while extending,Ff acts downwards. Friction force, furthermore, is a combination of three compo-nents:


• Coulomb friction Fc. The Coulomb friction is a constant friction contributionand thereby the (absolute) value is not dependent on the velocity (graph a,Figure 2.6) [6].

• Viscous friction Fv. Assumed to be proportional to the velocity and expressedas a function of a viscous friction coefficient B multiplied with the velocity(graph b) [6].

Fv = B · xc (2.14)

• The Stribeck friction Fstb. Phenomenon influencing the operation at low veloc-ities is the Stribeck effect (graph c). The Stribeck effect is a friction contribu-tion at low velocities, which is decreasing exponentially from the differencebetween the stiction (Breakaway friction force) and the Coulomb force [6].

Fstb = (Fbrk − Fc)|xc| (2.15)

Figure 2.6: Friction forces [6]

Based on the LuGre model, the steady-state friction force for constant velocity(graph d) can be stated as [7]:

Ff = (Fc + Fstb) · sign(xc) + Fv (2.16)


2.3.3 System equation

Mathematical model can now be derived:

Meq · xc = pa · Ap − pb · Ar − [(Fc + Fstb) · sign(xc) + Fv]−mcrane · g (2.17)

where the equivalent mass Meq is a crane mass translated and acting on the top ofthe cylinder.

2.3.4 Equivalent Mass

To calculate the equivalent mass, Law of conservation of energy is employed. Sincekinetic energy at the top of the cylinder is equal to one at the center of the mass ofthe crane, the equation can be stated as:

Ek1 = Ek2 ⇒Meq · xc

2

2=

mcrane · x2crane

2(2.18)

where xc represents the change of the piston position and xcrane represents thechange of the crane (center of the mass) position. Mass of the crane is assumed tobe mcrane = 224kg

Further, assuming the almost-vertical movement of the center of the mass, equiva-lent mass is considered constant:

Meq =mcrane · x2

crane

xc2 (2.19)

By using basic trigonometry (denoted in the figure bellow), the relationship be-tween piston position and crane position is obtained as:

cos(θ) =xc

L1=

xcrane

L2⇒ xcrane =

xc · L2

L1(2.20)


Figure 2.7: Trigonometric representation of the hydraulic crane

Implementing Eq. 2.17 into Eq. 2.16 yields to the equivalent mass acting on thetop of the cylinder:

Meq = mcrane ·(

L2

L1

)2

= 7671.23kg (2.21)

Chapter 3

Open-loop Model Validation

3.1 Experimental setup

All the experiments done on the crane setup, both for model validation and laterfor the fault detection, are of the same nature. Multiple step-input is used sinceit will cover wide range of the system process dynamics, including transients andfriction force effect.

Crane is given an input in terms of valve opening. Data is obtained using SimulinkReal Time and Simulink crane model given. Sample time used was Ts = 1ms.

This is possible due to system being equipped with pressure sensors, position sen-sor for piston position, flow meter and leakage flow meters. Opening of the valveis controlled and monitored directly. Variables measured from all the experimentsare given in the table bellow:

Sensor Number of sensors Variables measuredDCV sensor 1 xs

Position sensor 1 xc

Pressure sensor 4 ps, pt, pa, pb

Flow meter 1 Qs

Leakage flow meter 2 Qi, Qea, Qeb

Temperature sensor 1 Ts

Table 3.1: Sensors in hydraulic circuit

3.2 Validation

To validate the mathematical non-linear model, hydraulic and mechanical modelsare combined in a simulink model, representing the system.

15

3.2. Validation 16

3.2.1 Simulink model

Data obtained by the experiments include measured source (pump) pressure de-noted as ps and tank pressure denoted as pt. This two variables will be two inputsto the simulink model and third input is a valve opening position.

After processing the data, open-loop model ends with five outputs: three are theremaining variables measured by sensors, i.e. piston position xc, piston side pres-sure pa and rod side pressure pb; other two are calculated and taken from thesimulation: change in piston position - piston velocity xc and change in pistonvelocity - piston acceleration xc.

Figure 3.1: Simulink model of the hydraulic crane setup

3.2.2 System noise

For better accuracy (and also for future purposes) process v and measurementnoise n are taken into account and added to the model as stated:

x(t) = f (x(t), u(t)) + v(t)

y(t) = g(x(t), u(t)) + n(t)

Both are considered white Gaussian noise with zero mean and a respective vari-ance.

It is possible to capture measurement noise directly from the measurement. Byobtaining the data when the crane is in a steady-state, and removing the meanvalue from the data-set, variance can be determined for each variable. As such, itis implemented in the model:

3.3. Results 17

• measurement noise variance for position: σ2position = 1.7 · 10−6

• measurement noise variance for pressure: σ2pressure = 1.4 · 109

On the other hand, it is difficult to determine the process noise as it is not possibleto directly observe the process needed to be estimated, but also due to uncertaintiesin the system [8]. Process noise is therefore chosen as:

• process noise variance for position: σ2position = 1 · 10−3

• process noise variance for pressure: σ2pressure = 1 · 105

Due to system being non-linear it needs to be verified whether the system dy-namics and transient behaviours are modeled correctly and what is the degree ofaccuracy.

Each data-set obtained by the experiments is compared with the data-set from thesimulation. Piston side pressure, rod side pressure and piston position are thevariables that will be compared.

3.3 Results

0 1 2 3 4 5-1

0

1

2

3

4

5

6

Pre

ssur

e [P

a]

106 Piston side pressure

measured pacalculated pa

0 1 2 3 4 5-1

0

1

2

3

4

5

6

Pre

ssur

e [P

a]

106 Rod side pressure

measured pbcalculated pb

0 1 2 3 4 5

Time [s]

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Pos

ition

[m]

Piston position

measured xccalculated xc

0 1 2 3 4 5

Time [s]

-40

-20

0

20

40

Val

ve o

peni

ng [%

]

Valve opening

measured xsreference xs

Figure 3.2: Multiple step input ±10% and ±30%

3.3. Results 18

0 1 2 3 4 5-1

0

1

2

3

4

5

6Pr

essu

re [P

a]106 Piston side pressure

measured pacalculated pa

0 1 2 3 4 5-1

0

1

2

3

4

5

6

Pres

sure

[Pa]


measured pbcalculated pb

0 1 2 3 4 5Time [s]

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Posi

tion

[m]

Piston position

measured xccalculated xc

0 1 2 3 4 5Time [s]

-60

-40

-20

0

20

40

60

Valv

e op

enin

g [%

]

Valve opening


Figure 3.3: Multiple step input ±30% and ±60%

Figure 3.2 and 3.3 show comparison of two data-sets with their respective simu-lated data. In both cases simulated piston position is accurate to a high degree.Piston side pressure comparison shows that the main dynamic behaviours aremodeled properly. On the other hand, inconsistencies in rod side pressure aremainly influenced by valve coefficients as they were used as a tuning parameter.Any other set of valve coefficients would lead to a greater offset in both pressures.

Wide range of valve opening is covered and both simulated data-sets have similaraccuracy level. This indicates that the model accuracy does not depend on theinput in terms of the valve opening.

Overall inconsistencies could be also caused by a number of factors such as param-eter approximation, input signal noise or offset in the sensors. Regardless, derivedmathematical model is considered accurate.

Chapter 4

Fault Detection and Diagnosis

In the following chapter, the working principle of Fault Detection and Diagnosis(FDD) is briefly introduced. Analysis of the experimental application of ExtendedKalman Filter (EKF) for the hydraulic crane model is done and the obtained resultsare discussed.

4.1 Introduction to FDD

First, the difference between fault detection and fault diagnosis (isolation) needs tobe established. Fault detection system tells if a fault occurred. Fault diagnosis goesfurther into analysis and determines the location in the system where the faultoccurred and estimates the severity of the fault.

Fault detection and diagnosis tackles the following problem: for a system to bereliable and safe, automated supervision needs to be ensured through monitoringand automated protection. In the case when exceeding a threshold leads to systemoperating in a safety-critical state, the system should automatically enter a fail-safestate, which is often an emergency shut down [2]. FDD methods are distinguishedas: data-based and model-based methods [2]. A figure below shows the principleof a model-based FDD in a block diagram.

19

4.2. Extended Kalman Filter 20

Figure 4.1: Block diagram of a process in a model-based FDD [2]

Using available input and output information from the observed system, FDDgenerates a fault indicating signal, i.e., residual. Based on the residual, system issaid to be non-faulty (residual will be zero or close to zero), or faulty (for non-zeroresidual) [9].

4.2 Extended Kalman Filter

Extended Kalman Filter, a non-linear interpretation of Kalman filter, is a model-based FDD method based on linearization about the current state estimation [8].

In order to detect leakage faults, EKF is applied to the hydraulic crane model.Leakage coefficients are parameters considered in the system modeling. Theirparameter estimates are expected to detect faults. This is done by augmenting thesystem.

4.2.1 State of the art

In their paper [10], Liniger, Pedersen and Soltani present a brief review of stateof the art for designing reliable fluid power pitch systems. Review of methods islimited to the work publicly available whereby industry research is not includedunless evident from patents [10].


Choux, Tyapin and Hovland in [11] use two approaches to determine internaland external leakage flows in an experimental hydraulic test bed representing awind turbine: residual errors based on different assumptions on the leakage usingExtended Kalman Filter (EKF) and leakage detection from augmented states usingState Augmented Extended Kalman Filter (SAEKF).

Both approaches are based on source pressures and cylinder piston position mea-surements as inputs. The non-linear model was verified through the experimentaldata for state estimation.

Results presented show that both EKF and SAEKF can detect both external andinternal leakages in the hydraulic system. The computational time using SAEKFmethod was said to be approximately 12 times higher than those required by EKF[11], thus it is suggested to use a combination of EKF for leakage detection andSAEKF for the leakage isolation and diagnosis.

Since in [11] leakage flows as augmented states are used, for the purpose of thisresearch, similar approach is taken. SAEKF will be used with internal and bothexternal leakage coefficients as augmented states.

4.2.2 EKF equations

For the non-linear discrete system given by:

xk+1 = f (xk, uk) + vk (4.1)

yk = g(xk, uk) + nk (4.2)

process noise vk and measurement noise nk are stochastic variables assumed tobe statistically independent with a Gaussian distribution with zero mean and thecovariance matrices M and N, respectively.

EKF state estimation is done through the iteration process, for each time-step k,using following algorithm of prediction and update equations as stated in [2]:

Update

Predicted next state estimate:

xk+1|k = f (xk, uk) (4.3)

Predicted state error covariance:

P−k+1 = APk AT + M (4.4)


Correction

Kalman gain:Kk+1 = P−k+1CT[CP−k+1C + N]−1 (4.5)

Next state estimate:

xk+1|k+1 = xk+1|k + Kk+1[yk+1 − Cxk+1|k] (4.6)

State estimate error covariance:

Pk+1 = [I − Kk+1C]P−k+1 (4.7)

The derivation of the Kalman filter is valid only for the linear systems, thereforeJacobian system process matrices A and C are needed to be linearized around thepredicted state estimate for each time-step k [8]:

Ak+1|k =∂ f (xk, uk)

∂xk

∣∣∣∣∣xk+1|k ,uk

(4.8)

Ck+1|k =∂g(xk, uk)

∂xk

∣∣∣∣∣xk+1|k ,uk

(4.9)

4.2.3 State-space model

State-space model for the system at hand is obtained:

State, input and output (measurement) vectors

x =

x1

x2

x3

x4

x5

x6

x7

=

xc

xc

pa

pbKLiKLea

KLeb

; u =

u1

u2

u3

=

xs

ps

pt

; y =

y1

y2

y3

=

xc

pa

pb

(4.10)


Differential state equations

x =

x1

x2

x3

x4

x5

x6

x7

=

xc

xc

pa

pbKLiKLea

KLeb

=

for xs > 0:

x2

x3 · Ap − x4 · Ar + [(Fc + (Fbrk − Fc)|x2|) · sign(x2) + Fv]−mcrane · gMeq

[(Kv1 · u1 ·√|u2 − x3| · sign(u2 − x3))− x5 · (x3 − x4)− x6 · x3 − Ap · x2] · β

Ap · x1 + Vh[(Kv2 · u1 ·

√|u3 − x4| · sign(u3 − x4)) + x5 · (x3 − x4)− x7 · x4 + Ar · x2] · β

Ar · xcmax − x1 + Vh000

(4.11)

for xs < 0:

x2

x3 · Ap − x4 · Ar + [(Fc + (Fbrk − Fc)|x2|) · sign(x2) + Fv]−mcrane · gMeq

[(Kv1 · u1 ·√|x3 − u3| · sign(x3 − u3))− x5 · (x3 − x4)− x6 · x3 − Ap · x2] · β

Ap · x1 + Vh[(Kv2 · u1 ·

√|x4 − u2| · sign(x4 − u2)) + x5 · (x3 − x4)− x7 · x4 + Ar · x2] · β

Ar · xcmax − x1 + Vh000

(4.12)

Covariance matrices and initial conditions

Assuming noises are stationary, covariance matrices are considered constant. Thus,N and M are diagonal matrices chosen as:

N = diag[1.7e− 6 1.4e9 1.4e9] (4.13)

4.3. EKF results 24

M = diag[1e− 3 1e− 5 1e5 1e5 1e− 16 1e− 11 1e− 13] (4.14)

It should be noted that covariance matrix N values correspond to respective mea-surement noise variance as stated in the section 3.2.2. Covariance matrix M is usedas a tuning parameter for the EKF.

Initial state estimate x0 needs to be chosen which is usually first measurementvalue when the data is available or otherwise, reasonably assumed values. Finally,corresponding initial state error covariance is chosen to be:

Po = M · 10 (4.15)

4.3 EKF results

Once the simulink model (Figure 4.2) including the system process and the EKF isbuilt, its implementation needs to be validated.

Figure 4.2: EKF Simulink model

First, the data-set used for validating the hydraulic system model is used (shownin the Figure 3.3). Input to the EKF are vectors u and y from Eq. 4.10, experimentobtained measurements. No leakage is introduced to the simulation.

4.3. EKF results 25

0 1 2 3 4 5-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Posi

tion

[m]

Piston position

estimated y1measured y1

0 1 2 3 4 50

1

2

3

4

5

6

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

0

1

2

3

4

5

6

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

-40

-20

0

20

40

Valv

e op

enin

g [%

]

Valve opening

measured xsrefference xs

Figure 4.3: Estimated and measured output comparison

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

210-10 Internal leakage coefficient K Li

estimated x5reference x5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20

-15

-10

-5

010-10 External leakage coefficient KLea


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time [s]

-10

-5

0

5 10-10 External leakage coefficient KLeb


Figure 4.4: Estimated leakage coefficients

As seen in the Figure 4.3, EKF is able to estimate output accurately. Estimatedpressures are more noisy than measurements as expected, while piston positionestimate is almost identical as the measured.

4.3. EKF results 26

While from the Figure 4.3 it could easily be concluded that the EKF is correctlyimplemented, that claim would be incomplete without first observing the nextfigure. Since the scope of this research is to investigate State Augmented EKFimplementation, Figure 4.4 gives information on how augmented states are wellestimated.

Estimated leakage coefficients fail to follow reference signal, or at least, deviationfrom the expected values is significant. On the other hand, both estimated exter-nal leakage coefficients gravitate around zero, while internal leakage coefficientestimate discrepancy increases with time.

This could be explained by the fact that the leakage coefficients estimation containsome information from interacting with pressure state estimates. Moreover, fluc-tuating input (valve opening) also needs to be taken into consideration. Furtheranalysis will be carried out using the data-set obtained with a simple constant fora valve opening as an input. Again, leakage is not introduced.

0 1 2 3 4 50

0.05

0.1

0.15

0.2

Posi

tion

[m]

Piston position


0 1 2 3 4 50

1

2

3

4

5

6

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

0

0.5

1

1.5

2

2.5

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

16

17

18

19

20

21

22

23

Valv

e op

enin

g [%

]

Valve opening



4.3. EKF results 27

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

0

1

2

3 10-10 Internal leakage coefficient K Li


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

0

510-10 External leakage coefficient KLea


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time [s]

-2

-1

0

1 10-9 External leakage coefficient KLeb



Results obtained using constant as an input again show good output estimationand poor leakage coefficient estimation, although with more stable values. Next,the same data-set will be used but with introducing the external leakage KLea =

3e− 11 after one second into simulation.

0 1 2 3 4 50

0.05

0.1

0.15

Posi

tion

[m]

Piston position


0 1 2 3 4 50

1

2

3

4

5

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

0

1

2

3

4

5

6

Pres

sure

[Pa]



0 1 2 3 4 5Time [s]

16

17

18

19

20

21

22

23

Valv

e op

enin

g [%

]

Valve opening



4.3. EKF results 28

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10 10-10 Internal leakage coefficient K Li


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2

-1

0

1 10-9 External leakage coefficient KLea


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time [s]

-2

-1

0

110-9 External leakage coefficient KLeb



When the leakage is introduced to the process, output estimation remains fairlyaccurate, but more noisy. Introduced leakage leads to both piston and ring sidepressure drop as expected. Leakage coefficient estimation shows more informationnow: although values still deviate beyond desired, abrupt change can be seen at t =1s for external leakage coefficient KLea which indicate good EKF implementation.Drawback is that the change in KLea results also with the change in estimation ofKLeb.

Conclusion is that the State Augmented EKF could still be a good choice of methodfor estimating leakage coefficients, but the approach should be modified. Insteadof having three augmented states at once, system should be augmented with oneleakage coefficient at the time, leading to having five state augmented system threetimes in order to being able to capture all planned leakages.

Chapter 5

Conclusion

5.1 Discussion

In the introduction, the goal of the project was said to be application of the EKF onthe experimental setup in order to estimate the artificially implemented leakage.Internal and external leakage was only considered; internal representing leakagedue to piston seal being damaged/worn out and external representing fluid lossfrom piston side or rod side control volumes.

While obtaining the model, non-faulty system was considered. Mathematical modelderived consists of mechanical and hydraulic parts which were modeled separatelyand later combined in a simulink model. Due to complexity of the system, variousassumptions and approximations were made.

Hydraulic crane was employed as an experimental setup in order to obtain mea-surements which will then be used as input to the simulation and as a referencefor validation. System model was validated and said to be sufficiently accurate forEKF implementation.

FDD is performed in such way that the EKF, a non-linear version of regular Kalmanfilter, was adapted for the hydraulic system and augmented with leakage coeffi-cients as states. Their estimation was expected to detect faults. Although EKF wascorrectly implemented, augmenting the state-space model with three states did notyield to successful results. SAEKF failed to estimate leakage coefficients even forthe non-faulty system. It is concluded that the SAEKF should be performed byaugmenting only one leakage coefficient at the same time.

5.2 Future work

In addition to work presented, various improvements would lead to better perfor-mance of both obtained mathematical model and the EKF leakage estimation.

29

5.2. Future work 30

Better model accuracy

• Equivalent mass was assumed constant while in practice it is a function ofthe piston position.

• Since calculated pressures show inconsistencies compared to the measuredpressures, analysing unaccounted valve leakages could mitigate the discrep-ancy.

• Further analysis of parameters used for modeling the friction force wouldlead to better tracking system dynamics.

• Deeper analysis of Bulk modulus should be carried out.

EKF estimation

• Reducing the state-space model to a five state EKF with one leakage coef-ficient as augmented state should solve the problem of current augmentedstates not being able to estimate true leakage coefficient.

• Implementing bank of such EKFs in order to estimate all considered leakagecoefficients.

Bibliography

[1] Kolios A. Martinez Luengo M. Failure Mode Identification and End of Life Sce-narios of Offshore Wind Turbines: A Review. www.mdpi.com/journal/energies.2015.

[2] Rolf Isermann. Fault-Diagnosis Systems: An Introduction from Fault Detection toFault Tolerance. Springer. 2006.

[3] Meccano Manuals 1908 - 1981. https://www.meccanoindex.co.uk/Mmanuals/l2photo.php?Nmbr=12773id=1551104801, 25/02/2019.

[4] Michael Rygaard Hansen Torben Ole Andersen. Fluid Power Circuits: SystemDesign and Analysis. Third Edition. 2007.

[5] Craig A. Kluever. Dynamic Systems: Modeling, Simulation and Control. 2015.

[6] C. Hvoldal M.; Olesen. Friction Modelling And Compensation On A HydraulicAsymmetrical Cylinder. 2011.

[7] C. C. Åström K. J.; de Wit. Revisiting the LuGre friction model. IEEE ControlSystems Magazine, Institute of Electrical and Electronics Engineers. 2008.

[8] Gary Welch Greg; Bishop. An Introduction to the Kalman Filter.https://courses.cs.washington.edu/courses/cse571/03wi/notes/welch-bishop-tutorial.pdf. 2001.

[9] Zhenyu Yang. ZY-Lecture-2: State-Estimation-Based FDD Methods. Lecture Slidesfor Course: Fault Tolerant Control. 2018.

[10] Mohsen Soltani Jesper Liniger Henrik C. Pedersen. Reliable Fliud Power PitchSystems - A Review of State of the Art for Design and Reliability Evaluation of FluidPower Systems. 2006.

[11] Tyapin I. Hovland G. Choux M. Leakage-Detection in Blade Pitch Control Sys-tems for Wind Turbines. 2012.

31

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