KTH ROYAL INSTUTE OF TECHNOLOGY

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Master of Science Thesis Report

Harsha Cheemakurthy

Student | M.Sc. Naval Architecture

Load case analysis for a resonant

Wave Energy Converter

HARSHA CHEEMAKURTHY

Master of Science Degree Project in

Naval Architecture

Stockholm, Sweden 2015

KUNGLIGA TEKNISKA HÖGSKOLAN

MASTER THESIS

Load Case Analysis for a Resonant Wave Energy Converter

A thesis submitted in fulfillment of the requirements

for the degree of Master of Science

in the

Faculty of

Naval Architecture

Student Harsha Cheemakurthy

Supervisor Gunnar Steinn Ásgeirsson

Pär Johannesson

Examiner

Anders Rosén

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KUNGLIGA TEKNISKA HÖGSKOLAN

Abstract

Faculty Name

Naval Architecture

Master of Science Thesis

Load Case Analysis for a Resonant Wave Energy Converter

by Harsha Cheemakurthy

As we progress beyond the information age, there is a growing urgency towards sustainability. This word

is synonymous with the way we produce energy and there is an awareness to gradually shift towards

green energy production. Corpower Ocean aims at producing energy by utilizing the perpetual motion of

ocean waves through the motion of small floating buoys. Unlike previous designs, this buoy utilizes the

phenomenon of Resonance thus greatly enhancing the energy output.

In the thesis, the simulation model developed by Corpower Ocean to virtually describe the buoy in

operation was validated. This was done by comparing forces obtained from buoy scale model

experiments, simulation model and ORCAFELXTM software. After satisfactory validation was established,

the shortcomings in the simulation model were identified. Next the simulation model was used to

generate data for all sea states for a target site with given annual sea state distribution. This information

was then used to predict ultimate loads, statistical loads, motions and equivalent load for a given fatigue

life and loading cycles. The results obtained are then treated with a statistical tool called Variation Mode

and Effect Analysis to quantify the uncertainty in design life prediction and estimate the factor of safety.

The information will be used by the design team to develop the buoy design further. Finally the issue of

survivability was addressed by checking buoy behavior in extreme waves in ORCAFLEXTM. Different

survivability strategies were tested and videos were captured for identifying slack events and studying

buoy behavior in Extreme conditions.

The work aims at validating a technology that is green from environmental and economic point of view.

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Acknowledgements This master thesis is the culmination of all the knowledge that I gained during the past two years at KTH University,

Stockholm. I want to express my gratitude to CorPower Ocean for giving me an opportunity to use my knowledge

towards the development of a green energy solution. I feel there is a growing awareness towards non-

conventional sources of energy and technology like the Corpower WEC will greatly boost the motivation for

governments and companies to adopt green technology. I greatly enjoyed working and learning about wave

energy. It was very interesting to learn about the technology behind the WEC and also got an insight of how

development of new technology is managed. At the company, I really liked the atmosphere. There was a lot of free

exchange of ideas, discussions and independence and different stages of thesis. Along with this, there were several

mentors who were experts in their fields who guided me and gave valuable advice.

I would like to thank my supervisor at Corpower Ocean, Gunnar Steinn Ásgeirsson for constantly guiding me and

supporting with all my queries. I am really grateful for all the help that I received from him in terms of meetings,

supporting files and most importantly advise. His composed style of working was a great inspiration to me to look

at producing results and perform better analyses.

Then, I would like to thank my supervisor at SP, Pär Johannesson for meeting several times and guiding me

towards development of load case analysis and fatigue analysis. I learnt a lot about fatigue and statistical measures

under his guidance and was really inspired by his diligence and systematic approach.

I would like to thank the CEO of Corpower Ocean, Patrik Möller, for giving me the opportunity to do my master

thesis. His attitude is very encouraging and his ambition greatly inspiring me. Working under his leadership has

greatly convinced me to work in the field of green technology.

I would like to thank other people at Corpower Ocean, especially Oscar Hellaeus for his guidance in fatigue analysis

results extraction and Luiza Acioli for the collaborative work in slack event identification.

I would like to thank Matthieu Guérinel for running the simulation model in software and extracting the results.

I would like to thank for Dr. Jørgen Hals Todalshaug and Prof. Stefan Björklund for his inputs in Load Case Analysis

and Fatigue Estimations for mechanical parts.

I would like to express immense gratitude to Prof. Anders Rosén for helping me choose the topic of my thesis

work, guiding me in developing a project plan and keeping regular meetings to track my progress. I would like to

thank him for teaching core subjects and being a mentor.

Finally, I would like to thank my family and friends, especially my parents for constantly supporting me right from

day one. I feel immense gratitude for the love and support they have given me.

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Table of Contents

Abstract ......................................................................................................................................... 1i

Acknowledgements ...................................................................................................................... 2ii

Table of Contents ........................................................................................................................ 3iii

Abbreviations .............................................................................................................................. 6vi

Symbols...................................................................................................................................... vii

Chapter 1 ...................................................................................................................................... 1

Introduction .................................................................................................................................. 1

1.1 Thesis Statement .............................................................................................................. 1

1.2 Motivation ........................................................................................................................ 1

1.3 Objectives and Deliverables ............................................................................................. 2

1.4 Thesis Project Overview ................................................................................................... 3

1.5 Thesis Contributions to Project ........................................................................................ 4

Chapter 2 ...................................................................................................................................... 6

Background .................................................................................................................................. 6

2.1 Introduction ...................................................................................................................... 6

2.2 About Corpower Ocean (CPO) ......................................................................................... 6

2.3 The Wave Energy Converter ............................................................................................ 6

2.4 Forces acting on the WEC and its Equations of Motion ................................................. 13

2.5 WEC Scale Model Experiments ...................................................................................... 17

2.6 Simulation Model in SimulinkTM by CPO ........................................................................ 20

Chapter 3 .................................................................................................................................... 22

Theory ........................................................................................................................................ 22

3.1 Introduction .................................................................................................................... 22

3.2 Wave Energy ................................................................................................................... 22

3.3 Coordinate System ......................................................................................................... 28

3.4 Ocean Wave Theory ....................................................................................................... 29

3.5 Structure Failure Criteria ................................................................................................ 37

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3.6 Fatigue Theory and Estimation of Design Life ................................................................ 38

3.7 Modeling in OrcaflexTM .................................................................................................. 44

3.8 Variation Mode and Effect Analysis (VMEA) .................................................................. 47

Chapter 4 .................................................................................................................................... 51

Methodology .............................................................................................................................. 51

4.1 Introduction .................................................................................................................... 51

4.2 Load Case Analysis.......................................................................................................... 51

4.3 Ultimate and Statistical Loads ........................................................................................ 54

4.4 Fatigue Loads .................................................................................................................. 62

4.5 Automation Methodology .............................................................................................. 67

4.6 Methodology of Extracting Results from SimulinkTM Model ......................................... 68

4.7 Methodology for Operation in OrcaflexTM ..................................................................... 76

4.8 Variation Mode and Effect Analysis ............................................................................... 79

Chapter 5 .................................................................................................................................... 83

Results and Discussions ............................................................................................................. 83

5.1 Tools Developed for Analysis ......................................................................................... 83

5.2 Experimental Data Results ............................................................................................. 84

5.3 Discussion on Experimental Data Results ...................................................................... 90

5.4 Simulink Simulation Model Results ................................................................................. 92

5.5 Discussion on Simulation Model Results ..................................................................... 100

5.6 Discussion on Fatigue Results ...................................................................................... 104

5.7 Results for irregular wave Survival Condition Waves OrcaflexTM ................................ 105

5.8 Discussion on Results obtained from OrcaflexTM ......................................................... 106

5.9 Variation Mode and Effect Analysis ............................................................................. 108

Chapter 6 .................................................................................................................................. 111

Secondary Objectives, Results and Evaluation ........................................................................ 111

6.1 Introduction .................................................................................................................. 111

6.2 A: Saved time series of positions/accelerations of parameters .................................. 111

6.3 B: Scatter Plots of Buoy Motions in 6 DOF vs Rack Position ........................................ 113

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6.4 C: Peak acceleration summary in 6 DOF vs rack position ............................................ 120

6.5 D: Lateral and Vertical Force on tether vs rack position .............................................. 123

6.6 E: Wavespring Force vs Rack Position Scatter Plots for all sea states ......................... 126

6.7 F: Wire Force vs Rack Position ..................................................................................... 127

6.8 G: Transmission Force vs Rack Position Scatter Plots for all sea states ....................... 129

6.9 H: Number of Wavespring Cut off events in each sea state ........................................ 131

6.10 F: Number of slack events in each sea state ................................................................ 131

6.11 Discussion ..................................................................................................................... 133

Chapter 7 .................................................................................................................................. 135

Conclusions, Limitations and Future Work ............................................................................. 135

List of Figures .......................................................................................................................... 140

List of Tables ........................................................................................................................... 145

References ................................................................................................................................ 147

Appendix 1 WAFO Toolbox .................................................................................................. 152

Appendix 2 Review of Structures that undergo extensive Fatigue Loading .......................... 153

Appendix 3 Scaling of WEC from experimental model to life size model ............................ 158

Appendix 4 Sea States and Notations investigated in Tank Tests and OrcaflexTM .............. 160

Appendix 5 Outputs generated from Experimental Tests in Wave Tank ............................... 162

Appendix 6 Summary of Loads on Experimental Results ...................................................... 164

Appendix 7 Simulation Model – Peak and Load Statistics..................................................... 170

Appendix 8 Simulation Model – Fatigue Loads ..................................................................... 174

Appendix 9 Additional Objectives .......................................................................................... 178

Appendix 10 Peak Identification MatlabTM

Code ................................................................... 181

Appendix 11 Equivalent Load Estimation for Fatigue MatlabTM Code ............................... 191

Appendix 12 Wave Interference and production of Irregular waves ...................................... 196

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Abbreviations

DOF

CPO

WEC

QTF

CAD

PTO

RPM

FEM

FOS

KTH

IIT-M

HSLA

Degree of Freedom

Corpower Ocean

Wave Energy Converter

Quadratic Transfer Function

Computer Aided Design

Power Take-Off

Rotations per minute

Finite Element Method

Factor of Safety

Kungliga Tekniska Högskolan

Indian Institute of Technology Madras

High Strength Low Alloy

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Symbols

: Acceleration in direction j

: Acceleration Vector of an arbitrary point with respect to defined origin

AD : Projected Area of Bluff body normal to the flow direction

: Added mass of component k in direction j

Ax : Wet Surface Area of Buoy

b : Fatigue strength exponent (material property)

B : Number of Blocks

Bi : Wave Drift Damping Coefficient

CM : Inertial Coefficient

d : Damage experienced during the experimental signal duration

dS : Infinitesimal area on buoy’s body to be integrated

D : Diameter of submerged body at water surface

: Equivalent Damage

: Life time Damage on the Buoy

: Overall Error in estimation

: Mean Drag Force

: Excitation Force on Buoy

: Sum of External Forces

: Frequency of vortex shedding

, Fd : Drag Force

: Equivalent Load

: Gas Spring Force

: Hydrostatic Force

: Slow Drift Loads

: Inertial Force on cylinder

: Weight of Buoy

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: Gravitational Force due to weight of Buoy

: Lift Force

FM : Morrison Force for cylinders

Fn : Froude Number

: Sum of forces dues to Power Take Off Unit

: Transmission Force

: Radiation Force

: Friction Force

g : gravitational acceleration

H : Wave Height

H1/10 : Statistical Mean of top 10 peaks in a data set

H1/100: Statistical Mean of top 100 peaks in a data set

H1/3 : Statistical Mean of top 3 peaks in a data set

Hs : Significant Height

: Direction vectors along x, y and z axis respectively

: Moment of Inertia of flywheel

k : Wave Number

l : Distance between two adjacent vortices in the same row behind a bluff body

: Mass of oscillator

: Direction vector for component k

N : Number of Cycles of Loading

: Number of cycles of loading condition ‘k’

P : Total Pressure given as sum of static and dynamic pressure

: Atmospheric pressure at sea level

Rn : Reynolds Number

: Radius of pin

s : Scale

: Displacement Vector of an arbitrary point with respect to defined origin

t : Time duration of experimental data

T : Time Period of Wave

: Second Order Transfer Functions for Slow Drift Loads

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: Energy Period for irregular waves

: Natural Period of Wave Energy Device

: Horizontal velocity component of water particle

: Flow velocity far away from body such that the body has no influence on the flow

: Vertical velocity component of water particle

: Relative Velocity between Fluid and Body

: Modeled Scatter Vector in VMEA model

: water depth from water surface level

: Modeled Uncertainty Vector in VMEA model

: Phase angle of vortices shed

: Relative angle between wave and current

: Circulation

: Displacement of body in water

ϵ : Wave Phase

: Wave Elevation

: Wave Height

: Threshold value where the buoy is unlatched

: Heave Motion along z axis

: Sway Motion along y axis

: Surge Motion along x axis

: Roll Motion about x axis

: Pitch Motion about y axis

: Yaw Motion about z axis

: Estimated Parameter Vector in VMEA model

λ : Wave Length of wave

: Acceleration of oscillator

: Density of liquid under investigation

: Stress amplitude

: Fatigue strength coefficient (material property)

: Mean stress

: Ultimate stress (material property)

: Diffraction Potential of water

x

: Damage Parameter for Fatigue in VMEA model

: Velocity Potential of water

: Velocity Potential in Finite water depth

: Velocity Potential in Infinite water depth

: Wave Angular Frequency

ω0 : Incoming wave frequency

: Wave Encounter Frequency

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Chapter 1

Introduction

1.1 Thesis Statement

The thesis done in collaboration with Corpower Ocean (CPO) investigates the forces

experienced by the wave energy converter (WEC) in different seastates and validates existing

simulation models that describe the device.

1.2 Motivation

As we progress in to the next age, the world’s energy needs are growing at an alarming rate.

Over 80% of energy produced in the world comes from non-renewable sources like fossil fuels

which has caused an alarming rate of deterioration of the environment.I. Certain governments

are becoming aware of the problem and measures like the (20-20-20) are being set by the

European Council with aims to decrease greenhouse gas emissions, increase energy efficiency

and increase renewable sources of energy. Such similar policies and targets have brought about

investments in renewable forms of energy and given rise to many new ideas. CPO has taken a

step in this direction and is developing the WEC.

The device though proven successful in theory is still under nascent stages of development. It is

estimated that ocean waves can produce 4000 TWh of power if harnessed. If this device is

successful, potentially it could take care of 10-20% of world needs I. The work done in this

thesis would be a step in the development of this technology and one step closer to a greener

cleaner earth.

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1.3 Objectives and Deliverables

As stated in the motivation, the concept of WEC developed by CPO is required to be practically

validated. The objectives of this thesis focus on validating measured parameters in Tank Tests

done in Ecole Centrale de Nantes in 2014 against results obtained from Simulation Models and

Mooring Specific Software OrcaflexTM. The primary objectives and CPO deliverables are as

follows,

A. Theoretical Investigation

i. Ocean Wave Theory

ii. Rainflow Counting and Damage Accumulation Theory

iii. Review of similar machine designs with extensive fatigue loading

B. Development Tools

i. Graphical User Interface to compare two different Load Cases

ii. Matlab Code for automation of Data Filtering and Processing for Peak Identification

and recording of Statistical1 Parameters

iii. Matlab Code for Rain Flow Counting and Design Fatigue Life Estimation

C. Load Case Analysis

i. Deduction of Peak Loads on mooring line obtained from experiments for Buoy 1 and

Buoy 2 performed at École Centrale Nantes in 2014 and form basis for choice of

buoy and mechanism

ii. Deduction of Peak Loads under Extreme wave conditions simulated in Wave Tank

Experiments and using these loads as basis for deduction of minimum tether

dimensions for the two materials under investigation by CPO

iii. Validation of Simulation Model by Comparison of Loads obtained from Experiments

and Simulation Model Estimation of Statistical1 loads from simulation model for

given annual sea spectrum for selected European Atlantic coast site

1 Statistical Loads/Parameters refers to Peak Loads, RMS Loads, Mean Loads, A1/3 Loads, A1/10 Loads and A1/100 Loads

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iv. Estimation of Sea Loads for extreme cases in OrcaflexTM and comparison with

Simulation Model and form basis for selecting Buoy Survival Strategy

v. Estimation of Fatigue Related Damage and Estimation of Equivalent Load for

individual seastates at target site. Estimation of Equivalent Load for an entire

spectrum of Sea States with given seastate distribution data for the target site

D. Statistical Analysis

i. Uncertainty and reliability analysis for estimation of Factor of Safety using VMEA –

Variation Mode and Effect Analysis

1.4 Thesis Project Overview

The thesis addresses the objectives by dividing the contents into six chapters. Each chapter is

written such that it forms the basis for the next chapter. The overview of the thesis is as

follows,

In the beginning of the thesis a short one page abstract is written that highlights the

motivation, importance and contributions of the thesis.

The first chapter introduces the topic of the thesis in a broad sense. Then the motivation

behind the thesis work is established following which the objectives set by CPO and their utility

are listed. Then the project overview and thesis outline as done in this section is presented.

Finally, this chapter ends with the contributions this thesis made.

The second chapter establishes the background information required to better understand and

perform the objectives. The WEC technology is introduced in this section along with its parts

and governing mechanics. Previous experiments performed and simulation tools developed for

the study are introduced here. Comments on the work done so far by CPO and the need for

further analysis are established.

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The third chapter establishes the theory required to fulfill the objectives. Wave Energy, Types of

Converters, Ocean Wave Theory, Load Case Analysis, Fatigue Theory, Failure Criteria and VMEA

are covered in this chapter.

The fourth chapter establishes the methodology adopted at different steps to fulfill the

objectives. The chapter is arranged with different sections for treating experimental results,

simulation model, OrcaflexTM model and VMEA.

The fifth chapter lists out the results and discussions in a concise and effective manner. Since

the results are numerous, the majority has been shifted to the appendices and this chapter

contains only an overview and summaries of specific cases. The results are arranged in

accordance with the objectives. Evaluations, weaknesses and observations are discussed after

the results.

The sixth chapter introduces the additional objectives that were added to the scope at a later

stage. Methodology is briefly discussed and then results and discussions are presented.

The seventh chapter is the conclusionXXVII chapter and summarizes the conclusions for the

objectives followed by establishing scope for future work.

1.5 Thesis Contributions to Project

The data generated in the thesis work was of use to the mechanical team at CPO. They are

using it as design basis for designing parts of the WEC.

The comparison with experimental data served as a tool for improving the simulation model in

SimulinkTM which is now being extended to a 6 DOF model to cater for a more accurate

representation of the WEC.

The Fatigue Equivalent Load results were useful for the mechanical design team who are using

at as design basis. The Fatigue model developed in MatlabTM is useful in predicting the fatigue

life occurring in different combinations of sea states, thus extending the ability to predict for

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any given area in the world. This is of use for CPO in future analysis for predicting fatigue

behavior at new test sites.

Variation Mode and Effect Analysis was developed and generalized to be extended for

estimation of factor of safeties for future use for parts of the WEC device.

The results obtained from the thesis were featured in the company report and application for

further funding which was successful.

Finally, I believe the thesis has brought the technology one step closer to realizing Earth’s Green

Energy Requirement.

.

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Chapter 2

Background

2.1 Introduction

The WEC has already undergone several years of development from concept to scale model

stage. In order to investigate to achieve the objectives, it is important to describe the work

done so far that forms the basis for this thesis. This chapter introduces the Wave Energy

Converter, its parts, mechanisms along with the tools that CPO has developed.

2.2 About Corpower Ocean (CPO)

CPO is a company founded in 2009 with a goal to harness Ocean Energy and is currently

developing a WEC device. CPO uses the principle of resonance to increase the energy absorbed

from point absorber2 type WEC from incoming waves. CPO has been developing this technology

with a focus on finding feasible solutions for robustness, low cost and power absorption from a

broad spectrum of sea states.

2.3 The Wave Energy Converter

The wave energy converter by CPO is a light, low inertia device that is able to absorb energy

from a wide spectrum of sea waves due to its geometric properties. Also due to its small size, it

has good survivability in extreme waves and a low production cost.

2 More about types of wave energy converters can be found in Chapter 3, Section 3.2.2

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The small size has reciprocation that the natural period of the buoy becomes low. To

compensate this, an active control method is installed in the form of Wavesprings that ensure

the buoy is always in resonance with incoming waves. This combination of small size and active

control gives the device a power absorption efficiency of two to five times higher than other

similar WECs.

The WEC developed by CPO is a ‘Point Absorption’ type of Wave Energy Device. Its name

derives from the fact that the buoy is very small in comparison with the countering wave. The

heaving motion of the buoy is transferred to the Power Take-Off (PTO) where it is converted to

electrical energy with the help of inbuilt generators. See Figure 1 for summary of advantages.

Figure 1: Summary of Advantages of Wave Energy Device by Corpower OceanII

2.3.1 The Mechanism

The WEC developed by CPO is a heaving point absorber, (Figure 2) which uses phase control by

use of pneumatic gas springs. The aim is to have a light buoy that is held at its equilibrium

position by a pre-tensioned gas spring. This gives the opportunity for the buoy to move fast,

upwards due to the hydrostatic forces and back down into the water due to the gas-spring, with

low inertia. Using the phase control by latching the aim is to make the buoy able to use a wide

range of waves for power absorption. The phase control enables management of the buoy in a

way that in every cycle it moves in phase with the wave. This gives the possibility for the buoy

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to move closer to a higher response frequency (closer to the natural period)

resulting in larger heave amplification.

In simple words, the device converts oscillatory kinetic energy into electric

energy by exploiting the concept of resonance to maximize range of

motions.

2.3.2 Components of WEC

1. Power Take off Unit (PTO)

The PTO system is a custom designed unit that aims at combining the high

load capabilities from hydraulics with the efficiency of a direct mechanical

drive. The device is what converts the mechanical motion into useful

electrical energy. Temporary energy storage is done in two steps which

help in smoothing out the power absorbed as compared to impulsive power input signals. The

system has been designed for low overall inertia and high structural efficiency, aiming for a

device that is effectively energized by a relatively broad range of waves using inherent phase

control.

PTO has the following internal parts,

a. Oscillating Module

The PTO oscillator module consists of an oscillator that is connected to the tether, receiving the

forces from the buoy through a wire that connects them. It consists of two cylinders which are

interconnected through channels where a fluid interacts with two pistons. The compliance

chambers and pistons form a gas spring that pulls the lightweight buoy downwards and

balances it at its equilibrium position.

b. Transmission Module

The transmission module converts the linear motion of the oscillating rack into rotational

motion. The oscillator has a double sided gear rack that is connected to two flywheels, which

Figure 2:

Schematic of

WEC

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are accelerated as the rack moves. As the buoy and rack move upwards approximately half of

the energy is stored in the gas spring and half of it accelerates one of the flywheels. When the

buoy moves downwards the energy stored in the gas spring is released and the other flywheel

is accelerated. The energy can be temporarily stored in each flywheel before the next wave

cycle arises.

c. Electricity Generation Module

The generator module consists of two generators connected to each flywheel. They convert the

energy stored in the flywheels into electrical power, gradually decreasing the rotational speed

of the flywheels until they have come to a stop position before the next cycle starts. These

steps give a smoother and stable power output from the peak.

2. Tether

The tether could be made of polyester or steel3 and its main function is to fasten the buoy to

the sea bed. It will be in tension during its entire life span to avoid snapping and associated

impulse loads. Fatigue loads on the tether will be important to study as it is subjected to cyclic

loading.

3. Connector at Sea floor

The tether will be connected to the sea floor by means of a latch and pinions driven in to the

seabed.

4. Connector at Buoy

The tether will be connected to the PTO by means of a connector. This part will be subjected to

cyclic loading and could be studied for fatigue loading.

3 Choice of material is still under investigation by CPO

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5. Buoy

Currently there are two buoy designs under investigation as shown in Figure 3. Buoys are

designed to be light weight and hydrodynamically smooth in the vertical direction to avoid

energy losses due to friction or form resistance losses.

Figure 3: Buoys that are under investigation

2.3.3 What degrees of freedom are allowed

Based on the given geometry, only vertical motions are converted to electric energy in the PTO.

But in reality, the buoy will be subjected to all 6 degrees of freedom. The buoy should be

designed in such a way that Heave motion dominates while other motions are suppressed.

For example in the above buoy designs (Figure 3), Buoy 2 exhibits more resistance in heave

oscillatory direction. A Computational Fluid Dynamics (CFD) analysis is probably required before

one can quantify the performance of the buoy. In this thesis, choice of buoy is established by

studying individual forces based on experimental results performed on 1:16 scale models.

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2.3.4 Latching mechanism and its repercussions on impulse forces

Phase control by latching has been in development for many years and was originally proposed

around 1980 by J.Falnes. and K.Budal III. Latching is an interesting approach of controlling the

oscillation period of the system, bringing it closer to wave period of various sea states thus

encouraging resonance. This way the body’s motions get amplified giving it a maximum velocity

for that wave.

Latching is done by stopping the motion of the system at the extreme excursion when the

velocity is zero and holding it there for a certain time. Subsequently, the device is released at

the optimal moment. This is shown with curve c in figure 4. The main challenges when using

latching control, as many other active control schemes, is that the system must be able to

predict ahead of time the right moment to unlatch. For a heaving point absorber this

"anticipation" time is a quarter of the period of the natural frequency of the system before the

maximum peak in excitation forceIV. It is therefore important to know the natural period of the

WEC system, to be able to predict the time it should be released before the peak force. The

more complicated challenge is to know when that peak will occur.

Latching has shown that it has the capability to significantly increase the absorbed power from

the wave. Studies have shown a gain of up to a factor of 4 compared to a device without

latching control. A. Babarit and A.H. Clement showed in their paperV VI, a gain by latching almost

up to a factor of 3, depending on the peak period. The increase was observed in experiments in

regular waves. There the system knows the height and period of the incoming wave. In nature,

the sea has different sea states with different combinations of wave height and periods, making

the prediction complex as that would optimally be based on a future value.

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Figure 4: Latching Mechanism where Curve (a) is the incident wave, Curve(b) is the

resonant wave motion, Curve(c) is the actual movement of buoy subjected to latching..XXXIV

Nevertheless, researchers are trying to overcome these difficulties by developing systems to

cope with this challenge. There are predictive models that use local or distributed wave sensors

to attempt to predict the incoming wave or models using non-predictive methods. A promising

approach to provide a robust non-predictive method is to define an amplitude height for the

water surface elevation and form the zero position as a threshold value to unlatch the buoy.

This is known as "threshold unlatch control". This means as the buoy is latched at its bottom

position and the surface of the water reaches a given height (threshold) the buoy unlatches and

vice versa for when it is latched at its top position. This is a close to optimal power absorption.

The equation for the threshold found by Lopes et. al.VII is written as,

[

(

)] (1)

where, is the natural period of the device, H is the wave height and T is the period of the

wave, for regular waves. For irregular waves the threshold can be calculated in the same way,

where T is substituted by the energy period Te and H is substituted by . This has given

encouraging results as published by Lopes et. al.VII where for irregular waves the results gave

an increased capture width of a factor of 2,5 compared to a passive system.

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Despite the advantages with latching, there is an inherent problem with effective power

absorption. Latching involves sudden stopping and release of the buoy at critical positions to

ensure resonance. These sudden mechanisms give rise to steep power surges which are difficult

to capture in the short time they occur.

2.3.5 Wavespring and its improvement on impulse forces

To avoid the impulse problem with latching mechanism, pneumatic Wavesprings were

developed that smoothen out the motion of the buoy in waves while ensuring resonance. This

way the power absorbed does not come from steep surges in forces but instead comes from a

continuous buoy response.

The working of the Wavesprings is classified as per the requirements of CorPower Ocean and

will not be discussed here.

2.4 Forces acting on the WEC and its Equations of Motion

The forces on the point absorbing buoy can be represented according to Newton’s second law

of motion as,

Sum of all forces = mass x acceleration

(2)

where, m represents the mass of the system, the acceleration, as external forces due to

waves and FPTO as internal forces on buoy due to the PTO. The PTO is made up of several

components, the details of which can be found in Section 2.3.2.

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The internal forces due to PTO can be further split into,

(3)

where is the gravitational force due to weight of oscillator and , and are

transmission force, gas spring force and friction force respectively which are transmitted to the

buoy through the wire.

The external forces due to waves are pressure based forces due to different wave body

interactions. It can be further broken down into,

(4)

where, is the excitation force, is the radiation force, is the hydrostatic force and is

the drag force. The total power absorbed by the buoy can be calculated by multiplying the

external forces by the respective velocity component.

2.4.1 Excitation Force or Diffraction Force

The diffraction force is the result of integrating the pressure distribution over the wet surface

area of a fixed buoy for an incident wave. In other words, when the buoy is fixed and restricted

in its motion, the force experienced by it when an incoming wave passes is known as the

excitation or diffraction force. More about this force will be discussed in Chapter 3, 3.4.

2.4.2 Radiation Force

The radiation force is the force experienced by the body when it is forced to oscillate in the

absence of waves. It is found by integrating the pressure distribution over the body’s surface.

15

2.4.3 Hydrostatic Force

The hydrostatic force is the force experienced by a stationary buoy in calm water. It is simply

the difference between the buoyancy force and the gravitational force. It can be expressed as

Newton’s second law as,

(5)

where is the submerged volume of the body, is the weight of the buoy and is the

hydrostatic force.

2.4.4 Drag Force

Drag is the resisting force a body experiences when there is a relative motion between the body

and the surrounding fluid. Drag is a complex phenomenon and broadly it can be split into two

components,

1. Viscous Drag 2. Form Drag

There are numerous other sources of drag such that wave making drag, spray drag etc but they

are insignificant in this case.

Viscous Drag is due to skin friction while form drag is due to the body’s shape. More discussion

on this is presented in Chapter 3, Section 3.4.

16

For the case of WEC buoy, viscous drag will be most significant and can be expressed as,

(6)

where is the drag coefficient, is the wet surface area and is the relative velocity

2.4.5 Equations of Motion

During experiments and simulating modeling, data was also extracted that described the

motion of the buoy in 6 DOF. The governing equations for this motion are as follows.

The equations of motion for the buoy can be split into two cases,

1. Engaged to flywheel

2. Disengaged with flywheel

Engaged Condition

(7)

17

Disengaged Condition

(8)

2.5 WEC Scale Model Experiments

In July 2014, the wave tank at École Centrale de Nantes was booked to carry out experiments

on two 1:16 scale buoy designs. The goal was to obtain data and observe the behavior of the

buoys under the influence of waves. Data in the form of forces, power and buoy motions were

recorded with the help of sensors installed on the buoy.

2.5.1 Experimental Setup

The wave tank at the University is located at LHEEA Lab for Hydrodynamics, Energetics and

Atmospheric Environment Department. It is a very robust tank capable of simulating waves,

wind and currents. Figure 5 shows an experiment at the facility. Its specifications are in Table 1.

Parameter Dimension (m)

Length 50

Breadth 30

Depth 5

Table 1: Specification of Wave Tank Testing Facility

18

Figure 5: Wave Tank Testing Facility at École Centrale de Nantes in 2014

For the experiment, the buoy was attached to a tether which was driven through a simple

pulley placed at the bottom of the tank. The other end of the tether was then connected to

another device that provided a pre-tension and measured the tension in the device. The set-up

is as shown in Figure 6.

Figure 6: CAD representation of Buoy in Wave Tank with device to measure tension in tether

19

For the testing of the Buoy the following equipment was used,

a. A strain gauge to measure the tension in the tether

b. Motion sensors on top of buoy shown by bright white lights (Figure 7)

c. CPU to actively control the buoy motions

d. Cameras

Figure 7: Picture showing bright white lights installed on buoy to record the 6 DOF motion of buoy

Due to limitations in Tank Dimensions and available time, all seastates could not be

experimented. Hence, only selected seastates were tested. In Figure 8, the yellow boxes

represent the sea states for which experiments were carried out. The blue box represents the

tank limitation. Any seastates lying outside the blue box could not be tested.

These experiments were carried out for regular seas as well as irregular seas for latching (linear

damper) mechanism and Wavespring mechanism for both the buoy designs. In addition,

numerous other tests like radiation tests and calibration were carried out. In total, there were

296 experiments that were carried out.

20

Figure 8: Seastates that were tested in the wave tank (marked by yellow boxes)

The entire list of data obtained from an experiment can be found in Appendix 5. Since the

output signal was raw, it requires certain processing before useful results can be extracted. The

methodology for this can be found in Chapter 4.

2.6 Simulation Model in SimulinkTM by CPO

In the previous section we saw that experimental tests were performed to test the validity of

the technology. But since, it is very expensive and time consuming to book a wave tank, an

alternative way of testing the buoys was required.

Keeping these factors in mind, a simulated platform that would replicate the results from a tank

tests on a computer was devised. Such a model could be used at the user’s convenience to test

the buoy in all kinds of sea states for different buoy configurations. Thus, a mathematical model

based on Ocean Wave Theory, Buoy Motions and Forces described in Section 2.4 was

developed in SIMULINKTM, which is a special add-on package with MATLABTM, developed by

MathworksTM.

21

The model presents itself in the form of a GUI in which various parameters are entered and the

program outputs results. More details about this simulation model can be found in Chapter 4,

Section 4.6.

22

Chapter 3

Theory

3.1 Introduction

This chapter describes all the necessary theoretical background required to understand the

thesis and develop algorithms to establish the analyses performed in this thesis work. Beginning

with description of Wave Energy, the chapter progresses with sections on Ocean wave theory,

Fatigue theory with emphasis on rain flow counting method, review of other machines with

extensive fatigue loading, stress strain relationships, OrcaflexTM modeling and finally ends with

a section on variation mode and effect analysis (VMEA).

3.2 Wave Energy

3.2.1 Wave Energy and its Potential

Over 71% of the earth’s surface is covered with water and a natural consequence of the large

surface area in a dynamic atmosphere is the existence of waves. Ocean Waves can be visualized

as oscillating columns of water. These waves are not only perpetual but also propagate energy

across the globe. Wave Energy Converters are devices that are designed to harness the energy

stored in water waves by means of an electro-mechanical contraption. CorPower Ocean is a

company that is working on developing Wave Energy Convertors. The idea is to harness the

kinetic energy stored in sea and ocean waves and convert it into useful electricity by means of

electro-mechanical contraptions. There has been previous interest in the field of wave energy

but due to certain complications the devices have been expensive and unsustainable. But unlike

other previously patented designs, the design developed by CorPower Ocean exploits the

23

phenomenon of resonance thus greatly increasing the power output as compared to

conventional wave energy convertors. The current design has been tested over the last year

using a scale model in a wave flume in École Centrale de Nantes, France. Results have been

promising and it was observed, the energy density was over 5 times higher than previous

designs. The tests showed an energy/ton ratio comparable to wind energy. Full Scale models

are scheduled for testing in the coming year.

There is immense potential for wave energy along coast lines of major cities. Certain spots have

been identified as shown in Figure 9a and Figure 9b. It can provide green sustainable energy

and meet the present electric demand. In addition, the technology can be used to power

remote islands. The effect of the devices on marine life is yet to be studied but owing to no

exposed moving parts and no emissions, it can be guessed that marine life will not be impacted

greatly. But the presence of wave energy buoys might hinder the passage of sea traffic.

Figure 9a: Identified Locations where Wave Energy Device can be potentially used 1. (Source:

UserfulWaves) VIII

24

Figure 9b: Identified Locations color coded according to energy potential. 1. (Source: wikimedia)VIII

3.2.2 Wave Energy Converters and its types

Wave Energy is present in sea waves as kinetic and potential energy stored in the oscillating

water particles. Wave Energy Converters essentially convert this kinetic energy into useful

electrical energy or mechanical power.

The process of extraction of energy from waves has inspired many novel techniques working on

different principles in the past. Though most of the technologies are still in an experimental

stage, the interest in the field has led to a growing community and allowed archiving the

progress.IX

3.2.3 Types of Wave Energy Converters

Because of the immense number of designs, it was important to characterize them. Such a

distinction was made by Antnonio F. and O. FalcaoX. He divided them into three broad types.

1. Oscillating Water Column

2. Overtopping

3. Oscillating Bodies

25

There are then several sub categories under each of these categories. An entire list can be

found at Wikipedia’s wave energy pageXI but a few devices worth mentioning are Pelamis,

Wave Dragon, Wave Roller and PowerBuoy.

3.2.3.1 Oscillating Water Column

An Oscillating Water Column (OWC) is a wave energy device that uses the flow of air to turn a

turbine. A typical device has a large cavity of air in a sloping cavity such that it gets narrower as

we move up. The device has an opening on top and in this opening a turbine is placed. This

entire device is then put in water with waves. The schematic is shown in figure 10.

As the wave crest passes the structure, the water moves up in the cavity. The constriction in

space compresses the air and pushes it through opening on top while turning the turbine.

Similarly as the wave trough passes the structure, the water level in the cavity falls, thus

reducing the internal pressure. This sucks the air from outside thus turning the turbine as this

happens.

Figure 10: Schematic of how an Oscillating Water Column works. (Image Courtesy-

en.openei.org)XII

The turbine is designed to turn in one direction despite bi-directional airflow.XIII XIVThe device

can be both floating type as well as fixed type and is usually more suitable for shallower waters

26

since it has to be tethered to the sea bed. There are over 1890 patented examples of OWC type

of WEC devices.XXXV

3.2.3.2 Overtopping

An overtopping type of wave energy device (Figure 11) is unique in its way of capturing energy

from waves since it uses conversion of potential energy into useful mechanical energy to turn

turbines. This device is a partially submerged device and there can be found shore based and

floating models.

Figure 11: Schematic of an Overtopping type of wave energy converter (Image Courtesy-

en.openei.org )

When a wave crest passes the device, the water overflows into the device. The overflowing

water is then collected in a funnel where it is stored for a while. When the wave trough falls

directly under the device, the water in the funnel is released through a turbine situated at the

bottom of the funnel. This flow turns the turbine. An existing example of this type of device is

the sea dragon.

27

3.2.3.3 Oscillating Bodies

This is a very wide group and includes diverse technologies based on oscillatory motion of

device. The devices can be attenuator type (Figure 12) or heaving buoys (Figure 14) or of

pitching type (Figure 13). In general, these devices consist of a moving body that is influenced

by motion of waves. This motion is converted into useful electrical or mechanical energy.

Figure 12: An Attenuator type of Oscillating Body WEC (Image Courtesy-en.openei.org)

Figure 13: A Pitching type of Oscillating Body WEC (Image Courtesy-en.openei.org)

28

Figure 14: Heaving Buoy (Point Absorber) type of Oscillating Body WEC (Image Courtesy-

en.openei.org)

These devices are usually found in relatively deeper seas where wave heights are higher than in

shallow waters. This also means that they have to be relatively higher survivability in

comparison with other types of WEC devices.

Under this category, if the oscillating device is small compared to the incident waves, then the

WEC device is called a Point Absorber type Wave Energy Device. The WEC by CPO is a point

absorber type of device which will be discussed in detail in the subsequent chapters.

3.3 Coordinate System

For the purpose of the study, an earth fixed coordinate system has

been chosen as shown in figure 15. Typically, a body in water has

6 degrees of freedom. Three of them are translational while three

are rotational. The three translational degrees of freedom are,

a. X – Surge (η1)

b. Y – Sway (η2)

c. Z –Heave (η3) Figure 15: The axis for the

coordinate system

29

The three rotational degrees of freedom are,

a. XX – Roll (η4)

b. YY – Pitch (η5)

c. ZZ – Yaw (η6)

Based on the principal motions described above, the motion for an arbitrary point located at

(x,y,z) on the buoy can be calculated as,

(9)

For all calculations the reference frame used is an inertial frame of reference. This means the

coordinate system is not accelerated.

3.4 Ocean Wave TheoryXV

There are different types of waves that can be studied under ocean wave theory. They are,

a. Linear Waves – Steepness H/λ is small. Hence there is no breaking.

b. Non Linear Waves – Higher Order Wave theory used to account for wave breaking.

c. Long Crested Waves – 2D waves

d. Short Crested Waves – 3D waves

e. Regular Waves – Waves have a single ω (circular frequency) and λ (wave length)

f. Irregular Waves – Waves have several ω and λ.

g. Short-term sea state – Statistical measure of frequencies and directions for short

periods

h. Long-term sea state – Statistical measure of frequencies and directions for long periods

For a regular wave, its shape can be described as,

(10)

30

If we have several regular waves, we can add them to produce an irregular wave. So, in other

words an irregular wave can be described as a sum of sine or/and cosine functions.

Particle velocities in a wave are given by its velocity potential and can be written as,

(11)

for shallow and deep water respectively, where, g is the gravitational constant, is the wave

amplitude, is the wave frequency, k is the wave number, h is the water depth and z is the

depth at under investigation. Then the velocities are given as,

and

(12)

We are intereseted in the excitatition forces caused by a regular wave on a small volume

structure. Since the buoy can be considered as a small volume structure, the excitation forces

on it are,

∫ ∑

(13)

where P the total pressure and is given by,

(14)

which is the sum of dynamic and hydrostatic pressure, where is the water density, z is the

water depth, is the wave amplitude, is the wave frequency and k is the wave number.

Ocean waves often interact with each other to produce complex phenomenon that produce

different types of forces for different structures. For a Buoy, the following effects are relevant,

31

a. Wave Frequency Effect – Buoy is linearly excited by frequencies within the wave

frequency range.

b. Sum-Frequency Effect – This effect can excite resonant oscillations in heave, pitch and

roll. This phenomenon is known as ‘springing’ and can contribute to fatigue of tethers.

Since the buoy is restrained by vertical forces, its motion is dominated by natural periods in

heave, pitch and roll. In addition to these forces, it is also important to see which type of forces

dominate for the buoy.

We have from the figure 16, it can be seen that,

Figure 16: Classification of wave forces for different geomtry ranges against incoming wave lenghts

(Source: Marilena Greco Lecture Notes TMR4215: Sea Loads, NTNU)

a. For λ/D < 5 – Diffraction Forces Dominate

b. For λ/D > 5 and H/D < 10 – Mass forces Dominate

c. For H/D > 10 – Viscous Forces Dominate

Non linear effects become important as H/D = λ/7D is surpassed.

Depending on which area the buoy is operated, the dominating forces will vary.

In the case of a diffraction problem, the body is fixed and interacts with the incident waves. The

forces arising can be split into two forces arising from two separate potentials. One is the

incident wave velocity potential and the other is the diffraction velocity potential such that the

32

total excitation force can be given as the integral of these velocity potentials over the area of

the wet surface area given as,

∫

∫

(15)

In the case when viscous forces dominate, mean drift loads are caused which are connected

with the wave amplitude as follows,

a. The body’s capability in generating waves (invisid waves) – proportional to ζa2

b. Viscous Effects – proportional to ζa3

When the wave amplitude and wave length of a waves is sufficently large relative to the cross

sectional dimensions of the buoy, viscous effects can cause important wave drift forces. In such

a case, third order forces dominate over second order forces.

Viscous effects can create a mean drift force that causes the body to move against the waves.

This is because at the wave crest, the fluid velocity is parallel with the wave velocity whereas in

the trough fluid velocity is parallel with the wave velocity but in the opposite direction. Hence

there are opposite forces acting on the buoy at the same time due to viscous effects. If the

phase of the heave motion is such that the largest part of the buoy is at the wave trough, then

there will be a mean drag force in the opposite direction of the wave. See Figure 17 for

reference,

Viscous Drag force in

opposite direction

Figure 17: Slow Drift motions in opposite direction of wave due to viscous effects

33

Slow Drift motions are caused by resonance oscillations that are excited at frequencies lower

than the incoming wave frequencies. These motions are cause by nonlinear interactions in

steady state conditions. Since these motions are caused by low frequencies one needs at least

two incoming waves with different frequencies and amplitudes to cause these motions. When

these two waves interact destructively a new wave with lower frequency is formed which

causes these resonant oscillations. These type of oscillations are common in irregular waves.

For a moored structure with a small water plane area, the slow drift motions can occur in both

the horizontal as well as the vertical plane. Mathematically slow drift loads can be expressed as,

( )

( )

(16)

where

refer to transfer functions of the slow drift loads (2nd order transfer functions),

is the wave amplitude, is the wave frequency and is the wave phase. There transfer

functions depend only on first order solutions for regular waves.

3.4.1 Sum Frequency Effects

In an irregular sea, two waves with frequencies ω1 and ω2 may interact constructively to give

sum frequencies of the type,

a. 2 x ω1 b. 2 x ω2 c. ω1 + ω2

These effects are caused when an incident wave interacts with a reflected wave. An interesting

phenomenon associated with sum frequency effects is the phenomenon of springing. It is a

steady state elastic resonant motion in the vertical plane which results in the fatigue of tethers.

34

In survival conditions, sum frequency effects can cause another phenomenon called ringing. It

is a consequence of 3rd and 4th order sum frequency effects and is a transient resonant elastic

motion.

3.4.2 Viscous Wave Loads

In order to understand viscous wave loads, it is important to learn a bit about fluid mechanics

and specifically, the flow past a cylinder and the generation of vortices.

When considering flow past a cylinder, the behavior depends on the type of flow. The type of

flow is decided by the Reynolds Number (Rn). Different flow regimes for a circular cylinder are

as listed below,

a. Rn < 2 x 105 – Subcritical Flow

b. 2 x 105 < Rn <5 x 105 – Critical Flow

c. 5 x 105 < Rn < 3 x 106 – Super Critical Flow

d. Rn > 3 x 106 – Trans – Critical Flow

In the subcritical regime the boundary layer is always laminar, whereas in super critical and

trans-critical regimes the boundary layer becomes increasingly turbulent upstream of the

separation point.

Boundary layer can be defined as the area around the surface of the body where the fluid

velocity is lower than the ambient flow velocity. Its thickness can be defined as the distance

between the body’s surface and the point where the tangential velocity component is 99% of

the ambient flow velocity.

Laminar flow is a flow where there is no intermixing of fluid streams. It is a well-organized flow.

Turbulent flow is characterized by disorder and intermixing of fluid streams. It is defined by a

mean component and a fluctuating component about the mean.

35

Separation point is the point where the flow separates from the body and forms vortices

(Figure 18).

XVI

The vorticity in the boundary layer is not zero because of the differential in the tangential

velocity as one moves away from the cylinder. This causes a net rotation which gives rise to

vorticity. As the flow separates, this vorticity gives rise to vortices which are shed in the wake

region of the cylinder. Based on the flow regime, the vortices are shed in a different manner as

shown in figure 19.

Figure 19: Flow separation for different flow regimesXVII

Figure 18: Flow past a cylinder

36

Velocity of the vortex in the wake of the cylinder is given by,

(17)

where, is the circulation of the vortex and l is the distance between two adjacent vortices in

the same row.

The importance of vortex shedding is that it induces force components in parallel and normal

directions. In the normal direction alternate vortex shedding causes a force known as life force.

| | (18)

The vortex shedding also causes an oscillatory drag force which is given by,

(19)

Thus the lift force and drag force have different time periods. The lift force oscillates with a

period of while the drag force oscillates with a period of /2.

Viscous Wave Loads become important for oscillatory ambient flow which is the case with sea

waves. For cylinders, wave loads when viscous forces matter are calculated using the

Morrison’s Equation given as,

| | (20)

where ~ 1.8 and ~ 0.7 which have been found experimentally.

The equation assumes λ/D > 5. The equation is not valid at free surfaces as the velocity

distribution cannot be described by a linear wave, because at free surface, nonlinear effects

matter.

37

3.5 Structure Failure Criteria

Ultimate Load for a structure from a structural point of view is the magnitude of load beyond

which the structure will fail. By failure, it is meant that the structure will undergo a fatal

fracture. In practice, we try to make sure that the maximum occurring forces on a structure fall

well below the ultimate load capacity of the structure.

For a structure to be safe it has to satisfy 3 conditions,

1. Ultimate Strength criteria

2. Stiffness Criteria

3. Fatigue Strength Criteria

Fatigue Strength criteria will be discussed in detail in the next chapter.

3.5.1 Ultimate Strength

Consider figure 20 which shows the stress strain relationship for structural steel which is a

common construction material.

In the figure,

a. Point 1 refers to the Ultimate Strength. This is the maximum stress the material can

take. Beyond this point if further force is added, the materials stress bearing capacity

decreases.

b. Point 3 refers to the point where the material finally breaks or fractures fatally.

c. Point 2 refers to the yield strength. Until this point the ratio between stress and strain is

constant and the material traces back to its original shape on releasing of load.

d. Region 4 refers to Strain Hardening region. In this region, the material becomes very

stiff and hardens but can no longer come back to its original shape on release of loading

e. Region 5 refers to the necking region. In this region, the material starts to loose mass at

the weakest link and the stress bearing capacity decreases until fracture.

38

Figure 20: Stress Strain Relationship for Structural Steel

3.5.2 Yield Strength

While designing a structure, we should keep the yield strength in mind instead of ultimate

strength. For a material it is calculated using experiments. When a person ceases to come to its

original shape after applying stress, the point is marked as Yield Strength point as shown in

Figure 20.

If a material’s yield strength is known it can be tested for safety by computing the tensile stress

in the cross section by using Equation

(21)

3.6 Fatigue Theory and Estimation of Design Life

3.6.1 Introduction

Fatigue can be defined as the weakening of material as it is subjected to cyclic or repeated

loading. It is a progressive sort of phenomenon and causes localized structural damage. The

39

nominal maximum stresses that cause fatigue can be a lot lower than the ultimate tensile stress

or yield stress limit for the structure. Hence it is important to do a fatigue analysis and estimate

the design life.

Typically Fatigue is presented using S-N curves which are a correlation between the stress in a

structure and the number of cycles of loading. Figure 21 shows a typical S-N Curve.

Figure 21: Typical S-N (Stress vs Number of Loading Cycles) Curve

As seen from Figure 21, each stress state S1 corresponds to Number of Cycles N1. In other

words, if a structure was to be cyclically loaded such that the material develops a stress S1 then

it will survive until N1 cycles and will fracture after that.

The above graph represents an ideal situation where all loading cycles are of uniform

magnitude. In reality, the WEC is subjected to loading cycles that are non-uniform in magnitude

and occurrence. This is because waves in real life are irregular and they cause an irregular buoy

response. Hence an S-N curve cannot directly be used for the present scenario. However,

damage accumulation theory can be used in combination with the S-N Curve and the ‘Rain Flow

Counting Method’.

40

3.6.2 Rain Flow Counting Method

Rain Flow Counting Method is a tool for fatigue load analysis used to reduce a spectrum of

varying stress into a set of simple stress reversals. The algorithm was developed by Tatsuo Endo

and M. Matsuishi; 1968 XVIII and has been the most popular method lately for fatigue analysis.

3.6.3 Damage Accumulation and S-N Curve XIX

Usually for a typical loading there will be cases where the structure undergoes irregular loading.

In such cases, individual loads can be identified and clubbed into blocks (Figure22). Then the life

span of the structure can be determined by using Palmgren-Miner Rule. The damage

accumulation rule states that if there are k different stress amplitudes in a spectrum with

amplitude contributing cycles and if is the number of cycles to failure, then, failure

occurs when,

(

) (22)

The S-N Curve in Figure 21 can be expressed using the Basquin relationXIX,

(

)

(23)

where, is the fatigue strength coefficient (material property) corresponding to the stress at

failure for cycles, and is the fatigue strength exponent (material property). Here the

reference number of cycles is chosen to

41

3.6.4 Review of similar machine designs with Extensive Fatigue Loading

Fatigue is a common and very important part of design analysis as the failure can be very

sudden and can happen at loads much lower than the material’s yield strength. In order to

better prepare for fatigue, it is interesting to study similar existing machines that undergo

extensive fatigue loading. Two such machines have been studied and the findings can be found

in Appendix 2.

3.6.5 Fatigue and Equivalent Load Estimation

When we talk of fatigue related failure, the critical question then becomes – ‘how much time is

left until the structure fails due to fatigue damage’. Based on the S-N curve and damage

accumulation theory, one can predict the lifespan if we know exactly what loads have acted in

the past and what loads are going to act in the future. But, this is not realistic in most real life

cases.

Alternatively, if we know how much time we want the structure to survive for how many cycles,

we can deduce the one single load that would replace the entire spectrum of loading during the

structure’s life time. In other words, the damage will undergo the same damage due to this one

Figure 22: Clubbing of stresses according to Palmgren Miner Rule

(Source: Wikipedia)

42

load as it would normally under a full spectrum of loads for the given time period. This load is

called ‘Equivalent Load’.

For a material, the S-N curve is standard and can be found in literature. For example, if the

equivalent load was calculated for N cycles, then the corresponding stress amplitude can be

found from the S-N curve. Using this stress amplitude and Equivalent Load with FOS, the cross

section area of the concerned part can be deduced using Equation 21, Section 3.5.2.

In real life, we are interested in finding the equivalent load for a spectrum of sea states. If one

knows the exact distribution of seastates in a target area across the design life span, one can

assess the equivalent load for such a spectrum.

This is done in two steps. Initially, the damage caused by the cyclic loads for each sea state are

found with the assumption that only one sea state occurs in the spectrum for the design life

time. Finally, once damages are found for each sea state, they are multiplied with the spectrum

distribution of sea states normalized to one and then added to get total damage. This damage is

then used to deduce the Equivalent Load using equation 25. The method for estimating this is

further discussed along with Equivalent Load Results for ‘Yue’ target site in Chapter 5, Section

5.4.3.

3.6.5.1 Definition of Equivalent Load XX

We want to design the buoys’ tether such that it can survive for,

1. Design Life, = 25 years

corresponding to,

2. an equivalent fatigue load with amplitude repeated, N0 = 106 cycles

In addition, we have determined the value of b as 4.8 from the corresponding Wöhler curve for

steel and 5.5 for polyester.

43

Using the above information we can formulate,

∑

(24)

(25)

where,

= Life time Damage on the Buoy

= damage experienced during the experimental signal duration (with amplitudes )

= time duration of experimental data

= Equivalent Damage

= Equivalent Load amplitude

Equating the two equations,

(26)

we get the formula for the equivalent load as,

(

)

⁄

(27)

44

3.7 Modeling in OrcaflexTM

3.7.1 Introduction

During the experimental tests, in École Centrale de Nantes, there were some wave tank

limitations in terms of generation of higher sea states. Since higher sea states pertain to

extreme waves, it is very important to study them to see how the buoy reacts and what forces

it experiences in survival conditions. Results for survival cases can be generated using the

SIMULINK model but there is a need to validate these results as higher sea states are very

critical in determining survivability.

For validation and studying the motion of buoy in extreme sea states, OrcaflexTM is used. As

taken from the official website,“OrcaFlexTM is the world's leading package for the dynamic

analysis of offshore marine systems, renowned for its breadth of technical capability and user

friendliness. OrcaFlexTM also has the unique capability in its class to be used as a library,

allowing a host of automation possibilities and ready integration into 3rd party software.”XXI

Another advantage of using OrcaflexTM is the Graphic User Interface the software has (Figure

23). The graphics helps visualize the motion of the buoy under the influence of waves. The

visualization helps identify key motions and snapping events in the tether.

In addition, with OrcaflexTM one can test different survivability strategies and choose one that

causes the least forces on the connecting parts.

45

Figure 23: Graphic Use Interface for OrcaflexTM XXII

3.7.2 Theoretical Background for OrcaflexTM Simulation Setup

Second Order Wave Excitation Force

OrcaflexTM uses Newman’s approximation to establish the off-diagonal elements in the

Quadratic Transfer Function (QTF) matrix. Newman’s approximation was originally written as,

(28)

where the subscripts j and k are row and column numbers in the QTF matrix. Then, ‘jj’ and ‘kk’

correspond to the diagonal elements and ‘jk’ corresponds to an off diagonal element.

Equation 28 is based on arithmetic mean of diagonal elements to estimate off-diagonal values

in the QTF matrix. Instead of using the above formula, OrcaflexTM approximates by calculating

the geometric mean value.

Damping

46

OrcaflexTM estimates wave drift damping for the buoy using Aranha’sXXXVI simplified method. It

can be expressed as,

(29)

where Bi is the wave drift damping coefficient, Fi is the mean wave drift excitation, k0 is wave

number and ω0 is the wave frequency. Damping coefficient is found by differentiation of the

QTF matrix. the method can also include the effect of current by modifying the wave frequency

into an encounter frequency given by,

(30)

where U is the current velocity and is the relative angle between wave and current.

The new version of OrcaflexTM has made improvements in the computation by including

developments in ocean wave theory done by MolinXXXII and MalenicaXXXIII et al to make the

computation reliable for all water depths and current wave interactions.

For the mooring line, the slow drift damping is incorporated as part of the Morrison Equation

which is given by,

(31)

where ρ is density of water, D is the diameter of circular body, CM is the mass coefficient and a

is the undisturbed fluid acceleration at the strip’s center.

47

3.8 Variation Mode and Effect Analysis (VMEA)

3.8.1 Introduction

The WEC by CPO is subjected to cyclic loads as mentioned earlier in the chapter 5 on Fatigue.

Although the rain flow counting algorithm and fatigue theory give us specific equivalent loads

for a given design life, the load estimation as well as the fatigue model suffers from

uncertainty.XXIII This uncertainty of results is quantified with the Variation Mode and Effect

Analysis (VMEA). The presentation here will follow the same lines as (Svensson & Sandström,

2014).XXIV

This allows the designer to choose appropriate safety factors while designing the components

that are sensitive from a fatigue point of view. VMEA is also helpful in identifying factors that

are responsible in causing the most uncertainty. Such information helps the designer decrease

contribution from such factors during the design stage to reduce the overall uncertainty and

increase the overall efficiency to get an optimized product.

At this stage, no experiments have been carried out to obtain fatigue results on the tether.

Hence, the data is limited presently and is based on literature and data provided by CPO.

3.8.2 Reliability and VMEA

Reliability can be defined as the probability that the structure is intact at the end of its

predicted design life. In engineering, one aims for high reliability and this is usually done by

comparing the external loads with the strength/stiffness of the structure at each time step. If

the latter is greater than the external loads at all time steps until the design life, then

structure’s design life prediction can be called reliable.

Engineering Design for reliability is subjected to a lot of uncertainties which include,

1. Material uncertainties, external loads and geometry

2. Modeling and Human Errors

3. Vaguely known sources of deviations from expected performance

48

Figure 24 shows how these above mentioned factors can skew the predicted results for design

life. In the end we are interested in finding the safety factor ϒ which is directly influenced by the

uncertainties.

Figure 24: Illustration of the influence of uncertainty during the design process (Source: Svensson

& Sandström, 2014XXIV

)

Safety Factors can be found using many methods but these in essence can be reduced to

groups,

1. Combining safety factors on essential sources based on the worst case for all essential

inputs.

2. Assign statistical distributions to all essential sources, perform a probabilistic evaluation and

use a pre-determined low probability of failure to find a proper safety factor.

In engineering practice, methodologies are usually based on the first group but the drawback

with this group is the tendency to overdesign. A combination of worst cases often leads to

highly improbable case. Another drawback with this group is the lack of knowledge of the

actual probability of occurrence.

The second group focuses more on obtaining quantified probabilities of failure for different

sources of uncertainty by monitoring the entire process of uncertainty propagation through the

model for load and strength. A drawback with this method is the lack of knowledge pertaining

49

to uncertainties and their assigned statistical distributions. This leads to application of advanced

statistical methods based on inputs that can be very subjective. For point 2 and point 3 in the

sources of uncertainties described above, we can only have rough estimates of their actual

uncertainties.

VMEA approach belongs to the second group of safety factor prediction. The inherent problem

of weak knowledge on statistical uncertainties is solved by reducing the statistical complexity to

second moment statistics.XXV This reduces the uncertainty to a scalar measure of the standard

deviation of each source.

Since we are working with fatigue life estimation, standard deviation is not a very good

measure since it is variable for different lives. This is improved by converting the scale to a

logarithmic one.

Once the Logarithmic transformation of uncertainties is done, we are interested in calculating

the overall standard deviation of the difference between load and strength. The individual

standard deviations for each uncertainty source are calculated and combined using ‘Gauss

Approximation Formula’ to get the overall uncertainty.

3.8.3 Mathematical Principles of VMEA

Here is a simple model for prediction of uncertainty based on the summation of individual

contributions from different sources of uncertainty.

The logarithmic fatigue life prediction can be formulated as,

( ) (32)

where ( ) is the fatigue life model with damage parameter (subsea force, stress etc), the

estimated parameter vector .

The error in prediction can be written as,

( ) (33)

50

where is the actual relation for log life depending on damage driving parameter and the

involved scatter in load and strength. Then we can approximate the prediction error by a simple

summation,

(34)

where the quantities Xi, represent different types of scatters or uncertainties respectively, and

are assumed to have zero mean. In the analysis we only use the variances and co-variances of

Xi’s, and not their exact distributions, which are often not known to the designer. It is more

useful to convert the uncertainty into logarithmic form and then relate It to the overall life of

the structure using a sensitivity coefficient. This is motivated by the ‘Gauss Approximation

Formula’. For the transfer function from stress to design life, we have,

|

(35)

where is the stress corresponding to nominal values.

For summing up individual contributions we make use of a statistical theorem of convergence

called Central Limit Theorem.

The theorem states that a Sum converges to a normal

distribution with zero mean and finite variance when n tends to infinity, if Xk’s are independent

and equally distributed with mean zero and finite variance.

This theorem can be used to approximate log life as a normal distribution.

Another important simplification we make is to reduce the life prediction model

( ) as a linear regression model. This can be motivated using Basquin Equation found in

Chapter 3, Section 3.6.3. (Equation 23)

51

Chapter 4

Methodology

4.1 Introduction

On basis of the theory described in chapter 3, this chapter lists out the details of methodology

adopted to perform the objectives. The chapter is divided into sections for General Load Case

Analysis, Experimental Investigation, Simulation Results Extraction and Investigation, Fatigue

Results Extraction, Simulation in OrcaflexTM followed by VMEA.

4.2 Load Case AnalysisXXVI

4.2.1 Introduction

A load case can be defined as a set of forces acting on a buoy when subjected to a particular

combination of wave height and wave period known as a sea state. In figure 25, each empty cell

corresponds to a unique load case.

The wave energy device has many parts and consequently subjected to many dynamic and

static forces. The first step is to identify loads that are interesting to study. In this study, the aim

is to find,

1. Ultimate Loads

2. Statistical Load Statistics like RMS, Mean, H1/3, H1/10 and H1/100

3. Fatigue Loads

52

These forces will be calculated and recorded from different sources and compared so that we

get the most accurate values for the subjected forces. The following sources will be used to

record or compute forces,

a. Experimental Results4

b. Mathematical Model in SIMULINK5

c. Finite Element Model in OrcaflexTM

Based on the results obtained from above sources,

1. Mechanical Design Team will base the design of internal parts.

2. Material and thickness of tether will be chosen

3. Mathematical model will be validated

4. Buoy Design will be chosen from the two available alternatives

5. Design life for the buoy in the chosen area of operation will be estimated

4.2.2 Methodology

In the beginning we start with empty cells for sea states as shown in Figure 25 and we are

interested in filling the cells with values for the loads mentioned earlier.

The data needs to be filled for irregular seas, since in nature waves are always irregular.

4 Experiments were carried out it Centrale Nantes for 1:16 scale model of actual buoy design for different sea states including extreme conditions.

5 A mathematical model was developed in Simulink by Corpower Ocean, to simulate forces on a buoy when subjected to incoming waves.

53

Figure 25: Table of sea states that needs to be filled in to complete Load Analysis

First, we start with Experimental Results. Experiments in a wave tank were carried out for

certain sea states in École Centrale de Nantes for the sea states shown in Figure 26 In the

figure, the experimental sea states have been marked with yellow boxes.

Figure 26: Seastates that were tested in the wave tank (marked by yellow boxes)

These experiments were carried out for regular seas as well as irregular seas for latching

mechanism and Wavespring mechanism for both the buoy designs. In addition, numerous other

tests like radiation and calibration were carried out. In total, there were 296 experiments that

54

were carried out. During the experiments, a gauge was placed on the tether of the buoy that

measured the tensile loads on it.

Once the results for peak and RMS loads on the tether are obtained for regular seas, they are

used to validate6 the results obtained from the SIMULINKTM mathematical model. For the

purpose of validation irregular seas are not used since time of simulation for irregular seas in

the wave tank was very small and hence not reliable in predicting a long term irregular sea

state.

After validation of mathematical model is achieved, we generate simulation data for irregular

seas for all sea states of interest until the extreme sea states.

Use of OrcaflexTM for higher sea states

Since the higher sea states could not be validated in the experiments due to wave tank

limitations, it is necessary to have a second source of results for higher sea states for validating

the mathematical SIMULINKTM model. This is necessary since in higher sea states, the wave

behavior and buoy interaction can be unpredictable.

Higher sea states are modeled in OrcaflexTM for 6DOF single point moored buoy and the forces

are recorded for the duration of the simulation. The resulting forces are then compared with

the mathematical SIMULINKTM model for validation.

Using the above described method we deduce Ultimate Loads, RMS Loads and Fatigue Loads.

4.3 Ultimate and Statistical Loads

4.3.1 Peak Loads and Ultimate Strength

During the experiments at the wave tank, the tension force on the tether was recorded in a

time series. It is of interest to identify the peaks in the tensile forces. These peaks will give a

6 Validation is done by individually comparing the Peak and RMS values with the experimental results for different sea states. Due to tank limitations, experiments for higher sea states could not be performed.

55

design basis for choosing a suitable material and geometrical dimensions. The goal is to have a

material that has yield strength higher than the strength calculated for peak tensile force on the

tether after a suitable FOS (Factor of Safety) is applied.

4.3.2 Peak Identification Method for Ultimate Load Calculations

In Dec-Jan 2013, work was done on peak identification methods developed by the US NavyXXXI

and Mikael RazolaXXX. A part of the code was used to write a new code designed to identify

peaks in the data generated by the experimental tests carried out at École Centrale de Nantes

for a given input of unfiltered time series (Figure 27). See Appendix 10 for the MatlabTM code on

peak identification.

Algorithm for identifying Peaks

1. Raw Data is loaded, and separate vectors for acceleration and time are created. (Figure 27)

Figure 27: Unfiltered Data for Heave Acceleration

2. For the process of filtration, several thresholds are introduced. These thresholds

represent time and acceleration values which are represented by the following

variables. These variables are initialized.

56

a. mphDiff (threshold for force/acceleration in differential of force/acceleration)

b. mpdDiff (threshold for time in differential of force/acceleration)

c. mphAcc (threshold for force/acceleration)

d. mpdAcc (threshold for time)

These parameters are the choice of the user. The parameters will later on be used to

further filter beyond the general filter to identify peaks.

3. For initializing general filtration, Cutoff frequency is loaded. This is the choice of the

user. Default is 10 hz but for the buoy forces a frequency of 5 Hz gave satisfactory

filtration. Quality of filtration was determined by damage count. This is explained in the

fatigue section.

4. Then the frequency of the data is calculated by finding the reciprocal of time difference

between the first two readings.

(36)

where, fs represents the frequency of data recording while t1 and t2 represent the time

values of consecutive time steps.

5. The cutoff frequency must be chosen such that the condition ( ) is satisfied.

Then a Butterworth filter of order 9 is applied by default. The order can be changed by

modifying the code. (Filtered values are shown in figure 28). The need and consequence

of filtering is discussed in Section 5.3.4 and 5.3.5.

57

Figure 28: Comparison of filtered and unfiltered data (green is filtered data and blue is unfiltered

data)

6. Now in the filtered data, the first differential of entire data is computed. In this data all

positive points approaching infinity are made zero. See figure 29 after this step (the data

is reversed in sign for purpose of representation).

Figure 29: Differential of Heave Acceleration to filter out differentials lower than defined threshold

58

7. Next, the earlier loaded constant ‘mphDiff’ is called. This constant creates a cutoff for

the differential of heave acceleration. Any acceleration below the constant are filtered

out. 7 Since the value chosen for mphdiff is a factor, it is made relevant by multiplying it

with the standard deviation of the force differential vector before using as a cutoff

threshold in the next step.

(37)

8. Then locations of peaks are extracted using MatlabTM’s inbuilt ‘findpeaks’ function

9. Once the accelerations are filtered, it is necessary to filter on a time scale to remove

peaks occurring very close in time. The constant mpdDiff is called and made relevant like

by multiplying it with mean peak location distance. This creates a horizontal threshold.

8 (38)

10. Next a loop is set up for finding the locations of acceleration peaks based on parameters

defined in step 8 and 10.

a. For ‘one’ to ‘number of peaks’,

b. To find the highest peak within the horizontal threshold mpdDiff made in step

10.

c. Then the corresponding location is recorded and stored as ‘acclocs’.

11. In this step we define a threshold based on acceleration directly. This acts as a vertical

filter as it filters out accelerations lower than a certain threshold. This parameter is

mphAcc and is calculated as,

(39)

7 The choice of this constant needs to be evaluated critically so that there is no loss of essential infromation especially for fatigue calculations. The procedure of choosing is explained in more detail in Section 4.3.

8 Like mphDiff, mpdDiff is a function of itself. This step is done in order to make it relevant for the particular time series under investigation. For example, if mean peak distance is 4 seconds. Then mpdDiff being 0.25, it would create a threshold for 1 second for filtration.

59

12. All acceleration peaks greater than this value are selected from the pool of acceleration

locations that were recorded in step 11.

13. Now, we have a set of filtered acceleration values and their specific locations.

14. At this stage the result is pretty good but not complete yet. Now the final filter is

applied. In the acceleration domain, a horizontal time threshold is created by

multiplying the constant mpdDiff with the mean distance between peak locations.

(40)

15. The algorithm is set such that there can be only one peak in the horizontal time

threshold. This justifies the fact that there is a time gap between two consecutive heave

buoy motions. If there are two or more peaks within a time threshold, the program

picks the largest of the two.

16. The final peaks and locations are recorded and plotted as shown in Figure 30.

Figure 30: Final acceleration time series (Left figure shows only acceleration peaks while right

figure shows steepness of successive peaks)

The same algorithm is used to identify peak tensile forces. Figure 31 shows the identified peaks

for a sample test arranged in order of decreasing magnitude.

60

Figure 31: Sorted Peaks in order of magnitude

Apart from identifying the peaks, it is sometimes more important to note their occurrence.

Hence, an FFT transformation was applied on the peaks and locations to plot the frequency of

occurrence of different peaks. Figure 32 shows the spectrum of distribution for peaks

Figure 32: Frequency of occurrence of peaks

61

4.3.2 Methodology of Extracting Results

A total of 274 experiments were analyzed for peak forces. For each case,

1. Data was narrowed down to useful data based on start and stop time for each

simulation.

2. Data was then filtered and peaks were identified

3. Useful Statistical parameters,

a. H1/100

b. H1/10

c. H1/3

d. RMS

e. Mean

4. For each case the peak was calculated as,

(41)

Here pretension force refers to the initial force the buoy is given at the start of the experiment.

It is shown in Figures 33 and Figure 34.

Figure 33: Pretension force at the start of the experiment

Pretension Force

62

Figure 34: Zoomed in portion of the pretension force

4.4 Fatigue Loads

Methodologies adopted for Rainflow counting and design life estimation are described in this

section. The algorithms are based on understanding from Fatigue Theory in Chapter 3, Section

3.6.

4.4.1 Rain Flow Counting in MatlabTM

A MatlabTM model was developed with the

help of online resources and implemented

based on the above algorithm that takes in an

input array of stress values and gives out an

output for

1. amplitude

2. mean

3. number of cycles (cycle or half cycle)

Pretension Force

Figure 35: Rain Flow Counting

output for 3 input stress value

63

4. begin time of extracted cycle or half cycle

5. period of a cycle

A typical output is shown in Figure 35 and Figure 36.

Figure 36: Output from a Rain Flow Counting Method Script

Algorithm for counting cycles using Rain Flow method in MatlabTM

1. Reduce load-time data to a sequence of (tensile) peaks and (compressive) valleys.

2. Imagine that the time history is a template for a rigid sheet (pagoda roof).

3. Turn the plot clockwise by 90°.

4. Imagine each peak as a source of water which drips down on to the next peak.

5. Count the number of half-cycles by identifying flow terminations. Flow terminates when,

It reaches the end of the time history.

It merges with a flow that started at an earlier peak.

It flows and an opposite tensile peak has greater magnitude.

6. Repeat step 5 for valleys.

7. Assign a magnitude to each half-cycle equal to the stress difference between its start and

termination.

8. Pair up half-cycles of identical magnitude to count the number of complete cycles.

64

4.4.2 Algorithm in MatlabTM for estimating fatigue damage and equivalent loads for different sea states

Algorithm for computing equivalent loads in MatlabTM

1. Initialize data file.

2. Call subsea force time series from the file and then modify its time limits based on

experiment start and stop time. (This information is available in an excel file ‘runlist.xslx’)

See Figure 37.

Figure 37: Subsea Force after time series snipping based on start and end time

3. Initiate the WAFO9 toolbox and use function ‘dat2tp’ to compute all turning points.

4. Filter the turning points by removing insignificant turns. (Figure 38)

9 WAFO discussed in Appendix 1

65

Figure 38: Plot showing the rainflow cycles before (RED) and after (GREEN) filtration.

5. Estimate damage on the structure based on the turning points.

6. Compare damage before and after the turning point filtering.

7. Calculate the Rainflow Cycles using a function ‘tp2rfc’ in WAFO, after satisfactory filtering of

turning points is achieved. (Figure 39)

66

Figure 39: Rainflow Cycles with minima on X axis and maxima on Y axis for any given cycle

8. Plot graphs for Load Spectrum and Level Crossings (Figure 40).

Figure 40: Load Spectrum with load cycle amplitudes and frequency of occurrence and Level

Crossings distribution for estimating how many cycles cross which magnitude

9. Compute the Rainflow matrix by defining number of discretization levels. Plot the

distribution of Rainflow cycles in a contour style plot.

67

10. Calculate the equivalent load using the formulae given in the mathematics section in

Chapter 3, Section 3.6.5.1.

11. Scale the results to a full scale model by using appropriate scaling factors.

12. Estimate the RMS load from experimental/simulated data and compare it with the

equivalent load.

A total of 274 experiments and 146 simulation data files were analyzed for Equivalent Loads.

For each case,

1. Data was narrowed down to useful data based on start and stop time for each simulation.

2. Data was then filtered and turning points were identified.

3. A threshold for data reduction was set up to reduce computational time. The choice of the

threshold was computed using a ‘for’ loop with the condition, that new damage after

reduction should be at least 90% 10 of the original damage with full data.

4. The following output was extracted for each case,

a. Lifetime Damage

b. Max Load in lifetime

c. Equivalent Load

d. Data Reduction Threshold

e. Wave Height

f. Wave Period

4.5 Automation Methodology

As there are numerous cases in simulation and experimental data that need to be analyzed for

results, it was not practical to run the above algorithm for each case. Keeping this in time an

automation algorithm was developed. Essentially, if all data files are kept in a folder, then the

10 The percentage ‘90%’ was after consultation with thesis supervisor Pär Johannesson from SP

68

automation code would pick up one file at a time, process it and store necessary data. The

algorithm for automation is as follows,

1. Store all matlab data files for the seastates you want to analyze into one directory.

2. Initialize the directory.

3. Create a variable ‘FilesNames’ for the directory using ‘dir’ function.

4. Create a counter called ‘NumFiles’ such that its length is two less than the number of files in

the directory.

5. Create a ‘for’ loop from one to ‘NumFiles’ with a step size of 0.5.

6. Create variable A = FIlesNames(1 + 2*i).name

7. Then load the file using the load command as load([directory '\' A])

8. Paste the code you want to execute for this loaded file.

9. Close the loop with ‘end’.

This will cycle through all the files one after another in the loaded directory and process it for

results. This can be further improved by adding a name recognition system. This was done for

extracting results in a seastate matrix form. Its methodology is not discussed here.

4.6 Methodology of Extracting Results from SimulinkTM 11 Model

The GUI developed my Corpower in 2014 is designed to generate buoy motion and force data

for any given seastate that can be fed (Figure 41). The options and process for extracting results

are presented here. The constants are as mentioned in the figure.

11 “Simulink, developed by MathWorks, is a graphical programming environment for modeling,

simulating and analyzing multi-domain dynamic systems. Its primary interface is a graphical

block diagramming tool and a customizable set of block libraries.” as taken from Wikipedia.

69

Figure 41: GUI for running simulations of WEC for given set of input parameters

4.6.1 Input

Figure 41 shows the GUI for generating simulations for different wave parameters. As input, the

mathematical model takes in the following,

The chosen options are marked in bold for a comparative study.

i. Wave Data

a. Simulation Type – Batch or Single Wave

b. Wave Type – Regular or Irregular

c. Simulation Time – 30 minutes

d. Wave Period – Variable in steps of 1 sec

e. Wave Height – Variable in steps of 0.5 m

f. Peakness (gamma factor) – Default value 3.3

g. Water Depth – 50 m

h. Location (9 preset locations – E.g., West Islands, UK)

70

i. Alternatively an option to load wave data as time series – N.A. 12

ii. Buoy Data

a. Shape (6 buoy configurations available) – HA1

b. Scale – 1 (experiment results are scaled to full scale for comparison)

c. Drag Coefficient in Surge and Heave direction – 0. 9 in surge and 0.35 in heave13

d. Buoy Mass – 30000 kg

e. Buoy Period – 4.2 s

f. Buoy Volume – 403.3 m3

Point ‘c’ to ‘f’ are preloaded for each selected buoy but they can be changed

manually

iii. Controller Setting

a. Mechanism (6 configurations available; Ex, Latching, Wavespring)

b. Latch Control - NA

c. Control Parameters – Default

iv. PTO settings (12 specific settings for mechanical variations) – Default

4.6.2 Operation

After all the parameters are entered, the simulation is started by pressing the start simulation

button. Once the simulation is over, the program prompts for a location to save the data.

12 Not applicable in this case. This option allows importing of wave data directly from the target site.

13 Drag Coefficients are available automatically when the buoy shape is chosen. These coefficients were calculated in a previous study.

71

4.6.3 Output

The output after the simulation is completed is a .mat file. In addition a GUI with certain results

gets generated as shown in Figure 42.

The GUI gives results for,

1. Power Peak and mean Outputs for,

a. Mechanical

b. Transmission

c. Generator

d. Electrical

e. Friction

2. Rack position, velocity and acceleration mean and peaks

3. Graph depicting different parameters

The generated .mat file has information in the form of the following parameters,

1. Positions, Velocities and

accelerations for

a. Rack

b. Buoy

c. Flywheel

2. Force

a. Radiation

b. Drag

c. Excitation or Diffraction

d. Hydrostatic

e. Wavespring

f. PTO

g. Friction

h. Transmission

i. Tether

3. Moments

4. Power

76

Figure 42: Output GUI during simulation process

The simulation model is a 2 DOF model in Heave and Surge direction.

4.7 Methodology for Operation in OrcaflexTM

4.7.1 Coordinate System

The coordinate system of the buoy is chosen such that it coincides with the global coordinate

system in OrcaflexTM. This avoids unwanted moments saves work later related to coordinate

transformation for comparison with the mathematical SIMULINKTM model.

4.7.2 Elements and Geometry

The mooring lines are modeled as pipe elements with zero inner diameter and zero bending

stiffness since we are interested in analyzing for polyester and steel mooring lines with no

bending stiffness. Since, the mooring line is not a pipe in reality, equivalent pipe dimensions are

found to conserve the properties of weight and density.

77

The mooring line drag coefficient corresponding to nominal bar diameter was taken from DNV

rules, 2010 as,

CD = 2.4 for studless chain

CD = 2.6 for studlink chain

CD = 1.5 for fiber rope

OrcaflexTM uses an iterative method based on Newton-Rhapson method to find the system

equilibrium and uses an improved catenary equation to estimate the stiffness of mooring lines.

The two buoy geometries are imported in OrcaflexTM and a 6 DOF single point mooring system

is set up. The following two buoy geometries as shown in Figure 43 were input in the software.

Figure 43: The two Buoy Geometries that are input into OrcaflexTM

4.7.3 Load Definition

OrcaflexTM allows the user to input conditions for waves, wind and current.

78

4.7.4 Sea States for Load Analysis

The mooring system was subjected to the seastates OF2 to OF 9 as per Table in Appendix 4.

All waves were given a heading of 180 degrees. This is not a significant setting as the buoy is

symmetric around the z axis.

Since there was no current or wind data present, they were not included in the load definition.

4.7.5 Import of time series to generate wave elevation

It is possible to import the time series of wave elevation recorded during the model test in the

wave basin, if direct comparisons have to be made for irregular cases. OrcaflexTM uses Fast

Fourier Transform (FFT) to transform the input time series into a frequency distribution. Then

each frequency component defines a unique wave. These waves are then combined by the

principle of wave superposition to generate a wave form. This way one can generate the exact

irregular wave that was used in the experimental wave tank test.

It is interesting to note, the higher the number of components of wave, the higher is the

simulation time in OrcaflexTM. This time dependence is primarily due to FFT. In general, the

number of samples N that are used to represent a period must be a power of 2 such that N

number of samples produces N/2 components.

For the simulation only three wave components were used in one direction. Greater the

number of components, greater is randomness in the incoming irregular wave chosen for

simulation. See Appendix 12 for seeing how regular waves interact to produce irregular waves.

4.7.6 Import of second order drift coefficients from tank tests

The mean drift coefficients are imported into the OrcaflexTM. These coefficients are taken from

the diffraction tests done in the wave tank. This initiates the QTF matrix where terms for

damping are input by OrcaflexTM.

79

4.7.7 Outputs

Following outputs were extracted from the simulations for two degrees of freedom (surge and

heave)

1. Buoy Positions

2. Buoy Velocities

3. Buoy Accelerations

4. Force on Tether

5. Force on Buoy

6. Moments on Buoy

7. Simulation Videos to identify critical snapping events

5

4.7.8 Survival Strategies

Two survival strategies are tested in OrcaflexTM,

1. Strategy 1: The buoy is pulled down underwater where it is held until the wave passes

2. Strategy 2: The buoy is let loose and allowed to move with the incoming waves such that

it is detuned with the incoming waves.

Such strategies are tested and corresponding forces recorded. Figure 44 shows a slack event

for OF7.

Figure 44: Slender Buoy undergoing a slack event under the influence of an extreme sea state

OF7

4.8 Variation Mode and Effect Analysis

4.8.1 Some Definitions

Fatigue Strength: The stress range corresponding to fatigue life of one million cycles

Fatigue Load: The structure’s stress range scaled by a factor equal to ‘beta root’ of the

target life in cycles over one million, where beta is the fatigue exponent for the material.

Fatigue Beta Norm: The beta root of the average of stress ranges raised to the power of

beta.

SLACK

80

4.8.2 The Corpower WEC Buoy

As described in the chapter on Fatigue, there are several connections, the buoy body and

the tether that are sensitive to fatigue failure. As part of thesis work, VMEA estimations

were done for these several sensitive areas but in this report only the tether will be

presented.

The tether is estimated for two materials polyester and steel. In this report, results for only

the steel wire will be presented to preserve conciseness.

The tether is subjected to tensile loads as the buoy undergoes motions in the vertical plane

due to the influence of waves. As part of load data, we have inputs from a mathematical

model as well as experimental results. Hence all loading information was obtained from

these sources.

The strength data for the steel wire is obtained from literature.

4.8.3 Uncertainties

Values obtained for strength and load will be subjected to certain uncertainties. These are

assessed by means of their standard deviations and by the difference between their

logarithmic values.

For uncertainties that are termed as scatter, their sources are not very well understood or

random and they could be due to lack of knowledge. They may be improved later by further

study in the field.

4.8.4 Design Life

The material will be designed for a life time of 25 years strong enough to withstand at least

1 million cycles14 of Equivalent Load. VMEA will then predict the uncertainty of the

predicted life for the tether. Based on this information a fatigue strength representing 95%

survival probability will be estimated to give the steel tether dimensions.

14 Life Span of 25 years and 1 million cycles were given by CPO as inputs according to their design requirements.

81

4.8.5 Inputs for VMEA

Equivalent Fatigue Load

Values for Equivalent Fatigue Loads are taken from the fatigue analysis done in Chapter 5.

Fatigue Exponent

Next we need to estimate the fatigue exponents or beta factor for steel wire.

For this we use DNV rules for the estimation of fatigue component

(42)

The given DNV design equivalent strength needs to be transformed to the nominal

equivalent strength by increasing it with two standard deviations. We then have the fatigue

component as and nominal equivalent strength for steel rope as 302.2 MPa15.

15 Calculated from S-N Curve for steel with

82

4.8.6 Sources of Uncertainty

4.8.6.1 Nominal Equivalent Load

The Nominal Equivalent Load is based on scaled experiments which are extrapolated to real

environments by scaling, modeling and summation over sea states. This process can have

the following sources of uncertainty.

1. Scaling and Experimental Equivalence

2. Friction

3. Extrapolation Model

4. Relevance of Rain Flow count

5. Sampling Error in experiments

6. Sampling of service environment

4.8.6.2 Strength

For the assessment of material strength, the following sources of uncertainty are present.

1. Scatter in fatigue strength from experiments

2. Parameter Uncertainty

3. Model Error, Linearity

4. Model Error, Palmgren Miner

5. Model Error, Mean value influences

6. Laboratory Uncertainty

83

Chapter 5

Results and Discussions

5.1 Tools Developed for Analysis

5.1.1 Data Comparison Tool

For the purpose of comparison, a mathematical tool was developed in MatlabTM that takes

in two different experimental data files and then compares them for different parameters

like,

1. Minimum and Maximum Values

2. Sorted Peaks

3. Frequency Distribution

4. Statistical Measures

With the help of the tool, one can compare,

1. Two different Buoys for the same seastate

2. Different control mechanisms like latching or Wavesprings

3. A buoy in different seastates

Figure 45 shows the starting interphase and Figure 46 shows an example of sorted peaks for

a buoy in different sea states.

84

Figure 45: GUI for loading data files for comparison

Figure 46: Result GUI with options to compare two different data files

5.1.2 Other Tools

In addition to the Comparison Tool, specific codes were written for general future use at

CPO. These have been described in Chapter 4 and some of the codes can be found in

appendices. These tools are,

1. Rainflow Count Estimator

2. Equivalent Load for Fatigue Life Calculator

3. Data Filtration and Peak Identification

4. Factor of Safety estimator using VMEA

5.2 Experimental Data Results

5.2.1 Peak Loads for all experimental cases

All the experimental data was processed according to the methodology described in Chapter

4. Peak Loads and Fatigue Equivalent Loads were estimated for all experimental cases,

85

which have been summarized in Appendix 6. The cases are sorted in accordance with their

ID numbers which were assigned during experiments.

5.2.2 Peak Loads in Survival Seastates

From all the cases, the peak loads experienced by the buoy in survival conditions are

interesting as they can form the basis for designing the dimensions and selecting the

material for the tether.

Table 2 and Table 3 summarize tension force peaks recorded for Buoy 1 and Buoy 2 under

survival seastate simulations in wave tank. All forces in the table have been scaled to a full

scale model by selecting an appropriate scaling factor according to Appendix 3. The negative

sign indicates tension in the tether.

BUOY 1

ID No. Peak Load (MN) Hs (m) Tp (s) Type

166 -2.51 6 7 Wavespring

167 -2.82 8 8 Wavespring

168 -2.85 9 9 Wavespring

ID No.16 Peak Load (MN) Hs (m) Tp (s) Type

169 -3.09 11 11 Wavespring

170 -3.39 7.2 11 Wavespring

172 -3.1 8.4 15 Wavespring

290 -3.18 8.4 13 Wavespring

175 -3.72 9 9 Linear Damper

176 -3.71 8.4 13 Latching

293 -3.92 12 15 Latching

16 For more details on the ID number and type of experiment, please consult Runlist.xslx which can be

procured on request from CPO.

86

Table 2: Summary of Peak Forces acting on the tether for Buoy 1 for Survival

Sea States for a full scale buoy (The negative sign is an indication of tensile loads)

BUOY 2

ID No. Peak Load (MN) Hs (m)17 Tp (s) Type

279 -2.73 6 7 Wavespring

280 -2.61 8 8 Wavespring

281 -3.28 8.4 15 Wavespring

284 -3.39 9 9 Wavespring

289 -3.3 8.4 13 Wavespring

282 -3.16 9 9 Latching

283 -3.44 8.4 13 Latching

ID No. Peak Load (MN) Hs (m)18 Tp (s) Type

285 -3.74 8.4 13 Latching

Table 3: Summary of Peak Forces acting on the tether for Buoy 2 for Survival

Sea States for a full scale buoy (The negative sign is an indication of tensile loads)

5.2.3 Deduction of Cross-sectional area of tether based on Peak Experimental Loads

At the time, there are two primary materials that are under investigation, Steel and

Polyester. In addition HSLA steel has been added to the list for added reference.

For both Buoys,

The tensile stress in the tether can be calculated Equation 21 in Chapter 3 Section 3.5.2.

Since the dimensions of the tether are not decided at this point, the present information will

be used to deduce minimum cross-sectional area for the tether. This has been deduced in

Table 4.

17 Wave Height and Time Period in Table 2 and Table 3 have been scaled to full scale by using an appropriate scaling factor taken from Appendix 3.

18 Wave Height and Time Period in Table 2 and Table 3 have been scaled to full scale by using an appropriate scaling factor taken from Appendix 3.

87

Buoy Material Peak Tensile Load (MN)

Factor of Safety19

Yield Stress (MPa)

Cross Section Area (cm2)

1

Steel

-3.34

1.4 310 150.8

HSLA Steel 1.4 550 85

Polyester 1.75 115 508.2

2

Steel

-3.39

1.4 310 153.1

HSLA 1.4 550 86.3

Polyester 1.75 115 515.8

Table 4: Assessment of Minimum cross-section area of tether based on yield

strength and Maximum Experimental Loads in Wave Tank Test at Nantes, 2014

5.2.4 Fatigue and assessment of Equivalent Load for irregular seastate wave tank experiments

Fatigue is caused by cyclic loading on a structure. It is interesting to assess equivalent loads

for irregular seastate experiments since an irregular seastate will have a larger variation and

frequency of cyclic loads as compared to a regular wave,. Table 5 summarizes Equivalent

Loads for a design life of 25 years and 1 million cycles for Buoy 1.20 Similar results can be

found for Buoy 2 in Table 6.

BUOY 1

ID No. Equivalent Load (MN)

Wave Height (m)

Wave Period (s)

Ultimate Load/ Equivalent Load

109 0.51 1 6 4.51

110 0.81 1 8 3.01

111 1.02 1 10 2.54

112 1.57 2.5 8 1.80

113 1.81 2.5 10 1.61

114 1.96 2.5 12 1.46

115 1.91 2.5 12 1.50

116 1.81 2.5 12 1.58

19 Factor of Safeties are as deduced in section 5.9 using VMEA

20 Time span of 25 years and 1 million cycles were stated as requirements by CPO

88

117 0.25 1 6 8.15

118 0.25 1 8 8.38

119 0.49 2.5 8 4.65

120 0.55 2.5 10 4.11

121 0.68 2.5 12 3.43

122 0.78 2.5 14 3.14

123 0.22 1 12 8.44

124 0.27 1.5 12 6.84

125 0.22 1 12 8.32

126 0.96 1 10 2.68

127 2.78 2.5 12 1.01

128 1.79 2.5 12 1.60

129 1.76 2.5 14 1.66

Table 5: Equivalent Loads for Fatigue Design Life of 25 years and 1 million

cycles in irregular seas for Buoy 1

BUOY 2

ID No. Equivalent Load (MN)

Wave Height

(m)

Wave Period (s)

Ultimate Load/

Equivalent Load

257 0.73 1 6 3.12

258 1.13 1 8 2.00

259 1.36 1 10 1.85

260 1.92 2.5 8 1.40

261 1.95 2.5 10 1.37

262 1.99 2.5 12 1.31

263 2.02 2.5 14 1.33

264 2.19 4 10 1.34

265 1.39 2.5 8 1.79

266 0.71 2.5 10 2.82

267 0.56 2.5 12 3.44

Table 6: Equivalent Loads for Fatigue Design Life of 25 years and 1 million

cycles in irregular seas for Buoy 2

5.2.5 Fatigue Equivalent Loads and comparison with RMS Loads for Survival Cases

Table 7 and Table 8 summarize the Equivalent loads for survival cases for a 1:16 scale model

and its comparison with RMS loads.

89

BUOY 1

ID No. Equivalent Load

(kN) RMS Load on

Buoy (kN) Hs (m) Tp (s) Mechanism

Eq. Load/ RMS

166 3.69 3.05 6 7 Wavespring 1.21

167 7.25 5.84 8 8 Wavespring 1.24

168 7.99 6.54 9 9 Wavespring 1.22

169 1.59 8.61 11 11 Wavespring 1.84

ID No. Equivalent Load

(kN) RMS Load on

Buoy (N) Hs (m) Tp (s) Mechanism

Eq. Load/ RMS

170 8.7 7.18 7.2 11 Wavespring 1.21

172 5.95 5.23 8.4 15 Wavespring 1.14

290 11.71 6.91 8.4 13 Wavespring 1.70

175 8.9 6.75 9 9 Latching 1.32

176 9.01 7.51 8.4 13 Latching 1.20

293 12.03 9.32 12 15 Latching 1.29

Table 7: Fatigue Loads, Design Life and Equivalent Load for Buoy 1 for 1:16

scale model in irregular waves

BUOY 2

ID No. Equivalent Load (kN)

RMS Load on Buoy (N)

Hs (m) Tp (s) Mechanism Eq.

Load/ RMS

279 6.18 5.6 6 7 Wavespring 1.10

280 8.24 6.92 8 8 Wavespring 1.19

281 17.4 17.01 9 9 Wavespring 1.02

284 9.25 6.64 8.4 13 Wavespring 1.39

282 11.8 8.19 11 11 Latching 1.44

90

283 11.96 7.92 7.2 11 Latching 1.51

285 11.12 7.84 8.4 15 Latching 1.42

Table 8: Fatigue Loads, Design Life and Equivalent Load for Buoy 2 for 1:16

scale model in irregular waves

The aim of comparing Equivalent Loads with the RMS loads was to see if there is an

observable range. With a few exceptions, it can be said that the ratio lies between 1 and 1.4

usually.

5.3 Discussion on Experimental Data Results

5.3.1 Need for pretension

When the buoy was setup in the testing facility (Figure 6), the wire at the bottom of the

buoy went through the tensile force sensor. Since the buoy’s motion under the influence of

waves can be impulsive, a pretension was necessary to accurately record the change in

tension in the connecting wire.

So in the initial position, the buoy is pulled down a little to give the wire a pretension value.

As the buoy oscillates in water, the forces are measured with the pretension as the

reference value.

5.3.2 Wavespring/Linear Damper as compared to latching

As seen from the results for survival cases in Table 2 and Table 3, the maximum tension

recorded for A ‘Wavespring’ system was lower than ‘Latching’ system. This happens because

the Wavespring smoothens out the motions, thus the acceleration curves are continuous

and differentiable and the impulsive forces get minimized or negated.

5.3.3 Buoy Performance

It was generally observed from the results for all regular, irregular and survival cases that

Buoy one recorded lesser forces on tether in comparison with Buoy 2 for most of the cases,

especially the higher sea states. Another factor for choosing the buoy was the power

91

generated by the buoy in which Buoy one performed better overall. The overall lower force

and higher generated power can be explained by the principal of conservation of energy.

Here energy brought from waves is converted into power generated, kinetic energy, strain

energy and energy losses. Since the force on the tether is less, it will take lower strain

energy which in turn means more energy is available for conversion into useful power.

So, it can be concluded that Buoy 1 has better survivability and performance as compared to

Buoy 2.

5.3.4 Sources of Noise in Experimental Data and the need for filtration

During the tank testing, there are several factors that can create noise. Most prominent are

the reflection of waves from the side walls of the wave tank. Hence an experiment can be

performed only for a limited time until wave reflection from walls is insignificant. Other

sources of noise are micro vibrations due to generators that can cause the sensors to over

record. Noise is usually treated by using a suitable low pass frequency filter.

5.3.5 Choice of Filter and Corresponding Performance

The choice of filter and its characteristics can play a big role in the output of useful data. For

the purpose of filtering, 3 different filters were tried,

1. Butterworth Filter

This filter was the most suitable one gave fairly good filtration results for 9th order function

with a filtration frequency of 2.5 Hz.

2. Kaiser Filter

This filter relied on inputs for lower band and upper band frequencies and had room for

oscillations and ripples within the filtration process. This filter tended to over filter the

92

results either on the lower band or upper band. Narrowing down the exact frequency range

proved to be challenging as each raw_data case behaved differently.

3. Ideal Filter

This is a common digital filter that takes frequency as input. The filtration results were not

very good as it tended to shift the raw data vertically in force scale and gave spurious results

for some cases while it behaved well for other cases.

Of the three filters, the Butterworth filter seemed the most reliable.

5.4 Simulink Simulation Model Results

The Simulation model’s data was used to perform the following tasks,

1. Run Simulations for those sea-states which were tested in the wave tank as

shown in Figure 26 in Section 4.2.2.

2. Perform validation by comparing the results obtained from Experiments and

Simulation Model for same sea states.

3. Run Simulations for all missing sea states as shown in Figure 25 in Section 4.2.2.

4. Analyze data and generate outputs as per deliverables in Chapter 1.

Here comparison of results between Experimental and Simulation Results are presented.

Detailed results of Fatigue Loads can be found in Appendix 8 and results for Ultimate and

Statistical Loads can be found in Appendix 7.

F_Subsea in the experimental data file and F_wire in the Simulation data file were compared

for Mean, RMS and peak values. There was good agreement and the ratio of Simulation is to

Experiment was reasonable around 1.1. Figure 47, shows different ratios of RMS values that

were compared for the two sources.

93

Figure 47: Ratio of RMS Loads between Simulink simulation loads and experimental loads for

force on the buoy tether in irregular waves. Top half of table represents Buoy 1 for Wavespring

and Bottom Half of table represents Buoy 2 for Wavespring

Since Peak Loads can be rogue despite adequate filtration, a more dependable measure for

validating would be RMS Loads. Thought the ratio was not exactly 1 the range was

satisfactory with limits between 1.03 and 1.21.

Table 9 shows the ratio of Peak Loads between simulation and experimental model results.

As it can be seen, the ratio is around 1.27. The difference can be explained by the fact that

the simulation model is 2 DOF and by conservation of energy, overestimate in surge and

heave direction.

Buoy 1 Buoy 2

94

Wave Height

(m)

Wave Period

(s)

Simulation Peak/

Experimental Peak

1 6 1.23 1.19

1 8 1.25 1.28

1 10 1.27 1.23

2.5 8 1.30 1.30

2.5 10 1.28 1.32

2.5 12 1.30 1.35

2.5 14 1.27 1.30

4 10 1.27 1.23

4 12 1.27 1.20

Table 9: Ratio of Peak Forces in tether obtained from experimental and

simulation model for Buoy 1 and Buoy 2

5.4.1 Statistical Loads

Maximum Loads

Table 10: Peak Loads in N for a full scale buoy recorded on the tether based on

simulation data

As seen from Table 10, the peak loads become quite significant and similar in magnitude for

sea states with time periods greater than 10 seconds and wave height greater than 2.5 m.

The highest peaks were observed for the highest waves with Hs = 7.5 m and Tp = 13

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 2569466 2570460 2599280 2599280 2815371 2848313 2789925 3085854 3112638 3172704 3149524 3233747 0 0 0

1 0 2648407 2758648 2855616 2872700 3069794 3286005 3259287 3256369 3390833 3598085 3467098 3501718 3544118 3528087

1.5 0 0 3528087 3528087 3528087 3528087 3528087 3678234 3704150 3704172 3685022 3648875 3613062 3613062 3575382

2 0 0 0 3555525 3555525 3727436 3722567 3672569 3712815 3810069 3740045 3691047 3688583 3687799 3687799

2.5 0 0 0 3687799 3687799 3687799 3700773 3715317 3708967 3740140 3704588 3700175 3661172 3667260 3642304

3 0 0 0 3636663 3636663 3694462 3790383 3823552 3724746 3818686 3801719 3795879 3715663 3715663 3715663

3.5 0 0 0 0 3829244 3813726 3812150 3846320 3785856 3785856 3808170 3804094 3804094 3847795 3804094

4 0 0 0 0 0 3894951 3905611 3829495 3856294 3883561 3825330 3898286 3776560 3807547 3943448

4.5 0 0 0 0 0 0 3871694 3886359 3845992 3881007 3882093 3970824 3973283 3796832 3808254

5 0 0 0 0 0 0 0 3911742 3883289 3845508 3845256 3885905 3918571 3873717 3879551

5.5 0 0 0 0 0 0 0 4021836 4007429 3917940 3925140 3955033 3945685 4002351 3923978

6 0 0 0 0 0 0 0 0 3878512 3890056 3791233 3997424 4015979 3873419 3932779

6.5 0 0 0 0 0 0 0 0 0 4025487 3965232 3961036 3986397 3922685 3916497

7 0 0 0 0 0 0 0 0 0 3949321 3990567 4050576 4027331 4040061 3973969

7.5 0 0 0 0 0 0 0 0 0 4046951 4179908 4179908 3968861 4019146 4019146

Max Loads_Peaks

Tp

Hs

95

seconds. It is interesting to note that the worst loading is not observed for longer wave

periods. This is a consequence of constructive interference and resonance phenomenon at

certain wave periods. Table 11, 12 and Table 13 show the results for the Mean, RMS and

average of top 10 forces.

The maximum recorded Peak Load was 4.18 MN at Hs = 7.5 m and Tp = 13 s. In addition, a

factor of safety as determined by VMEA will need to be applied depending on the material

used. The FOS’s can be found in Table 21.

Mean Loads

Table 11: Mean Loads in N for a full scale buoy recorded on the tether based on

simulation data

The maximum recorded Mean Load was 3.46 MN at Hs = 7 m and Tp = 13 s. In addition, a

factor of safety as determined by VMEA will need to be applied depending on the material

used. The FOS’s can be found in Table 21.

RMS Loads

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 2534623 2530851 2530726 2532694 2537357 2544047 2542860 2549020 2563160 2566367 2569471 2579059 0 0 0

1 0 2538292 2539919 2547139 2548414 2581124 2582937 2596913 2604862 2595753 2598578 2620377 2635966 2639026 2662891

1.5 0 0 2596112 2605368 2609401 2630387 2621253 2648791 2655250 2637331 2683195 2691852 2677888 2689373 2718271

2 0 0 0 2634935 2644635 2668143 2687371 2693413 2713714 2761880 2756670 2798838 2791258 2809328 2771405

2.5 0 0 0 2705579 2727948 2755722 2789026 2812793 2825912 2856355 2888122 2872531 2867164 2854874 2875501

3 0 0 0 2783218 2806149 2857270 2865493 2951779 3010283 2981671 3029335 3007625 2988318 2998749 2992707

3.5 0 0 0 0 2913986 2949558 3006387 3134475 3114953 3134430 3158393 3126843 3093476 3116546 3099411

4 0 0 0 0 0 3071514 3111549 3227998 3261981 3229576 3240613 3280618 3270964 3266263 3245153

4.5 0 0 0 0 0 0 3269214 3295870 3407669 3414135 3369658 3387679 3403357 3368467 3365514

5 0 0 0 0 0 0 0 3404977 3428023 3455498 3478915 3462252 3462323 3444938 3442739

5.5 0 0 0 0 0 0 0 3426026 3496904 3477871 3451334 3477567 3487107 3464362 3412970

6 0 0 0 0 0 0 0 0 3400633 3485575 3447201 3442155 3446892 3432769 3390779

6.5 0 0 0 0 0 0 0 0 0 3436168 3458769 3430652 3429331 3471776 3428384

7 0 0 0 0 0 0 0 0 0 3404490 3468868 3440373 3429228 3434795 3441881

7.5 0 0 0 0 0 0 0 0 0 3475039 3396851 3429299 3483369 3424070 3457184

Hs

Max Loads_Mean

Tp

96

Table 12: RMS Loads in N for a full scale buoy recorded on the tether based on

simulation data

The maximum recorded RMS Load was 3.05 MN at Hs = 7.5 m and Tp = 12 s. In addition, a

factor of safety as determined by VMEA will need to be applied depending on the material

used. The FOS’s can be found in Table 22.

H1/10 Peak Loads (Average of Top 10 highest loads)

Table 13: A 1/10 Loads in N for a full scale buoy recorded on the tether based on

simulation data

The maximum recorded H1/10 Load was 3.85 MN at Hs = 7.5 m and Tp = 15 s. In addition, a

factor of safety as determined by VMEA will need to be applied depending on the material

used. The FOS’s can be found in Table 22.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 2520011 2521921 2527809 2561014 2594519 2643985 2649995 2695887 2694225 2676641 2675668 2681171 0 0 0

1 0 2535871 2543211 2580909 2618427 2668264 2663372 2696294 2688408 2663667 2641541 2638683 2643031 2606885 2615189

1.5 0 0 2554641 2590391 2623121 2663313 2651764 2671620 2654018 2669064 2659917 2651905 2642833 2606733 2612939

2 0 0 0 2602699 2630676 2645177 2646375 2679675 2635125 2653436 2650757 2666318 2650745 2624609 2629219

2.5 0 0 0 2609238 2622423 2654059 2651251 2684719 2662962 2667372 2680697 2657021 2662068 2655748 2646981

3 0 0 0 2620918 2631555 2655980 2653574 2688234 2701050 2674913 2685745 2667688 2689050 2654647 2632061

3.5 0 0 0 0 2657824 2675316 2677419 2732337 2727309 2721175 2708983 2668927 2688692 2675017 2649389

4 0 0 0 0 0 2699426 2692668 2772425 2764023 2750418 2745205 2736040 2710610 2702887 2710343

4.5 0 0 0 0 0 0 2696612 2797328 2822392 2787156 2814450 2761501 2741620 2762729 2720779

5 0 0 0 0 0 0 0 2845094 2855680 2852351 2839930 2818608 2788649 2774951 2759669

5.5 0 0 0 0 0 0 0 2863828 2886621 2907429 2872010 2896855 2837605 2807650 2785454

6 0 0 0 0 0 0 0 0 2931426 2955258 2888610 2868277 2851590 2868860 2835377

6.5 0 0 0 0 0 0 0 0 0 2945466 2995268 2971548 2926347 2900740 2875775

7 0 0 0 0 0 0 0 0 0 3011079 3035284 2984967 2953446 2941110 2921236

7.5 0 0 0 0 0 0 0 0 0 3054688 3029974 3032548 3067314 2990835 3000191

Hs

Max_Loads_RMS

Tp

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 2556359 2557460 2582165 2599280 2815371 2848313 2789925 3085854 3083118 3104500 3106663 3136181 0 0 0

1 0 2619835 2698275 2855616 2872700 3049307 3259100 3244469 3238620 3368928 3594129 3451492 3495259 3514345 3486332

1.5 0 0 3499272 3499272 NaN 3474888 3499272 3675511 3704150 3614260 3664448 3621727 3588744 3604288 3561390

2 0 0 0 3553095 3553791 3725002 3722567 3661590 3673416 3715168 3704166 3666408 3651527 3628972 3626182

2.5 0 0 0 3648210 3661421 3683803 3694761 3706591 3682232 3688818 3681718 3646931 3637286 3638681 3607435

3 0 0 0 3618443 3635805 3683445 3773004 3750810 3707129 3748204 3746233 3715676 3669558 3666752 3648699

3.5 0 0 0 0 3692951 3779821 3750973 3756029 3726811 3739235 3721922 3724839 3742243 3759329 3719608

4 0 0 0 0 0 3838214 3803893 3783300 3739597 3751360 3735993 3753073 3728262 3745386 3753881

4.5 0 0 0 0 0 0 3826896 3763361 3756856 3797161 3764818 3804703 3811689 3751620 3766128

5 0 0 0 0 0 0 0 3804803 3769068 3753066 3763388 3791133 3770380 3774942 3801250

5.5 0 0 0 0 0 0 0 3793507 3839803 3781046 3771325 3765930 3873256 3775715 3773813

6 0 0 0 0 0 0 0 0 3771587 3782294 3748179 3848138 3801627 3769193 3771407

6.5 0 0 0 0 0 0 0 0 0 3808749 3787270 3782861 3790440 3829491 3785079

7 0 0 0 0 0 0 0 0 0 3767556 3803631 3850661 3799455 3816058 3839448

7.5 0 0 0 0 0 0 0 0 0 3851388 3816912 3835645 3853162 3859566 3817329

A10_Max Loads

Tp

Hs

97

5.4.2 Deduction of Cross-sectional area of tether based on Peak Simulation Loads

In line with Section 5.2.3, there are two primary materials that are under investigation by

CPO, Mild Steel and Polyester. In addition HSLA steel has been added to the list for added

reference.

In Section it was deduced that Buoy 1 has better performance and hence the following

analysis has been done only for it.

The tensile stress in the tether can be calculated Equation 21 in Chapter 3 Section 3.5.2.

Since the dimensions of the tether are not decided at this point, the present information will

be used to deduce minimum cross-sectional area for the tether. This has been deduced in

Table 14.

Material Peak Tensile Load (MN)

Factor of Safety21

Yield Stress (MPa)

Cross Section Area (cm2)

Buoy 1

Steel

4.18

1.4 310 188.7

HSLA Steel 1.4 550 106.4

Polyester 1.75 115 636.1

Table 14: Assessment of Minimum cross-section area of tether based on yield strength and

Maximum Simulation Loads in Wave Tank Test at Nantes, 2014

21 Factor of Safeties are as deduced in section 5.9 using VMEA

98

5.4.3 Fatigue Loads

Equivalent Load

Table 15: Equivalent Loads in N for a full scale buoy for fatigue predicted for

the tether based on simulation data

If one observes Table 15 for Equivalent Load for different sea states, the equivalent load

keeps increasing as the significant wave height increases but it is really interesting to note

that the equivalent load for any wave height increases up to a time period of 11 seconds

and then decreases thereafter. A wave period of 11 seconds might coincide with the

periodic of the buoy’s natural period which causes constructive interference resulting in

resonance.

Life time Damage

Table 16: Life time damage for full scale buoy due to fatigue predicted for the

tether based on simulation data at Yue

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 48662.37 113113.4 283000.5 413467 639272.4 640201 808937.8 988816.4 1017887 986569.6 1065811 1055498 0 0 0

1 0 325154.4 730932.5 966061.9 1214395 1415688 1600277 1740124 1774629 1798576 1780514 1803675 1733694 1785156 1741280

1.5 0 0 1131082 1491341 1795050 2093922 2173921 2293324 2256953 2188696 2237558 2229274 2225190 2130110 2129120

2 0 0 0 2036105 2319711 2497820 2546713 2528391 2548239 2512650 2518962 2460365 2431655 2375971 2349253

2.5 0 0 0 2390482 2686136 2754976 2813283 2764153 2776615 2770262 2736806 2628031 2628797 2576905 2543234

3 0 0 0 2691443 2924193 3012345 3007548 3022218 2956616 2889378 2876932 2783847 2786075 2743495 2682201

3.5 0 0 0 0 3119658 3137575 3129102 3201029 3092443 3110293 3070668 2953908 2912772 2829589 2782744

4 0 0 0 0 0 3332027 3277060 3330866 3278659 3195147 3208645 3075696 3027572 2983435 2910244

4.5 0 0 0 0 0 0 3446756 3357021 3362135 3303878 3268607 3206435 3164875 3051704 3012549

5 0 0 0 0 0 0 0 3411112 3432240 3357367 3349350 3315936 3220906 3172422 3091575

5.5 0 0 0 0 0 0 0 3578084 3548526 3518120 3364759 3430947 3365270 3277175 3229667

6 0 0 0 0 0 0 0 0 3469029 3546849 3463096 3379263 3366779 3344514 3225584

6.5 0 0 0 0 0 0 0 0 0 3490741 3466031 3396966 3470549 3329087 3345315

7 0 0 0 0 0 0 0 0 0 3546837 3573208 3482830 3457586 3375980 3380748

7.5 0 0 0 0 0 0 0 0 0 3608938 3633674 3556597 3595654 3545479 3321358

Hs

Fatigue_Equivalent Load

Tp

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 3.15E+28 1.81E+30 1.47E+32 9.1E+32 7.37E+33 7.42E+33 2.28E+34 5.98E+34 6.87E+34 5.91E+34 8.57E+34 8.18E+34 0 0 0

1 0 2.87E+32 1.4E+34 5.35E+34 1.6E+35 3.35E+35 6.03E+35 9.01E+35 9.9E+35 1.06E+36 1.01E+36 1.07E+36 8.85E+35 1.02E+36 9.04E+35

1.5 0 0 1.14E+35 4.3E+35 1.05E+36 2.19E+36 2.62E+36 3.39E+36 3.14E+36 2.71E+36 3.01E+36 2.96E+36 2.93E+36 2.38E+36 2.37E+36

2 0 0 0 1.92E+36 3.58E+36 5.11E+36 5.61E+36 5.42E+36 5.62E+36 5.26E+36 5.32E+36 4.75E+36 4.49E+36 4.02E+36 3.81E+36

2.5 0 0 0 4.14E+36 7.24E+36 8.18E+36 9.04E+36 8.31E+36 8.49E+36 8.4E+36 7.92E+36 6.52E+36 6.53E+36 5.93E+36 5.57E+36

3 0 0 0 7.31E+36 1.09E+37 1.26E+37 1.25E+37 1.28E+37 1.15E+37 1.03E+37 1.01E+37 8.6E+36 8.63E+36 8.01E+36 7.19E+36

3.5 0 0 0 0 1.48E+37 1.53E+37 1.51E+37 1.68E+37 1.42E+37 1.46E+37 1.38E+37 1.14E+37 1.07E+37 9.3E+36 8.58E+36

4 0 0 0 0 0 2.04E+37 1.88E+37 2.03E+37 1.89E+37 1.67E+37 1.7E+37 1.39E+37 1.29E+37 1.2E+37 1.06E+37

4.5 0 0 0 0 0 0 2.4E+37 2.11E+37 2.13E+37 1.96E+37 1.86E+37 1.69E+37 1.59E+37 1.34E+37 1.26E+37

5 0 0 0 0 0 0 0 2.28E+37 2.35E+37 2.11E+37 2.09E+37 1.99E+37 1.73E+37 1.61E+37 1.42E+37

5.5 0 0 0 0 0 0 0 2.87E+37 2.76E+37 2.64E+37 2.13E+37 2.34E+37 2.14E+37 1.88E+37 1.75E+37

6 0 0 0 0 0 0 0 0 2.47E+37 2.75E+37 2.45E+37 2.18E+37 2.14E+37 2.07E+37 1.74E+37

6.5 0 0 0 0 0 0 0 0 0 2.55E+37 2.46E+37 2.23E+37 2.48E+37 2.03E+37 2.08E+37

7 0 0 0 0 0 0 0 0 0 2.75E+37 2.85E+37 2.52E+37 2.43E+37 2.17E+37 2.18E+37

7.5 0 0 0 0 0 0 0 0 0 2.99E+37 3.09E+37 2.79E+37 2.94E+37 2.74E+37 2.01E+37

Fatigue_Lifetime Damage

Hs

Tp

99

The life time damage as shown in Table 16 is a measure that in itself does not give any

information but can be translated into predicting the equivalent load for a desired life time.

This means that the above data can be used to compute the equivalent lifetime damage for

a target site with given sea state scatter information. Further this value can be used to

compute one equivalent load for an entire area.

5.4.4 Equivalent Load Estimation for ‘Yue’ target site

For estimating the equivalent load, first the equivalent damage is to be estimated for a

target site. It is done by multiplying the normalized sea state distribution factors (Table 17)

for a target site with lifetime damages as shown in Table 18. Results here are presented for

a target site named ‘Yue’.

Table 17: Normalized Scatter distribution of different sea states for target site

‘Yue’

After Table 16 and Table 17 are multiplied we get the target life time damage distributions

as shown in Table 18. Here each cell in the table corresponds to damage contribution due to

that sea state at ‘Yue’ over a life time of 25 years.

Yue

time 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 0.000148 0.006499 0.009306 0.007829 0.007533 0.007238 0.004431 0.001477 0.000148 0 0 0 0 0 0

1 0 0.006647 0.025554 0.031315 0.039439 0.043131 0.028508 0.015805 0.007238 0.000443 0.000148 0.000148 0 0 0

1.5 0 0.000148 0.004284 0.019055 0.032496 0.032792 0.025111 0.016987 0.014476 0.010044 0.002068 0.000443 0.000295 0 0

2 0 0 0 0.008124 0.026292 0.027474 0.020532 0.017134 0.007533 0.007238 0.002659 0.001329 0.000739 0 0

2.5 0 0 0 0 0.009453 0.040325 0.037814 0.031758 0.012408 0.008419 0.005022 0.001329 0.000295 0 0

3 0 0 0 0 0.001773 0.032792 0.039734 0.029247 0.013146 0.010192 0.006795 0.003693 0.001182 0 0

3.5 0 0 0 0 0 0.008124 0.034269 0.022452 0.013885 0.007681 0.006056 0.004284 0.002659 0.000886 0.000148

4 0 0 0 0 0 0.000443 0.012851 0.014919 0.007681 0.005761 0.00325 0.00325 0.002659 0.001773 0.000443

4.5 0 0 0 0 0 0 0.003102 0.005022 0.00709 0.002511 0.001477 0.000739 0.000591 0 0.000148

5 0 0 0 0 0 0 0.000295 0.002363 0.003988 0.001773 0.000886 0.000148 0 0 0

5.5 0 0 0 0 0 0 0 0.000886 0.002806 0.001477 0.000739 0 0 0 0

6 0 0 0 0 0 0 0 0.000443 0.001625 0.001034 0 0.000148 0 0 0

6.5 0 0 0 0 0 0 0 0 0.000295 0.000886 0.000148 0 0 0 0

7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7.5 0 0 0 0 0 0 0 0 0 0.000295 0 0 0 0 0

100

Table 18: Life Time Damage distribution of different sea states for target site

‘Yue’

The summation of Table 18 gives the life time damage for the entire sea state for 25 years.

This corresponds to 7.19433 x 1036.

This information is used to compute the equivalent life using Equation 27. For ‘yue’ scatter

site the equivalent load is estimated as 2682 KN.

The same principle is extended to compute equivalent loads at other target sites around the

world.

5.5 Discussion on Simulation Model Results

5.5.1 RMS values vs peaks to validate

When we compare the results of experimental data and simulation data, it is more useful to

compare the RMS values instead of the peaks. Since, peaks can originate from sources of

noise and may not give an accurate representation of the actual phenomenon if its

occurrence is very rear. Hence for the purpose of validation, both peaks and RMS values

were used.

5.5.2 Lack of 6 DOF model

The simulation model is designed for two degrees of freedom in the direction of heave and

surge. Hence rotations are not captured in the model. This accounts for the difference in

Yue Life Time Damage per sea state for 25 years

time 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 4.65525E+24 1.17E+28 1.37E+30 7.12E+30 5.55E+31 5.37E+31 1.01E+32 8.83E+31 1.01E+31 0 0 0 0 0 0

1 0 1.91E+30 3.58E+32 1.67E+33 6.32E+33 1.44E+34 1.72E+34 1.42E+34 7.17E+33 4.68E+32 1.49E+32 1.58E+32 0 0 0

1.5 0 0 4.88E+32 8.19E+33 3.4E+34 7.18E+34 6.59E+34 5.76E+34 4.55E+34 2.72E+34 6.23E+33 1.31E+33 8.67E+32 0 0

2 0 0 0 1.56E+34 9.42E+34 1.4E+35 1.15E+35 9.28E+34 4.24E+34 3.8E+34 1.41E+34 6.32E+33 3.32E+33 0 0

2.5 0 0 0 0 6.85E+34 3.3E+35 3.42E+35 2.64E+35 1.05E+35 7.07E+34 3.98E+34 8.67E+33 1.93E+33 0 0

3 0 0 0 0 1.93E+34 4.12E+35 4.95E+35 3.73E+35 1.51E+35 1.05E+35 6.84E+34 3.17E+34 1.02E+34 0 0

3.5 0 0 0 0 0 1.24E+35 5.16E+35 3.77E+35 1.98E+35 1.12E+35 8.34E+34 4.89E+34 2.84E+34 8.24E+33 1.27E+33

4 0 0 0 0 0 9.03E+33 2.42E+35 3.03E+35 1.45E+35 9.59E+34 5.52E+34 4.51E+34 3.42E+34 2.12E+34 4.71E+33

4.5 0 0 0 0 0 0 7.43E+34 1.06E+35 1.51E+35 4.91E+34 2.74E+34 1.25E+34 9.4E+33 0 1.85E+33

5 0 0 0 0 0 0 0 5.39E+34 9.37E+34 3.74E+34 1.85E+34 2.94E+33 0 0 0

5.5 0 0 0 0 0 0 0 2.54E+34 7.73E+34 3.91E+34 1.58E+34 0 0 0 0

6 0 0 0 0 0 0 0 0 4.02E+34 2.84E+34 0 3.22E+33 0 0 0

6.5 0 0 0 0 0 0 0 0 0 2.26E+34 3.64E+33 0 0 0 0

7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7.5 0 0 0 0 0 0 0 0 0 8.83E+33 0 0 0 0 0

101

ratios for different sea states. By conservation of energy, due to lack of rotations, the

motions in surge and heave get exaggerated as compared to a realistic case.

The model is currently being developed to include all 6 degrees of freedom. On completion,

the model will be able to give a much clearer representation of the actual phenomenon.

5.5.3 Variation of Peak Loads with wave period and wave height

Equivalent Loads for Fatigue

As can be seen from figure 48, the calculated equivalent loads, for a life span of 25 years,

increase in magnitude as the wave height increases. The slope of the curve is steep for wave

heights up to 2.5 m and gradually flatten beyond 5.5 m wave height. This interesting

observation indicates to the fact that, if the significant wave height increases beyond 5.5 m,

it does not affect the material choice and dimensions of the concerned part. A possible

reason behind this observation is the relative size of the buoy with respect to the incoming

wave. Beyond 5.5 m large part of the buoy remains submerged and this could cause the

normalization of Equivalent Load. This observation needs further study to validate the

reason.

Figure 48: Variation of Fatigue Equivalent Load for 25 years with Wave Height

The variation of equivalent loads with time period is not monotonous and there are certain

peaks and troughs that are observed at different time periods. These peaks are not same for

900000

1400000

1900000

2400000

2900000

3400000

3900000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Variation of L Eq with Hs

Tp = 13 Tp = 15 Tp = 14

N

m

Variation of F Eq with Hs

102

all wave heights and can occur at different time periods. A likely cause of this is the

interference of incoming waves with the natural period of the buoy. Constructive

interference results in peaks while destructive interference results in troughs. This can be

observed in Figure 49.

Figure 49: Variation of Fatigue Equivalent Load for 25 years with Time Period

Peak Loads

As seen from Figure 50, the peak loads variation with wave height shows a general trend

that is flat from 1.5 m onwards but looking closely it is observed that the peaks undulate

along this flat line. It is interesting to see that the peak loads don’t vary so steeply after a

wave height of 1.5 m. This is a good thing in terms of material selection and dimensions of

the concerned part when designing for different offshore sites.

3300000

3400000

3500000

3600000

3700000

11 12 13 14 15 16 17 18

Variation of L Eq with Tp

Hs = 7.5 Hs = 7 Hs = 6.5

N

s

Variation of F Eq with Tp

103

Figure 50: Variation of Peak Loads for 25 years with Wave Height

A possible reason for the shallow rise and undulation between 1.5 m and 6 m could be

related to resonance. At certain wave heights, constructive interference might be causing

the humps while destructive interference causing the troughs. Further study is required to

ascertain the exact reason behind the shallow rise. A possible reason could be the influence

of the shape of the buoy.

Figure 51: Variation of Peak Loads for 25 years with Time Period

It can be seen in Figure 51 that the variation of Peak Loads with wave height is similar in

nature with that for equivalent loads. There are crests and troughs observed and it is likely

that this is caused due to constructive and destructive interference between the incoming

wave and the buoy motions.

3000000

3200000

3400000

3600000

3800000

4000000

4200000

4400000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Variation of Peak Loads with Hs

Tp = 13 Tp = 12 Tp = 14

3900000

3950000

4000000

4050000

4100000

4150000

4200000

4250000

11 12 13 14 15 16 17 18

Variation of Peak Loads with Tp

Hs = 7.5 Hs = 7 Hs = 6.5

N

m

N

s

104

5.6 Discussion on Fatigue Results

5.6.1 RMS vs Equivalent Load

As can be seen from Table 12 and Table 15, the RMS value of Loads acting on the buoy are

always lower than the equivalent load. This is a good indication since the analysis is based

on the predilection that the buoy survives one million cycles of loading equal to the

equivalent load. A similar trend was observed for all experimental cases. Also a comparison

between peak forces and equivalent load was made. The respective ratios can be found in

Appendix 6.

5.6.2 Estimation of Equivalent Load for a target site using damage factor

for individual sea states

During the estimation of equivalent load for each sea state for a given life time, one of the

steps is to estimate the damage undergone by the tether during the said period. If the

damage for all the sea states are known for the target life, then these values can be

normalized to one and multiplied with sea state occurrence frequency to compute the

overall damage in the target site. This overall damage can then be used to estimate the Life

time Equivalent Load for the target site.

5.6.3 Uncertainty in Fatigue Life Prediction

When a fatigue experiment is carried out for the same material in the exact same physical

conditions, the results can still vary. This is due to certain internal and external factors that

result in the overall variance of results from mean value. This is usually addressed by

including a factor of safety that is estimated using past experience or derived after treating

the results with statistical tools. This is addressed in VMEA in Chapter 4, Section 4.8.

5.6.4 Fatigue Sensitive Parts in Buoy

In addition to the tether, the internal mechanism of the buoy also undergo extensive cyclic

loading. Some of these forces are available through the simulation model designed in

105

SimulinkTM, but other mechanical parts like frames and connectors need an FEM model to

be studied for fatigue damage. This was not part of the scope but currently work is ongoing

in modeling the buoy in SolidworksTM by the Mechanical Engineer for Corpower Ocean.

5.6.5 Fatigue Equivalent Load Estimation for a Target site

The life time damage estimated for each sea state can be extended to calculate the life time

damage for a target site with sea state scatter distribution. This is done by multiplying

distribution of each sea state with the life time damage for that sea state. Then the

summation of damages for each sea state gives the overall damage for 25 years. This can

then be translated to calculate the Equivalent Load for the target site. Calculations are

based on the results obtained from the SimulinkTM mathematical model. Results of this can

be found in section 5.4.4.

5.7 Results for irregular wave Survival Condition Waves OrcaflexTM

Peak Accelerations of the buoy in surge and heave direction have been presented in Table

19.

As can be seen from the table, the accelerations are extremely large and this could possibly

be a modeling error. Since the software was unavailable in Corpower and Remote Access

time was limited, the case could not be further investigated.

Sea State

Hs (m) Tp (s) Max

Acceleration (Surge (m/s2))

Min Acceleration

(Surge (m/s2))

Max Acceleration

(Heave (m/s2)

Min Acceleration

(Heave (m/s2)

106

OF222 5.66 1.5 6.55 -5.34 5.07 -5.93

OF3 5.66 3 11.26 -7.75 8.67 -11.39

OF4 7.07 5.5 17.01 -11.78 23.25 -22.72

OF5 8.49 6.25 21.14 -9.43 46.56 -45.59

OF6 9.9 7.5 87.66 -51.25 70.51 -157.76

OF7 11.91 8.5 91.36 -52.53 69.15 -242.87

OF8 12.73 8.5 137.17 -52.01 102.25 -204.62

OF9 5.66 1.5 121.23 -65.77 104.60 -138.38

Table 19: Summary of accelerations (surge and heave) on Buoy 1 under survival

conditions - Survival Strategy 2

5.8 Discussion on Results obtained from OrcaflexTM

5.8.1 Which survival case is better

Based on the simulation results, it was concluded that the case when the buoy is pulled

under water and stored performed much better in terms of forces on buoy and tether as

compared to the case when the buoy was left to move with the waves. Figure 44 shows a

case when the buoy is left to move with the waves and in this case, there were slack events

that were observed. From a strength point of view, one wants to avoid slack events as they

impulsive forces that may lead to failure.

5.8.2 Identification of Slack Events and Buoy Survival Behavior

With the help of simulations, it was visually possible to see the buoy in motion under the

influence of incoming waves. The two survival strategies could be visually checked and

critical events like snapping were identified. Even though the software overestimated the

22 The Sea State IDs are according to Appendix 4.

107

forces, the motions were able to give the engineers at CPO good insight. More information

on number of slack events can be found in Chapter 6.

5.8.3 Why OrcaflexTM results overestimate all accelerations

When the OrcaflexTM model was done, the buoy was done as one single unit that is

connected to the tether. This means the relative motion between the buoy and the rack was

not modeled in OrcaflexTM due to design limitations.

Due to this the buoy behaves like a rigid system that results in over estimation of buoy

accelerations. It would be interesting to see if this design limitation can be overcome to get

more realistic results.

5.8.4 Lack of OrcaflexTM at Corpower Ocean

OrcaflexTM software was not available at Corpower Ocean Stockholm Office and only access

to the software was through a consultant engineer in Portugal. All design inputs were

provided to him and he executed the modeling and extraction of results for the study.

In parallel, it was possible to get remote access to OrcaflexTM server at Indian Institute of

Technology Madras (IIT-M) to carry out some simulation studies. But as the access time was

limited, a complete independent study could not be performed.

5.8.5 Comparison with Simulation Model Results

Since the accelerations estimated by the software were very high it was deduced that there

has been a modeling error. Since the results were erroneous, they were not compared. It

was envisaged to do a further study and rectify the problem but lack of software, Limited

support from CPO Consultant Engineer for OrcaflexTM in Portugal and limited Remote Access

at IIT-M were impeding.

108

5.9 Variation Mode and Effect Analysis

5.9.1 Uncertainty Evaluation

The presented table is from experimental data and scatter/error estimations provided by

(Svensson).XXIV

Table 20: VMEA results for steel tether based on experimental data

The factors of uncertainty listed in the list in Table 20 are for Strength, Load and Wohler

Exponent which are added together quadratically to give the overall uncertainty of 0.21.

This number is the uncertainty in the difference between logarithms of strength and load. In

other words, it can be said that the uncertainty is at 21% between strength and load.

Assuming a normal distribution for the difference between logarithms of strength and load,

we calculate the 95% quantiles in the distribution corresponding to 1.64 times the overall

uncertainty. Thus we have our new overall uncertainty as 0.21 x 1.64 = 0.34. This is denoted

as the variation distance and this value is the value required to ensure 95% probability of

survival during the design life. A variation distance of 0.34 corresponds to a safety factor of

1.41 obtained by taking the anti-logarithm. (e0.34 = 1.41)

Uncertainty Components Scatter Uncertainty

Sensitivity

Coefficient

( c )

t-correction

factor

( t )

standard

deviation

( s )

ScatterUncertai-

ntyTotal

Strength

Strength Scatter x 0.208 1.060 0.540 0.119

Statistical Uncertainty in Strength x 0.208 1.000 0.200 0.042

Adjustment Uncerainty CA/VA x 0.208 1.000 0.100 0.021

Reference Data Relevance x 1.000 1.000 0.100 0.100

Mean Value Influence x 1.000 1.000 0.050 0.050

Laboratory Uncertainty x 1.000 1.000 0.029 0.029

Total Strength Uncertainty 0.119 0.125 0.172

Load

Pool Measurements, Scatter x 1.000 1.300 0.040 0.052

Scaling x 1.000 1.000 0.012 0.012

Distribution of Hf x 1.000 1.000 0.014 0.014

Model Uncertainty x 1.000 1.000 0.023 0.023

Friction x 1.000 1.000 0.029 0.029

Total Load Uncertainty 0.052 0.041 0.066

Wohler Experiment x 0.200 1.000 0.500 0.100

Total Exponent Uncertainty 0.000 0.100 0.100

Total Uncertainty 0.130 0.165 0.210

Factor of Safety Assessment for Steel

Input Result

109

Extending the above analysis for Polyester tether, see (Svensson)XXIV, we have in Table 21,

Table 21: VMEA for polyester tether based on experimental data

5.9.2 Reliability Evaluation

Steel Tether

Total Uncertainty 0.210

Variation Distance 0.344

(correction for 95% probability of survival)

Factor of Safety 1.41

Polyester Tether

Total Uncertainty 0.341

Normal Distribution Correction 0.56

(correction for 95% probability of survival)

Factor of Safety 1.75

Table 22: Reliability and factor of safety for Steel and Polyester tethers for

experimental data

Uncertainty Components Scatter Uncertainty

Sensitivity

Coefficient

( c )

t-correction

factor

( t )

standard

deviation

( s )

ScatterUncertai-

ntyTotal

Strength

Strength Scatter x 0.183 1.060 0.600 0.116

Statistical Uncertainty in Strength x 0.183 1.000 0.115 0.021

Palmgren Minor Error x 0.183 1.000 0.289 0.053

Mean Value Influence x 0.183 1.000 1.155 0.211

Laboratory Uncertainty x 1.000 1.000 0.029 0.029

Total Strength Uncertainty 0.116 0.221 0.250

Load

Pool Measurements, Scatter x 1.000 1.300 0.040 0.052

Relevance of Rainflow count x 1.000 1.000 0.200 0.200

Model Uncertainty x 1.000 1.000 0.023 0.023

Friction x 1.000 1.000 0.029 0.029

Scaling x 1.000 1.000 0.012 0.012

Total Load Uncertainty 0.052 0.204 0.210

Wohler Experiment x 0.200 1.000 0.500 0.100

Total Exponent Uncertainty 0.000 0.100 0.100

Total Uncertainty 0.127 0.317 0.341

Factor of Safety Assessment for Polyester

Input Result

110

111

Chapter 6

Secondary Objectives, Results and

Evaluation

6.1 Introduction

In early May 2015, additional objectives were added to the scope of thesis. The entire list of

objectives can be found in Appendix 9. Some results will be presented discussed here. These

results are of importance to the mechanical design team who are working with the internal

dimensions of PTO and mechanical drive system. In this chapter, only specific results have

been presented. Full results can be found in the supporting data folder on request from

CPO.

6.2 A: Saved time series of positions/accelerations of parameters

This was a very interesting requirement and poised a challenge addressing the difference

between theory and practice. The FEM Software SolidworksTM was to be used in assessing

the internal fatigue stresses in a half scale buoy. Though very robust, the software had the

limitation that it could not take more than 50,000 points for each time series input. Since

the data generated by the SimulinkTM model had over 78,000 points for each sea state,

there was a need to condense the data. Another limitation with the software was that of

time. Setting up of one time series took approximately 7 minutes of the designer’s time. For

170 sea states, the time was very large and the work tedious. A solution of using a Macro

was suggested but since each time series had certain different parameters, setting up a

Macro was not helpful.

Given these two limitations, the following solution was thought of and implemented,

112

1. The time series was run through different filters and reduced to a combination of peak

and trough points. So, any point in between a crest and a trough in a wave was

discarded.

2. This reduced data was then analyzed for the life time damage it caused in a matlab

program. Now the data was filtered against vertical peak thresholds and horizontal time

thresholds and life time damage was checked after filtration. A 90% of original damage

was considered as the limiting factor.

Based on these techniques, the data points in each time series was greatly reduced. (Table

23)

Table 23: Final count of data points after reduction based on above algorithm

But there still remained the problem of manually entering each sea state that took 7

minutes per sea state. This was solved by combining sea states into one long sea state upto

50,000 points.

1. For a given target site, the scatter of occurrence was noted in a matrix. (See Table 24).

2. For each se astate, the ratio of current sea state occurrence and minimum sea state

occurrence was calculated. For example, if sea state for Hs=3 and Tp=4 the occurrence

was 1800 hours and the minimum sea state occurrence was for Hs= 4 and Tp=5 at 18

hours, then the ratio for the former sea state is 100.

3. Based on these ratios, the time series for sea states were multiplied by the ratio factor

and added at the end of the first sea state’s data. The addition was continued while the

total number of points was less than 50,000 points. Since addition and scaling large

ratios was consuming lot of data points, the data sets were separated for ratios up to 4.

In other words, for any given data combination group the highest ratio between

maximum and minimum occurrence within the group would be 4. Such data segregation

113

was possible since SolidworksTM has the ability to multiply a given time series input by a

factor.

This greatly reduced the number of input files. Finally there were only 12 inputs that had to

be input into the FEM software.

Table 24: Scatter Distribution of each Sea State at offshore site name ‘Yue’

6.3 B: Scatter Plots of Buoy Motions in 6 DOF vs Rack Position

In this report results only for one particular case for experimental results have been

presented. An exhaustive list of figures for Experimental data have been compiled in a

separate file.

The following graphs pertain to ID 115 in experimental results given in Table 25.

Hs 1:16 Hs 1:1 Tp 1:16 Tp 1:1

0.15625 2.5 3 12

Table 25: Wave Parameters for ID115

The recorded accelerations in the following groups represent the buoy motion in a short

time interval.

time 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 1.2659 55.699 79.751 67.092 64.561 62.029 37.977 12.659 1.2659 0 0 0 0 0 0

1 0 56.965 219 268.37 337.99 369.64 244.32 135.45 62.029 3.7977 1.2659 1.2659 0 0 0

1.5 0 1.2659 36.711 163.3 278.5 281.03 215.2 145.58 124.06 86.081 17.723 3.7977 2.5318 0 0

2 0 0 0 69.624 225.33 235.46 175.96 146.84 64.561 62.029 22.786 11.393 6.3295 0 0

2.5 0 0 0 0 81.017 345.59 324.07 272.17 106.34 72.156 43.04 11.393 2.5318 0 0

3 0 0 0 0 15.191 281.03 340.53 250.65 112.66 87.347 58.231 31.647 10.127 0 0

3.5 0 0 0 0 0 69.624 293.69 192.42 118.99 65.827 51.902 36.711 22.786 7.5954 1.2659

4 0 0 0 0 0 3.7977 110.13 127.86 65.827 49.37 27.85 27.85 22.786 15.191 3.7977

4.5 0 0 0 0 0 0 26.584 43.04 60.763 21.52 12.659 6.3295 5.0635 0 1.2659

5 0 0 0 0 0 0 2.5318 20.254 34.179 15.191 7.5954 1.2659 0 0 0

5.5 0 0 0 0 0 0 0 7.5954 24.052 12.659 6.3295 0 0 0 0

6 0 0 0 0 0 0 0 3.7977 13.925 8.8613 0 1.2659 0 0 0

6.5 0 0 0 0 0 0 0 0 2.5318 7.5954 1.2659 0 0 0 0

7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7.5 0 0 0 0 0 0 0 0 0 2.5318 0 0 0 0 0

114

b. Heave

The buoy acceleration in heave direction is usually fluctuates between -0.1 m/s2 and 0.1

m/s2 except for one instance where there is a steep rise in acceleration that is observed at

mean position. In the case, the acceleration rises up till 0.4 m/s2. This is most likely due to a

coding error and can be ignored. See Figure 52 and Figure 53 for details.

Figure 52: Buoy acceleration (m/s2) in heave direction vs rack position (m)

Figure 53: Buoy acceleration (m/s2) in heave direction vs rack position (m) and their

occurrences

c. Surge

115

The surge of the buoy in this particular case is more fluctuating as compared to heave. This

could be resonance induced. As seen in figure 54 and figure 55, there is sharp impulsive

acceleration observed at mean position and the peak goes from -0.2m/s2 to 0.2 m/s2. This is

again due to a coding error during mathematical model formulation.

Figure 54: Buoy acceleration (m/s2) in surge direction vs rack position (m)

Figure 55: Buoy acceleration (m/s2) in surge direction vs rack position (m) and their

occurrences

d. Sway

116

As seen from figure 56 and 57, the acceleration patters in similar to that in surge direction.

This is expected since the buoy is symmetric in all directions. The peak at mean position is

observed in surge and heave as well due to the error. The undulations in sway accelerations

with respect to rack positions could be interesting in the internal parts’ fatigue behavior.

Figure 56: Buoy acceleration (m/s2) in sway direction vs rack position (m)

Figure 57: Buoy acceleration (m/s2) in sway direction vs rack position (m) and their occurrences

e. Pitch

The pitching is quite undulating over one buoy cycle as seen from Figure 58 and Figure 59.

117

Figure 58: Buoy acceleration (degree/s2) in pitch direction vs rack position (m)

Figure 59: Buoy acceleration (degree/s2) in pitch direction vs rack position (m) and their

occurrences

f. Roll

As expected due to symmetry, the acceleration pattern is very similar to that in pitching.

The peak roll acceleration is observed at 0.01m rack position as seen in Figure 60 and Figure

61.

118

Figure 60: Buoy acceleration (degree/s2) in Roll direction vs rack position (m)

Figure 61: Buoy acceleration (degree/s2) in Roll direction vs rack position (m) and their

occurrences

g. Yaw

The observed yaw accelerations in Figure 62 and Figure 63 are usually small except during

one instance where there is a sharp acceleration observed at mean position which could be

due to a modeling error. The present yaw values indicate that torsion should be kept in

mind during design.

119

Figure 62: Buoy acceleration (degree/s2) in yaw direction vs rack position (m)

Figure 63: Buoy acceleration (degree/s2) in yaw direction vs rack position (m) and their

occurrences

h. Resultant Acceleration in XY plane

By combining accelerations in Surge and Sway direction, the resultant XY plane acceleration

was calculated. As seen in Figure 64 and Figure 65, the peak acceleration was observed

nearmean position and the peak is at 0.21 m/s2.

120

Figure 64: Buoy acceleration (m/s2) in XY plane vs rack position (m)

Figure 65: Buoy acceleration (m/s2) in XY plane vs rack position (m) and their occurrences

6.4 C: Peak acceleration summary in 6 DOF vs rack position

a. Maximum Acceleration Summary (Table 26)

121

Table 26: Maximum

accelerations in 6 DOF vs

respective rack positions

b. Minimum

Acceleration Summary (Table 27)

m/s

^2m

m/s

^2m

m/s

^2m

de

g/s^

2m

de

g/s^

2m

de

g/s^

2m

m/s

^2m

Bu

oy

Full

Sca

leFu

ll S

cale

ID N

o.

Surg

e a

Rac

k P

osn

Sway

aR

ack

Po

snH

eav

e a

Rac

k P

osn

Ro

ll a

ccn

Rac

k P

osn

Pit

ch a

Rac

k P

osn

Yaw

acc

nR

ack

Po

snR

esu

ltan

t X

Y Rac

k P

osn

Nu

mb

er

Wav

e H

Wav

e T

109

1.57

1544

0.01

3998

1.29

2513

0.00

3962

0.74

7459

-0.0

1559

0.00

9948

-0.0

0019

0.12

8972

-0.0

0567

044

441.

6412

690.

0130

78B

11

6

110

1.85

3178

-0.0

3726

0.96

3829

9.89

E-03

1.14

7798

1.75

E-04

044

440

4444

044

441.

8567

61-3

.73E

-02

B1

18

126

2.24

9183

0.00

5903

0.32

3032

0.04

2275

1.25

8382

-0.0

5081

0.25

0515

0.00

986

0.17

8943

-0.0

3764

0.23

0524

-0.0

0915

2.24

9437

0.00

5903

B1

110

112

3.91

9343

-0.0

7493

1.20

1105

0.02

7156

2.78

8667

-0.0

3581

044

440

4444

044

444.

0402

210.

1537

47B

12.

58

113

2.89

4047

-0.0

2783

1.26

0835

-4.6

5E-0

23.

3099

170.

0354

310

4444

044

440

4444

3.00

4265

7.01

E-03

B1

2.5

10

128

4.58

7292

-0.0

8894

1.43

1314

-0.1

3515

2.88

7502

-0.0

1229

7.42

1639

0.11

5503

4.31

0253

-0.0

3114

11.4

0519

0.10

3873

4.60

3148

-0.0

8875

B1

2.5

12

129

5.93

5564

-0.0

5765

1.61

8111

0.04

067

2.81

4189

0.07

825

7.39

2846

-0.1

2222

4.12

4931

-0.0

5409

10.5

7825

-0.0

121

6.31

9173

-0.0

5783

B1

2.5

14

148

6.95

8442

-0.0

0988

1.06

9507

-0.0

6357

3.04

4871

0.09

1886

4.89

9723

-0.0

4404

2.59

3509

-0.0

5647

5.59

6954

-0.0

0811

6.96

4421

-0.0

0988

B1

410

149

5.97

1932

0.07

7149

1.22

2908

-0.0

1155

2.69

7022

-0.1

1785

5.42

7548

-0.0

5367

3.85

0544

-0.0

1167

8.14

3578

0.01

352

5.97

2955

0.07

7149

B1

412

257

1.34

706

-2.1

3E-0

20.

2775

181.

49E-

021.

0275

32-0

.030

960.

1297

420.

0023

390.

0271

53-3

.18E

-03

0.14

1996

-0.0

1773

1.34

72-2

.13E

-02

B2

16

258

1.47

1684

0.07

9934

0.52

3889

0.05

6764

1.17

8013

0.04

6674

0.17

5299

0.01

0457

0.31

4678

-0.0

3219

0.49

977

-0.0

1222

1.48

7994

0.04

0314

B2

18

259

1.44

0107

0.05

0799

0.51

4334

0.00

3563

1.27

9565

0.02

0414

0.32

6536

-0.0

4634

0.53

3606

0.01

8721

0.93

5984

-0.0

2614

1.45

3811

0.05

0799

B2

110

260

4.47

1047

-0.0

8558

1.89

6693

-0.0

8431

3.02

2461

-0.0

993

1.73

762

0.01

1713

1.77

1133

0.00

8651

4.36

6347

-0.0

8824

4.60

0153

-0.0

8558

B2

2.5

8

261

4.19

9353

-0.0

6088

1.32

9608

0.10

8824

3.13

6198

-0.1

6103

3.27

0669

-0.0

4681

2.73

4832

-0.0

2466

7.20

284

-0.0

1891

4.82

7004

-0.0

7566

B2

2.5

10

262

3.25

9679

-0.0

393

1.31

1866

-0.0

9629

3.13

254

-0.1

8074

6.32

3339

-0.0

4591

5.46

8873

0.00

2468

10.9

5785

-0.0

7452

3.46

3592

-0.0

393

B2

2.5

12

263

5.07

6492

-0.0

3428

1.51

0633

0.00

2215

2.69

0634

0.13

3763

3.75

5325

0.06

0075

4.15

5853

-0.1

0588

6.15

3995

0.14

8485

5.52

1674

-0.0

3686

B2

2.5

14

264

6.01

6506

-0.0

2572

1.82

8866

-0.0

569

2.94

7355

-0.1

0013

0.98

1881

-0.1

2098

1.32

9315

0.01

726

0.16

813

0.06

5548

6.23

0019

0.12

5248

B2

410

277

3.71

0633

0.16

0148

1.19

8797

-0.0

4225

2.98

9317

-0.0

7741

7.59

0882

0.12

3212

6.02

4912

0.15

9538

15.4

5766

-0.0

4761

3.72

7506

0.05

2011

B2

412

Max

Acc

ele

rati

on

s

122

Table 27: Minimum

accelerations in 6 DOF vs

respective rack positions m/s

^2m

m/s

^2m

m/s

^2m

de

g/s^

2m

de

g/s^

2m

de

g/s^

2m

m/s

^2m

Bu

oy

Full

Sca

leFu

ll S

cale

ID N

o.

Surg

e a

Rac

k P

osn

Sway

aR

ack

Po

snH

eav

e a

Rac

k P

osn

Ro

ll a

ccn

Rac

k P

osn

Pit

ch a

Rac

k P

osn

Yaw

acc

nR

ack

Po

snR

esu

ltan

t X

Y Rac

k P

osn

Nu

mb

er

Wav

e H

Wav

e T

109

-1.5

1179

-0.0

1808

-1.2

5646

-0.0

1324

-0.7

447

0.00

9435

-0.0

1076

-0.0

0019

-0.1

299

-0.0

0978

044

440.

0015

59-0

.010

41B

11

6

110

-1.8

2305

-1.4

5E-0

2-0

.914

210.

0027

36-1

.174

31-5

.05E

-02

044

440

4444

044

440.

0001

9-3

.95E

-04

B1

18

126

-2.0

5647

0.00

0296

-0.2

9111

-0.0

6138

-1.0

2836

0.01

5559

-0.2

6017

-0.0

2678

-0.1

7059

-0.0

6845

-0.2

2723

-0.0

0769

0.00

0605

-0.0

1825

B1

110

112

-4.0

2351

0.15

3747

-1.2

0887

0.07

8338

-2.6

1619

0.15

095

044

440

4444

044

440.

0020

60.

0084

72B

12.

58

113

-2.8

5079

1.67

E-01

-1.3

0883

-0.0

557

-3.1

6203

-1.2

9E-0

10

4444

044

440

4444

0.00

1275

0.04

962

B1

2.5

10

128

-3.6

3885

0.10

7892

-1.4

2009

-0.1

8312

-2.9

0858

1.67

E-01

-7.6

5604

0.00

7143

-4.7

3949

0.02

4999

-11.

2888

-0.0

6394

0.00

1003

0.02

0729

B1

2.5

12

129

-6.3

1524

-0.0

5783

-1.6

0871

-0.0

633

-2.6

4258

0.15

6973

-6.9

7862

-0.0

5605

-4.0

1066

0.08

613

-10.

5737

-0.0

1029

0.00

0694

-0.0

0264

B1

2.5

14

148

-6.7

873

-0.0

4427

-1.0

982

0.14

8172

-3.0

1499

0.17

7826

-4.4

5455

0.07

4331

-2.5

7099

-0.0

452

-5.4

7869

0.08

6249

0.00

1428

-0.1

2626

B1

410

149

-5.4

0899

0.05

3994

-1.2

7606

-0.0

8446

-2.4

4662

0.19

3877

-5.9

6011

-0.0

7177

-3.8

6116

0.03

6729

-9.0

5974

-0.1

0371

0.00

0882

0.00

1341

B1

412

257

-1.3

1533

-0.0

0251

-0.2

9853

-0.0

3237

-0.9

1244

-0.0

4045

-0.1

4328

-0.0

3008

-0.0

2732

-1.7

8E-0

2-0

.132

40.

0137

60.

0013

7-0

.000

37B

21

6

258

-1.4

8639

0.04

0314

-0.5

2626

0.07

4645

-1.2

792

-0.0

5925

-0.1

7887

-0.0

1055

-0.3

023

-0.0

3148

-0.5

4629

-0.0

2245

0.00

0516

-0.0

3212

B2

18

259

-1.0

9281

-0.0

3568

-0.5

0743

0.00

2447

-1.3

6674

-0.0

3675

-0.2

7573

-0.0

2031

-0.5

5089

0.02

0599

-0.9

1405

-0.0

2293

0.00

142

-0.0

2756

B2

110

260

-3.4

9644

0.14

0386

-1.8

6498

-0.0

7573

-3.1

519

0.08

188

-1.7

0272

-0.0

0586

-1.6

7231

-0.0

0474

-4.5

6482

0.04

8789

0.00

2343

0.02

9732

B2

2.5

8

261

-4.7

7828

-0.0

7566

-1.4

7335

-0.0

9059

-3.1

913

0.09

7336

-3.3

2071

0.08

5747

-2.7

4367

-0.0

118

-6.6

0049

-0.0

9535

0.00

3054

-0.0

0587

B2

2.5

10

262

-2.3

6459

0.22

7034

-1.2

1935

-0.0

9736

-2.3

9807

0.19

0971

-6.4

1793

-0.0

9382

-5.4

3478

0.03

4919

-11.

7351

0.00

3549

0.00

2023

-0.0

442

B2

2.5

12

263

-5.5

1084

-0.0

3686

-1.5

3394

0.06

843

-2.5

5451

0.14

2594

-3.7

0933

-0.1

0109

-4.2

4971

0.00

1689

-5.6

955

-0.0

1162

0.00

2363

-0.0

7671

B2

2.5

14

264

-6.2

2797

0.12

5248

-1.7

4188

0.07

1492

-2.9

6984

0.00

8038

-1.0

9231

0.08

4276

-1.8

5007

0.12

3561

-0.1

6843

0.08

9861

0.00

029

0.02

812

B2

410

277

-3.7

0484

0.05

2011

-1.1

9185

0.19

717

-2.9

803

-0.0

5825

-7.6

3764

0.09

3772

-6.0

1047

-0.0

84-1

5.89

5-0

.119

310.

0012

830.

1542

49B

24

12

123

If one observes Table 26 and Table 27, In general the sea state corresponding to Hs = 4 m

and Tp = 10 s was the worst in terms of accelerations for Buoy 1 and Buoy 2. Buoy 1

recorded higher accelerations in surge and heave as compared to Buoy 2.

The values presented here are for a 1:16 scale model.

On the negative side of the cycle, the maximum accelerations were observed for the same

seastate corresponding to Hs = 4 m and Tp = 10 s for both Buoys.

6.5 D: Lateral and Vertical Force on tether vs rack position

During the experiments, simulation modeling and OrcaflexTM modeling, the forces for

vertical and lateral component on the tether were not separated. There was only tension

force that was recorded. In order to resolve this in vertical and horizontal components, the

buoy position data was used.

From the known buoy position at each time step, the angles with respect to vertical were

deduced. These angles are then used to resolve the tensile force on tether in the two

respective vertical and horizontal components.

For ID 115, the scatter plots of resolved forces vs rack positions are as follows in Figure 66,

67, 68 and Figure 69.

Horizontal Force

124

Figure 66: Horizontal Wire Force and its distribution with respect to rack position

Figure 67: Horizontal Wire Force and its distribution with respect to rack position and number

of occurrences

Vertical Force

125

Figure 68: Vertical Wire Force and its distribution with respect to rack position

Figure 69: Vertical Wire Force and its distribution with respect to rack position and its

occurrences

A table of bins and occurrences was also created that can be easily extended to represent

the scenario in a test site with given sea state distributions.

126

6.6 E: Wavespring Force vs Rack Position Scatter Plots for all sea states

Wavespring force during the experimental stage was simulated to be executed through the

motor. Since this is digital, it is expected to have a smooth behavior. This can be seen in

Figure 70 and Figure 71 for ID 115. Also plotted is the number of occurrences for different

rack positions.

70

Figure 70: Wavespring Force and its distribution with respect to Rack Position

127

Figure 71: Wavespring Force and its distribution with respect to Rack Position and number of

occurrences

6.7 F: Wire Force vs Rack Position

ID 004 Regular wave with parameters given as,

Hs 1:16 Hs 1:1 Tp 1:16 Tp 1:1

0.03 0.50 3.25 13.00

Table 28: Wave parameters for ID 004 in simulation model

Figure 72 shows the distribution for wire force for a regular wave with parameters listed in

Table 28. It is interesting to note how predictable the distribution pattern is. This raises the

important point of unreliability of regular wave experiments for studying real life scenarios.

128

Figure 72: Wavespring Force vs Rack Position for Regular Wave ID 004

ID 108 Irregular wave with parameters

Hs 1:16 Hs 1:1 Tp 1:16 Tp 1:1

0.25 4.00 3.00 12.00

Table 29: Wave parameters for ID 108 in simulation model

129

Figure 73: Wavespring Force vs Rack Position for irregular Wave ID 108

As can be seen from the Figure 72 and Figure 73, the wire force is a less predictable for an

irregular wave, with parameters in Table 29. In a previous section this force was resolved

into two respective components.

A bin table was also created to estimate the number of occurrences.

6.8 G: Transmission Force vs Rack Position Scatter Plots for all sea

states

For ID 115 with parameters in Table 25 we have the following distribution as shown in figure

74 and figure 75,

130

Figure 74: Transmission Force and its distribution with respect to rack position

Figure 75: Transmission Force and its distribution with respect to rack position and number of

occurrences

131

6.9 H: Number of Wavespring Cut off events in each sea state

The number of Wavespring cut off events corresponds to the number of brakes the

mechanism experiences in 30 minutes. These values can be extrapolated to represent values

for a period of 20 years.

Braking was identified by looking at turning points and checking the number of occurrences

when the turning point is higher than 2.5 m.

Table 30 shows the number of brake occurrences in 30 min. This information can then be

used to dimension the valves. Adjusting the valves might decrease the number of brakes.

Braking per 30 min time 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 5 5 4 9 3 3 8 4

1.5 0 0 0 0 0 24 21 44 49 49 56 72 71 55 58

2 0 0 0 4 21 64 79 78 109 110 117 120 122 102 102

2.5 0 0 0 22 93 123 156 143 173 180 172 153 161 146 150

3 0 0 0 60 148 193 229 215 236 173 209 179 192 187 173

3.5 0 0 0 0 164 201 242 282 253 243 237 208 204 187 171

4 0 0 0 0 0 253 266 280 278 250 259 230 224 219 201

4.5 0 0 0 0 0 0 293 272 288 260 238 228 237 211 200

5 0 0 0 0 0 0 0 303 292 271 276 243 243 229 208

5.5 0 0 0 0 0 0 0 333 312 305 258 271 260 246 228

6 0 0 0 0 0 0 0 0 300 308 273 255 254 237 215

6.5 0 0 0 0 0 0 0 0 0 298 267 259 263 245 223

7 0 0 0 0 0 0 0 0 0 290 271 261 248 233 232

7.5 0 0 0 0 0 0 0 0 0 305 287 283 245 231 228

Table 30: Number of Wavespring Cut off events for a 30 min cycle23

6.10 F: Number of slack events in each sea state

For each sea state, it was identified the number of occurrences when the tension in the

tether became zero. This indicated a slack in the tether since it cannot take any compressive

loads. The number of occurrences were identified for each sea state from the experimental

data and tabulated as in Table 31. The number of slack events was identified based on the

23 Analysis done by Corpower Ocean Engineer Gunnar Stein Ásgeirsson

132

pretension in the buoy tether. This pretension is measured in the sensor by submerging the

buoy in water until a specified marker on the buoy as a starting condition.

It was observed that there were no slack events for irregular non survival sea states. For

some cases, the tension in the tether came close to zero but did not reach zero.

The experiments corresponded to about 10-15 minutes of runtime. Since the number of

slacking occurrences need to be scaled for a 20 year period, the observed slacks can be very

large over the lifetime of the buoy.

ID No. Number of Slack Events

Buoy No.

Experiment Type

Hs (m) Tp (s)

168 1 B1 Survival 9 9

170 6 B1 Survival 7.2 11

171 5 B1 Survival 8.4 13

173 13 B1 Survival 9 9

174 16 B1 Survival 8.4 13

281 1 B2 Survival 8.4 15

282 40 B2 Survival 9 9

283 47 B2 Survival 8.4 13

296 2 B1 Focus 32 -

Table 31: Number of Slack Events for each Case

Figure 76 shows a slack event for ID 296 which is a focus wave with a wave height of 32 m.

133

Figure 76: Slack Event marked at t = 62 seconds with measure subsea force falling below zero

6.11 Discussion

6.11.1 Torsion Stress

It was observed from yaw angular velocity and acceleration results, that the buoy is yawing

considerably. This motion can cause torsion in the attached tether. To overcome this

situation, a swivel is placed at the interface that will take care of any twisting motions of the

buoy. Due to this addition, there will be negligible torsional stress developed in the tether.

6.11.2 Number of Break Occurrences

As can be seen from Table 30, the number of brake occurrences corresponds to around 2

million brake cycles per year. This is a very big number as the number of oscillations per

year corresponds to 5 million. In other words, there is a brake event roughly every 2.5

oscillations. This high number of brake occurrences can be greatly reduced with a “proper

combination of breaking algorithm and generator control.24 Another study indicates that the

24 Comment made by Corpower Ocean Scientist - Jørgen Hals Todalshaug

Slack Event

134

mechanism of wave to wave generator control strongly reduces the number of braking

events.25

6.11.3 Number of Slack Events

It was observed that there are negligible slack events that were observed for irregular cases.

This implies that during the service condition of the buoy, it will rarely experience slack

events or impulsive forces.

Although for the survival cases, a number of slack events were observed and this needs

further development of survival strategies and further studies in a simulated environment

for higher sea states. This is particularly important since these numbers only correspond to

15 minutes of simulated data. If scaled to a lifetime of 20 years, number of slack events can

be very large.

25 Result from Master thesis by Tianzhi Zhou which is still in process of completion

135

Chapter 7

Conclusions, Limitations and Future WorkXXVII

The study was set out to validate the simulation model by comparison with experimental

data and generate new data, in the form of Forces, Motions, Equivalent Loads for Fatigue

Loading, Uncertainty and tether dimensions, useful for the design team at CPO to develop

the WEC. The study also sought in developing tools for analyses and generation of new data

for future use. During the process, certain trends in Statistical and Equivalent Fatigue Loads

were noticed which have been given possible explanations. The study also delved into

investigating WEC interactions in extreme conditions in OrcaflexTM but due certain

limitations the results suffered from unreliability. Following this, the study dealt with an

uncertainty study using Variation Mode and Effect Analysis for the prediction of the Factor

of Safety. Finally, the study culminated with answering secondary objectives added to the

scope on a later date.

The subject of the thesis was wide and its goals were accomplished by achieving

intermediate goals like understanding what Wave Energy was, how it is connected to

principles of marine design and mechanics, how the WEC worked, to be able to develop

algorithms and finding solutions to objectives. The following list compiles the findings with

respect to the major objectives achieved during the study with reference to Section 1.3.

- Development Tools

A Graphical User Interface with options to compare two different load cases enabled

comparison of buoy shapes, mechanisms, sea states and wave type for forces.

Two different algorithms in MatlabTM were developed for filtration of raw data, using

four alternate filter options, and identifying peaks and recording load statistics like

RMS, Mean, H1/10, H1/3 and H1/100.

136

An algorithm in MatlabTM was developed to estimate equivalent load for a given

design life and number of cycles based on Rain Flow Counting and Damage

Accumulation Theory.

- Load Case Analysis

Peak Loads on mooring line were deduced for all the experiments carried out at

wave tank test in École Centrale Nantes in 2014. They can be found in Appendix 6.On

Basis of results, Buoy 1 was chosen as it registered lower forces in comparison with

Buoy 2 which results in a less loaded tether and provides greater survivability in

extreme conditions. Another observation was that the Wavespring system registered

lower forces than the latching system.

Some extreme wave conditions were simulated in the wave tank and the forces

encountered by the buoy can be found in Table 2 and Table 3 for Buoy 1 and Buoy 2

respectively. On basis of most extreme load for each buoy, cross section of tether

was deduced for three materials; regular steel, HSLA steel and Polyester. Of the

materials, HSLA steel required the least cross section area for the tether at 85 cm2

and 86 cm2 for buoy 1 and buoy 2 while Polyester required the highest cross section

area at 508 cm2 and 516 cm2 respectively.

The simulation model was validated by comparing load cases for irregular waves and

Wavespring configuration for both buoys with load cases from experimental tests.

For validation, RMS loads were used as a basis for comparison. The ratio of

Simulated RMS loads to Experimental RMS loads was found to lie between 1.03 and

1.21. The Simulation model was deemed reasonable and formed basis for data

generation for other objectives. The higher prediction by the simulation model was

attributed to it being a 2 DOF model instead of a realistic 6 DOF model which caused

amplification in heave and surge responses following the principle of conservation of

energy. A similar ratio between Peak loads of simulated data and experimental data

varied between 1.19 and 1.35.

From the validated simulated model, data for all missing sea states in Figure 8 were

generated for target site ‘Yue’, the results for which have been compiled in Appendix

7. The most extreme peak load was identified as 4.18 MN for wave height 7.5 m and

time period 13 s. The cross section of the tether was determined on basis of this load

137

for three materials of steel, HSLA steel and Polyester. HSLA steel gave the lowest

cross section as 106.4 cm2.

Survival sea states that could not be tested during wave tank experiments were

simulated in OrcaflexTM and buoy accelerations in heave and surge were extracted.

But the results suffered from unreliability as the model over predicted parameters.

Additionally, videos were generated to show the motion of the buoy under the

influence of waves which were used to identify critical snap events and test two

buoy survival strategies of latching and free moving. It was found that latching the

buoy proved a better strategy.

Equivalent Load and fatigue damage for all sea states were generated for ‘Yue’ for a

design life of 25 years and one million cycles in Table 16 and Table 18. The

cumulative damage for 25 years at ‘Yue’ was found to be 7.19433 x 1036 and

equivalent load as 2682 kN.

- Statistical Analysis

The uncertainties in theory, modeling and literature based on experimental findings

were treated and quantified to assess the overall uncertainty in predicting design

loads. The overall uncertainty was transformed into a factor of safety which was

calculated for steel as 1.41 and for polyester as 1.75.

- Secondary Objectives

On basis of simulation model generated data, interesting trends of buoy internal

forces in relation with rack position were recorded and can be found in Chapter 6

Slack events were investigated numerically and it was observed that for irregular non

survival sea states, no slack events were observed. This has a great positive

repercussion on the survivability of the buoy in normal operational conditions.

There was a braking event roundabout every 3 cycles and this inspires the need to

optimize the generator wave control to reduce the number of braking events that

causes a loss of efficiency.

The work in the thesis was very extensive and multifaceted and hence it was not possible to

make one specific conclusion or answer a specific question but provide several answers and

data for development of WEC. The work done was very interesting and rewarding from a

knowledge point of view but there were a few limitations, which are,

138

Lack of 6 DOF simulation model. Its repercussions were,

o The simulation model always over predicted the forces on the buoy in surge and

heave.

o The rotational motions of the buoy could not be studied or compared with

experimental results.

Absence of OrcaflexTM software access at CPO. Its repercussions were,

o Higher Survival sea state results from Simulation Model could not be validated

with software generated results.

o Buoy motions could not be generated for the missing 4 DOF in simulation model

Lack of previous Hydrodynamic study on Buoy response in waves.

o Certain trends like flattening of equivalent load at sea states beyond 2 m, was

explained on logic instead of theoretical backing

The study has offered an evaluative perspective on wave energy technology and the

following work for the future can be envisaged.

There have been several design changes since the previous experiments were carried

out. It would be particularly interesting to test a scaled buoy with PTO and check its

performance.

Since data could not be obtained for higher survival sea states it would be interesting

to perform the tests in a larger wave tank to get data corresponding to extreme

cases.

The OrcaflexTM model tended to overestimate the buoy accelerations and forces on

the components. It would be interesting to further study the modeling and

incorporate a more exhaustive buoy design with internal moving parts.

Fatigue analysis for the internal frames and connectors could be studied for stresses

in an FEM atmosphere. These parts were not simulated in the simulation model and

it would be great to study these parts in depth.

In spite of development several wave energy technologies in the past, we are yet to see a

fully commercial unit. The WEC by CPO has made a great effort in its innovative approach to

envisage the wave energy converter. The data produced so far looks sturdy and I feel

confident that this technology could one day provide power for us in a green way.

139

140

List of Figures

Figure 1: Summary of Advantages of Wave Energy Device by Corpower Ocean ........................... 7

Figure 2: Schematic of WEC ............................................................................................................ 8

Figure 3: Buoys that are under investigation................................................................................ 10

Figure 4: Latching Mechanism where Curve (a) is the incident wave, Curve(b) is the resonant

wave motion, Curve(c) is the actual movement of buoy subjected to

latching………………………..12

Figure 5: Wave Tank Testing Facility at École Centrale de Nantes in 2014 .................................. 18

Figure 6: CAD representation of Buoy in Wave Tank with device to measure tension in tether 18

Figure 7: Picture showing bright white lights installed on buoy to record the 6 DOF motion of

buoy .............................................................................................................................................. 19

Figure 8: Seastates that were tested in the wave tank (marked by yellow boxes) ...................... 20

Figure 9a: Identified Locations where Wave Energy Device can be potentially used 1. (source

Wikimedia) VIII ................................................................................................................................ 23

Figure 9b: Identified Locations color coded according to energy potential. 1. (Source:

wikimedia) ..................................................................................................................................... 24

Figure 10: Schematic of how an Oscillating Water Column works. (Image Courtesy-

en.openei.org) ............................................................................................................................... 25

Figure 11: Schematic of an Overtopping type of wave energy converter (Image Courtesy-

en.openei.org) ............................................................................................................................... 26

Figure 12: An Attenuator type of Oscillating Body WEC (Image Courtesy-en.openei.org) .......... 27

Figure 13: A Pitching type of Oscillating Body WEC (Image Courtesy-en.openei.org) ................. 27

Figure 14: Heaving Buoy (Point Absorber) type of Oscillating Body WEC (Image Courtesy-

en.openei.org) ............................................................................................................................... 28

Figure 15: The axis for the coordinate system ............................................................................. 28

141

Figure 16: Classification of wave forces for different geomtry ranges against incoming wave

lenghts (Source: Marilena Greco Lecture Notes TMR4215: Sea Loads, NTNU) ........................... 31

Figure 17: Slow Drift motions in opposite direction of wave due to viscous effects ................... 32

Figure 18: Flow past a cylinder ..................................................................................................... 35

Figure 19: Flow separation for different flow regimes ................................................................. 35

Figure 20: Stress Strain Relationship for Structural Steel ............................................................. 38

Figure 21: Typical S-N (Stress vs Number of Loading Cycles) Curve ............................................ 39

Figure 22: Clubbing of stresses according to Palmgren Miner Rule (Source: Wikipedia) ............ 41

Figure 23: Graphic Use Interface for OrcaflexTM .......................................................................... 45

Figure 24: Illustration of the influence of uncertainty during the design process (Source:

Svensson & Sandström, 2014XXIV ) ................................................................................................. 48

Figure 25: Table of sea states that needs to be filled in to complete Load Analysis .................... 53

Figure 26: Seastates that were tested in the wave tank (marked by yellow boxes) .................... 53

Figure 27: Unfiltered Data for Heave Acceleration ...................................................................... 55

Figure 28: Comparison of filtered and unfiltered data (green is filtered data and blue is

unfiltered data) ............................................................................................................................. 57

Figure 29: Differential of Heave Acceleration to filter out differentials lower than defined

threshold ....................................................................................................................................... 57

Figure 30: Final acceleration time series (Left figure shows only acceleration peaks while

right figure shows steepness of successive peaks) ....................................................................... 59

Figure 31: Sorted Peaks in order of magnitude ............................................................................ 60

Figure 32: Frequency of occurrence of peaks ............................................................................... 60

Figure 33: Pretension force at the start of the experiment ......................................................... 61

Figure 34: Zoomed in portion of the pretension force ................................................................. 62

Figure 35: Rain Flow Counting output for 3 input stress value .................................................... 62

Figure 36: Output from a Rain Flow Countine Method Script ...................................................... 63

142

Figure 37: Subsea Force after time series snipping based on start and end time ....................... 64

Figure 38: Plot showing the rainflow cycles before (RED) and after (GREEN) filtration. ............. 65

Figure 39: Rainflow Cycles with minima on X axis and maxima on Y axis for any given cycle ..... 66

Figure 40: Load Spectrum with load cycle amplitudes and frequency of occurrence and Level

Crossings distribution for estimating how many cycles cross which magnitude ......................... 66

Figure 41: GUI for running simulations of WEC for given set of input parameters ..................... 69

Figure 42: Output GUI after simulation is completed .................................................................. 76

Figure 43: The two Buoy Geometries that are input into OrcaflexTM ........................................... 77

Figure 45: GUI for loading data files for comparison .................................................................... 84

Figure 46: Result GUI with options to compare two different data files ..................................... 84

Figure 47: Ratio of RMS Loads between simulation loads and experimental loads for force on

the buoy tether in irregular waves. Top half of table represents Buoy 1 for Wavespring and

Bottom Half of table represents Buoy 2 for Wavespring ............................................................. 93

Figure 48: Variation of Fatigue Equivalent Load for 25 years with Wave Height ....................... 101

Figure 49: Variation of Fatigue Equivalent Load for 25 years with Time Period ........................ 102

Figure 50: Variation of Peak Loads for 25 years with Wave Height ........................................... 103

Figure 51: Variation of Peak Loads for 25 years with Time Period ............................................. 103

Figure 52: Buoy acceleration (m/s2) in heave direction vs rack position (m) ............................. 114

Figure 53: Buoy acceleration (m/s2) in heave direction vs rack position (m) and their

occurrences ................................................................................................................................. 114

Figure 54: Buoy acceleration (m/s2) in surge direction vs rack position (m) .............................. 115

Figure 55: Buoy acceleration (m/s2) in surge direction vs rack position (m) and their

occurrences ................................................................................................................................. 115

Figure 56: Buoy acceleration (m/s2) in sway direction vs rack position (m) .............................. 116

Figure 57: Buoy acceleration (m/s2) in sway direction vs rack position (m) and their

occurrences ................................................................................................................................. 116

Figure 58: Buoy acceleration (degree/s2) in pitch direction vs rack position (m) ...................... 117

143

Figure 59: Buoy acceleration (degree/s2) in pitch direction vs rack position (m) and their

occurrences ................................................................................................................................. 117

Figure 60: Buoy acceleration (degree/s2) in Roll direction vs rack position (m) ........................ 118

Figure 61: Buoy acceleration (degree/s2) in Roll direction vs rack position (m) and their

occurrences ................................................................................................................................. 118

Figure 62: Buoy acceleration (degree/s2) in yaw direction vs rack position (m) ........................ 119

Figure 63: Buoy acceleration (degree/s2) in yaw direction vs rack position (m) and their

occurrences ................................................................................................................................. 119

Figure 64: Buoy acceleration (m/s2) in XY plane vs rack position (m) ........................................ 120

Figure 65: Buoy acceleration (m/s2) in XY plane vs rack position (m) and their occurrences .... 120

Figure 66: Horizontal Wire Force and its distribution with respect to rack position ................. 124

Figure 67: Horizontal Wire Force and its distribution with respect to rack position and

number of occurrences ............................................................................................................... 124

Figure 68: Vertical Wire Force and its distribution with respect to rack position ...................... 125

Figure 69: Vertical Wire Force and its distribution with respect to rack position and its

occurrences ................................................................................................................................. 125

Figure 70: Wavespring Force and its distribution with respect to Rack Position ....................... 126

Figure 71: Wavespring Force and its distribution with respect to Rack Position and number

of occurrences ............................................................................................................................. 127

Figure 72: Wavespring Force vs Rack Position for Regular Wave ID 004 ................................... 128

Figure 73: Wavespring Force vs Rack Position for irregular Wave ID 108.................................. 129

Figure 74: Transmission Force and its distribution with respect to rack position ..................... 130

Figure 75: Transmission Force and its distribution with respect to rack position and number

of occurrences ............................................................................................................................. 130

Figure 76: Slack Event marked at t = 62 seconds with measure subsea force falling below

zero ............................................................................................................................................. 133

Figure 77: Components of a Gas Turbine Jet Engine XVIII ............................................................ 153

144

Figure 78: Gas Turbine Blade and varying strain and temperature distributions during

operationXVIII ................................................................................................................................ 154

Figure 79: Scatter of Strain measured on a turbine blade after different cycles of loadingXVIII . 154

Figure 80: Crack initiation in notches and its propagation trajectory as seen through FEM

AnalysisXIX .................................................................................................................................... 155

Figure 81: Design improvements to improve the fatigue strength in mechanical partsXIX ........ 157

145

List of Tables

Table 1: Specification of Wave Tank Testing Facility .................................................................... 17

Table 2: Summary of Peak Forces acting on the tether for Buoy 1 for Survival Sea States for a

full scale buoy (The negative sign is an indication of tensile loads) ............................................. 86

Table 3: Summary of Peak Forces acting on the tether for Buoy 2 for Survival Sea States for a

full scale buoy (The negative sign is an indication of tensile loads) ............................................. 86

Table 4: Assessment of Minimum cross-section area of tether based on yield strength and

Maximum Experimental Loads in Wave Tank Test at Nantes, 2014 ............................................ 87

Table 5: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular

seas for Buoy 1 .............................................................................................................................. 88

Table 6: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular

seas for Buoy 2 .............................................................................................................................. 88

Table 7: Fatigue Loads, Design Life and Equivalent Load for Buoy 1 for 1:16 scale model in

irregular waves .............................................................................................................................. 89

Table 8: Fatigue Loads, Design Life and Equivalent Load for Buoy 2 for 1:16 scale model in

irregular waves .............................................................................................................................. 90

Table 9: Ratio of Peak Forces in tether obtained from experimental and simulation model for

Buoy 1 and Buoy 2 ........................................................................................................................ 94

Table 10: Peak Loads in N for a full scale buoy recorded on the tether based on simulation

data ............................................................................................................................................... 94

Table 11: Mean Loads in N for a full scale buoy recorded on the tether based on simulation

data ............................................................................................................................................... 95

Table 12: RMS Loads in N for a full scale buoy recorded on the tether based on simulation

data ............................................................................................................................................... 96

Table 13: A 1/10 Loads in N for a full scale buoy recorded on the tether based on simulation

data ............................................................................................................................................... 96

146

Table 14: Assessment of Minimum cross-section area of tether based on yield strength and

Maximum Simulation Loads in Wave Tank Test at Nantes, 2014 ................................................ 97

Table 15: Equivalent Loads in N for a full scale buoy for fatigue predicted for the tether

based on simulation data .............................................................................................................. 98

Table 16: Life time damage for full scale buoy due to fatigue predicted for the tether based

on simulation data at Yue ............................................................................................................. 98

Table 17: Normalized Scatter distribution of different sea states for target site ‘Yue’ ............... 99

Table 18: Life Time Damage distribution of different sea states for target site ‘Yue’ ............... 100

Table 19: Summary of accelerations (surge and heave) on Buoy 1 under survival conditions -

Survival Strategy 2 ...................................................................................................................... 106

Table 20: VMEA results for steel tether based on experimental data ....................................... 108

Table 21: VMEA for polyester tether based on experimental data ............................................ 109

Table 22: Reliability and factor of safety for Steel and Polyester tethers for experimental

data ............................................................................................................................................. 109

Table 23: Final count of data points after reduction based on above algorithm ....................... 112

Table 24: Scatter Distribution of each Sea State at offshore site name ‘Yue’ ............................ 113

Table 25: Wave Parameters for ID115 ........................................................................................ 113

Table 26: Maximum accelerations in 6 DOF vs respective rack positions .................................. 121

Table 27: Minimum accelerations in 6 DOF vs respective rack positions .................................. 122

Table 28: Wave parameters for ID 004 in simulation model ...................................................... 127

Table 29: Wave parameters for ID 108 in simulation model ...................................................... 128

Table 30: Number of Wavespring Cut off events for a 30 min cycle .......................................... 131

Table 31: Number of Slack Events for each Case ........................................................................ 132

Table 31: Table of scaling factors for different parameters related to buoy water interaction 159

Sea states and their notations analyzed in experiments and software (Grayed sea states

were analyzed in ORCAFLEXTM and white sea states were tested in a wave tank) .................... 160

Cases tested in OrcaflexTM with Wave Spectrum Type used for analysis. .................................. 161

147

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152

Appendix 1

WAFO Toolbox

WAFO is a toolbox of MatlabTM routines for statistical analysis and simulation of random

waves and random loads.26 The toolbox has tools for the following calculations.

Fatigue Analysis

Fatigue life prediction for random loads

Theoretical density of rainflow cycles

Sea modelling

Simulation of linear and non-linear Gaussian waves

Estimation of seamodels (spectrums)

Joint wave height, wave steepness, wave period distributions

Statistics

Extreme value analysis

Kernel density estimation

Hidden Markov models

26 http://www.maths.lth.se/matstat/wafo/

153

Appendix 2

Review of Structures that undergo extensive Fatigue Loading

Two cases have been presented and discussed here.

Gas Turbine Components in Jet Engines

A typical gas turbine is composed of components as shown in Figure 77. In particular, the

turbine is subjected to high cycle fatigue loads. “This is the single largest cause of

component failure in modern military gas turbine engines.”XXVIII.

Figure 77: Components of a Gas Turbine Jet Engine XVIII

The gas turbine is essentially a propeller with multiple blades coming out of a pod as shown

in figure 78. The blade of the turbine is subjected to repeating negative and positive

pressure distributions. This results in high frequency cyclic loads on the blade. The problem

is further accentuated by the presence of temperature fluctuations.

This high frequency of cyclic loading abbreviated as HCF is what causes the turbine blades to

fail during operation at loads much lower than yield strength of blade material.

154

Figure 78: Gas Turbine Blade and varying strain and temperature distributions during

operationXVIII

Figure 79, shows the distribution of strain on the blade against the number of load cycles. It

can be observed, as the number of cycles increase, the allowable strain range keeps

decreasing which indicates failing resistance against cracking.

We can follow the minimum curve (dotted line) to design a part but this often leads to over

dimensioning. Several statistical methods like Bayesian Approach and VMEA have been

developed to calculate more realistic outputs. VMEA (Variation Mode and Effect Analysis)

will be used in this report to assess the fatigue in the WEC.

Figure 79: Scatter of Strain measured on a turbine blade after different cycles of loadingXVIII

155

Notched Structural Components

Surface and through-thickness cracks are a common occurrence in holes and at notches in

structural components. It is interesting to note that, “such cracks are present during a large

percentage of the useful life of these components”.XXIX These cracks originate as micro

cracks which slowly propagate until they become critical enough to cause failure.

Figure 80 shows the typical places where cracks due to fatigue originate and propagate.

These areas represent areas where stress concentrations are present and over repeated

loading cycles, these areas are much more susceptible to failure than other parts.

Figure 80: Crack initiation in notches and its propagation trajectory as seen through FEM

AnalysisXIX

For notches and holes, as concluded by the paper ‘Fatigue Life Estimation of Notched

Structural Components’19, fatigue analysis can be done with fair accuracy using an FEM

environment. They had good correlation between experimental and computational results.

Based on analysis, fatigue strength can be increased in notches and holes by making design

changes as shown in Figure 81.

156

157

Figure 81: Design improvements to improve the fatigue strength in mechanical partsXIX

158

Appendix 3

Scaling of WEC from experimental model to life size model

Based on Ocean Wave Theory, scaling from experimental model to real life model is done

best using Froude Scaling. Froude number is the ratio between inertia and gravitational

force. It is hence useful in ensuring dynamic scaling between model and full scale is

maintained. Froude scaling ensures gravity forces are correctly scaled. Since waves in the

ocean are gravity waves, Froude scaling ensures that wave resistance and wave forces are

correctly scaled.

(43)

Then dynamics similarity can be achieved by equating the Froude numbers for model and

full scale as follows,

√

√

(44)

where U is the relative velocity between body and fluid and L is the length of body along the

direction of flow.

By using Froude scaling we compromise on the viscous scaling and surface tension effects

due to water’s viscosity. Since this is of minor importance, it can be ignored.

Given below in Table 31 are Froude scaled factors for different parameters that are used as

part of the analysis.

159

Table 31: Table of scaling factors for different parameters related to buoy water

interaction

160

Appendix 4

Sea States and Notations investigated in Tank Tests and OrcaflexTM

The following table lists all sea state parameters and associated symbols,

Seastate Notation

Wave Period (s)

Wave Height (m)

Seastate Notation

Wave Period (s)

Wave Height (m)

I2 3.54 0.5 OF5 7.07 5.5

I3 4.95 0.5 OF6 8.49 6.25

I4 6.36 0.5 OF7 9.9 7.5

I7 4.95 1.25 OF8 11.91 8.5

I8 6.36 1.25 OF9 12.73 8.5

I9 7.78 1.25 S1 4.24 3

I10 9.19 1.25 S2 4.95 4

I11 6.36 2 S3 5.66 4.5

I12 7.78 2 S4 7.07 3.5

OF2 5.66 1.5 S5 8.49 4

OF3 5.66 3 S6 9.9 4

Sea states and their notations analyzed in experiments and software (Grayed sea

states were analyzed in ORCAFLEXTM

and white sea states were tested in a

wave tank)

161

Cases tested in OrcaflexTM

with Wave Spectrum Type used for analysis.

Water

depth Hs Tp γ

Wave

spec.

State

no. [m] [m] [s] type

OF1 25,00 3,00 4,2 5,0 JONSWAP

OF2 25,00 1,50 5,7 1,5 JONSWAP

OF3 25,00 3,00 5,7 5,0 JONSWAP

OF4 25,00 4,50 5,7 5,0 JONSWAP

OF5 25,00 5,50 7,1 5,0 JONSWAP

OF6 25,00 6,50 8,5 5,0 JONSWAP

OF7 25,00 7,50 9,9 4,9 JONSWAP

OF8 25,00 8,50 11,3 3,6 JONSWAP

OF9 25,00 8,50 12,7 2,1 JONSWAP

OF10 40,00 8,50 12,0 2,8 JONSWAP

OF11 40,00 10,50 14,0 2,2 JONSWAP

OF12 40,00 11,00 16,0 1,2 JONSWAP

OF13 40,00 11,00 18,0 1,0 JONSWAP

OF14 40,00 11,00 20,0 1,0 JONSWAP

162

Appendix 5

Outputs generated from Experimental Tests in Wave Tank

163

164

Appendix 6

Summary of Loads on Experimental Results

ID No. Eq. Load Fatigue

Ultimate Load

Wave Height

Wave Period

Buoy No. Reg/Irreg Ultimate / Eq. Load

22 476526.8 -2123756 0.48 13 1 3 4.46

23 491748.2 -2123639 0.48 11 1 3 4.32

24 501494.2 -2123888 0.48 9 1 3 4.24

25 511858 -2105277 0.48 7 1 3 4.11

26 467308.7 -2069931 0.48 5 1 3 4.43

27 1279293 -2519705 1.28 13 1 3 1.97

28 1316688 -2511996 1.28 11 1 3 1.91

29 1343011 -2497717 1.28 9 1 3 1.86

30 1361183 -2462256 1.28 7 1 3 1.81

31 1235401 -2358175 1.28 5 1 3 1.91

32 379018 -1940298 1.28 7 1 3 5.12

33 408369.8 -2344405 1.28 7 1 3 5.74

34 1205027 -2803442 0.5 15 1 3 2.33

35 1081295 -2561675 0.5 12 1 3 2.37

36 952139 -2553778 0.5 14 1 3 2.68

37 1059192 -2487469 0.5 11 1 3 2.35

38 897467.5 -2401985 0.5 13 1 3 2.68

39 1127033 -2474954 0.5 10 1 3 2.20

40 1001171 -2578525 0.5 15 1 3 2.58

41 1326106 -2584544 0.5 9 1 3 1.95

42 469221.7 -2188852 0.5 6 1 3 4.66

43 1469218 -2638990 0.5 8 1 3 1.80

44 274218.3 -2068559 0.5 5 1 3 7.54

45 1614410 -2703877 0.5 7 1 3 1.67

46 259578.1 -2053193 0.5 5 1 3 7.91

47 2008100 -3491076 1.6 13 1 3 1.74

48 1547041 -2658748 1.6 11 1 3 1.72

49 1633356 -2633713 1.6 9 1 3 1.61

50 1748255 -2636025 1.6 7 1 3 1.51

51 1654016 -2485654 1.6 5 1 3 1.50

52 1564951 -2740515 0.5 9 1 3 1.75

53 1711871 -2686433 0.5 9 1 3 1.57

54 1651467 -2758920 0.5 9 1 3 1.67

55 1526528 -2699788 0.5 9 1 3 1.77

56 1309038 -2673937 0.5 9 1 3 2.04

57 805191.9 -2291751 1.5 10 1 3 2.85

58 1224630 -3435754 1.5 13 1 3 2.81

59 978688.6 -2338868 1.5 13 1 3 2.39

165

60 1001551 -2340859 1.5 12 1 3 2.34

61 774441.5 -2300215 1.5 9 1 3 2.97

62 1266297 -2148591 1.5 6 1 3 1.70

63 752486.3 -2265023 1.5 8 1 3 3.01

64 801970.6 -2320168 1.5 10 1 3 2.89

65 692302.6 -2231097 1.5 7 1 3 3.22

66 657392.7 -2197765 1.5 6 1 3 3.34

67 569221.3 -2200541 1.5 6 1 3 3.87

68 879997.1 -2360993 1.5 11 1 3 2.68

69 1060505 -2424988 1.5 14 1 3 2.29

70 506936.8 -2119624 1.5 5 1 3 4.18

71 399412.6 -2077921 1 6 1 3 5.20

72 538718.5 -2184332 1 9 1 3 4.05

73 603533.8 -2217636 1 12 1 3 3.67

74 1046568 -2407453 2 9 1 3 2.30

75 706146.2 -2242314 2 6 1 3 3.18

76 297856.4 -2080271 0.5 12 1 3 6.98

77 280410.1 -2062412 0.5 9 1 3 7.35

78 223113.2 -2002344 0.5 6 1 3 8.97

79 1648760 -2769790 0.5 9 1 3 1.68

80 1108160 -2527034 0.5 12 1 3 2.28

81 956722.8 -2406342 0.5 9 1 3 2.52

82 496429.8 -2172104 0.5 6 1 3 4.38

83 968979.1 -2340424 1 6 1 3 2.42

84 1536518 -2678804 1 9 1 3 1.74

85 1478740 -2726016 1 12 1 3 1.84

86 858210.4 -2333911 0.5 8 1 3 2.72

87 1079550 -2522749 0.5 13 1 3 2.34

88 1086602 -2497857 0.5 11 1 3 2.30

89 751218 -2223474 0.5 7 1 3 2.96

90 1016849 -2414433 0.5 10 1 3 2.37

91 1159459 -2553844 0.5 14 1 3 2.20

92 774992.5 -2147537 3 6 1 3 2.77

93 1461989 -2580033 3 6 1 3 1.76

94 1754544 -2823521 3 9 1 3 1.61

95 2364448 -2835370 3 12 1 3 1.20

96 506270.5 -2122836 1 6 1 3 4.19

97 493928.4 -2154655 0.5 6 1 3 4.36

98 1005986 -2407531 0.5 9 1 3 2.39

99 1172286 -2561904 0.5 12 1 3 2.19

100 1577454 -2703121 1 9 1 3 1.71

101 1529774 -2791490 1 12 1 3 1.82

102 730419.3 -2235480 0.5 7 1 3 3.06

103 1054265 -2442889 0.5 10 1 3 2.32

104 1124479 -2554427 0.5 13 1 3 2.27

166

105 1214101 -2567432 0.5 14 1 3 2.11

106 1358849 -2587751 1.5 6 1 3 1.90

107 2246306 -2929870 1.5 9 1 3 1.30

108 2535097 -2874727 1.5 12 1 3 1.13

109 514319.1 -2322092 1 6 1 4 4.51

110 811292.2 -2442704 1 8 1 4 3.01

111 1027219 -2604665 1 10 1 4 2.54

112 1579645 -2844666 2.5 8 1 4 1.80

113 1811226 -2907621 2.5 10 1 4 1.61

114 1960242 -2853294 2.5 12 1 4 1.46

115 1906754 -2860915 2.5 12 1 4 1.50

116 1808755 -2849298 2.5 12 1 4 1.58

117 251328.5 -2047894 1 6 1 4 8.15

118 246994.4 -2070283 1 8 1 4 8.38

119 487047.8 -2263874 2.5 8 1 4 4.65

120 550747.6 -2266315 2.5 10 1 4 4.11

121 686506.3 -2355813 2.5 12 1 4 3.43

122 782142.2 -2455277 2.5 14 1 4 3.14

123 214765.4 -1813625 1 12 1 3 8.44

124 265695 -1816503 1.5 12 1 3 6.84

125 218331.4 -1817561 1 12 1 3 8.32

126 961604.5 -2578381 1 10 1 4 2.68

127 2777001 -2818096 2.5 12 1 4 1.01

128 1790724 -2872760 2.5 12 1 4 1.60

129 1761432 -2921555 2.5 14 1 4 1.66

130 270787.3 -2035928 0.5 6 1 3 7.52

131 529853.1 -2169322 0.5 9 1 3 4.09

132 684909.8 -2288468 0.5 12 1 3 3.34

133 545338.5 -2141980 1 6 1 3 3.93

134 1014514 -2385455 1 9 1 3 2.35

135 1098238 -2539740 1 12 1 3 2.31

136 782721.2 -2257783 1.5 6 1 3 2.88

137 1358088 -2560038 1.5 9 1 3 1.89

138 1352068 -2669510 1.5 12 1 3 1.97

139 995661.4 -2353033 2 6 1 3 2.36

140 1551556 -2687483 2 9 1 3 1.73

141 1466326 -2760717 2 12 1 3 1.88

142 1238485 -2488263 2.5 6 1 3 2.01

143 1699012 -2784686 2.5 9 1 3 1.64

144 1582228 -2792812 2.5 12 1 3 1.77

145 1861837 -2841584 3 9 1 3 1.53

146 1741972 -2837721 3 12 1 3 1.63

147 2119981 -2809432 3.5 12 1 3 1.33

148 1964092 -3042291 4 10 1 4 1.55

149 2120606 -3055852 4 12 1 4 1.44

167

150 392598 -2130710 2 12 1 3 5.43

151 576145.4 -2198787 2 12 1 3 3.82

152 484691.7 -2107983 2.5 6 1 3 4.35

153 675337.8 -2249665 2.5 9 1 3 3.33

154 734258.3 -2269899 2.5 12 1 3 3.09

155 802071.2 -2300404 3 9 1 3 2.87

156 882491.8 -2337921 3 12 1 3 2.65

157 1693394 -3381863 3.5 12 1 3 2.00

158 1030107 -2394193 3.5 12 1 3 2.32

159 170135.7 -2036660 0.5 9 1 3 11.97

160 572414.2 -2220361 1.5 12 1 3 3.88

161 718843 -2264839 2 9 1 3 3.15

162 1417089 -2602315 3.5 12 1 3 1.84

163 132260.7 -3143326 0.5 9 1 3 23.77

164 172109.1 -3163705 0.5 12 1 3 18.38

165 454317.1 -3198422 1.5 12 1 3 7.04

177 1464842 -2805741 2.5 8 1 4 1.92

178 2158230 -2201320 4 10 1 4 1.02

179 1932431 -3059915 4 10 1 4 1.58

180 952482.4 -2207998 0.5 12 2 3 2.32

181 670876.6 -1925316 0.5 9 2 3 2.87

182 925796 -2070573 0.5 13 2 3 2.24

183 750600.9 -2089006 0.5 10 2 3 2.78

184 998226.7 -2086890 0.5 14 2 3 2.09

185 872472.8 -2087338 0.5 11 2 3 2.39

186 1092669 -2116872 0.5 15 2 3 1.94

187 358359.9 -1898562 0.5 6 2 3 5.30

188 570210.8 -1776957 0.5 8 2 3 3.12

189 481865 -1953992 0.5 7 2 3 4.06

190 678068.2 -1775716 1 6 2 3 2.62

191 1204479 -2290432 1 9 2 3 1.90

192 1329577 -2287987 1 12 2 3 1.72

193 794059.9 -2032265 1.5 5 2 3 2.56

194 1540162 -2576481 1.5 12 2 3 1.67

195 1515926 -2461016 1.5 9 2 3 1.62

196 960061.9 -2115835 1.5 6 2 3 2.20

197 1546193 -2412403 1.5 13 2 3 1.56

198 1601261 -2393032 1.5 10 2 3 1.49

199 1240790 -2238519 1.5 7 2 3 1.80

200 1545040 -2583701 1.5 14 2 3 1.67

201 1651200 -2583169 1.5 11 2 3 1.56

202 1396669 -2229021 1.5 8 2 3 1.60

203 1251216 -2106148 2 6 2 3 1.68

204 1741009 -2599715 2 9 2 3 1.49

205 1665827 -2638835 2 12 2 3 1.58

168

206 1525685 -2255039 2.5 6 2 3 1.48

207 1868013 -2702038 2.5 9 2 3 1.45

208 1766278 -2738233 2.5 12 2 3 1.55

209 2046774 -2611747 3 9 2 3 1.28

210 1991270 -2567900 3 12 2 3 1.29

211 2185093 -2581631 3.5 12 2 3 1.18

212 277449.6 -1932200 1 6 2 3 6.96

213 349663.3 -1775040 1 9 2 3 5.08

214 386529.9 -1769019 1 12 2 3 4.58

215 403784.3 -1922624 1.5 6 2 3 4.76

216 517143.5 -1957232 1.5 9 2 3 3.78

217 554158.1 -1845227 1.5 12 2 3 3.33

218 521673 -1808068 2 6 2 3 3.47

219 687067.9 -1917378 2 9 2 3 2.79

220 760454.7 -1954599 2 12 2 3 2.57

221 643413.4 -1892858 2.5 6 2 3 2.94

222 839515.3 -2009685 2.5 9 2 3 2.39

223 955375.6 -2033132 2.5 12 2 3 2.13

224 982906 -2052753 3 9 2 3 2.09

225 1099321 -2095208 3 12 2 3 1.91

226 1340203 -2134296 3.5 12 2 3 1.59

227 616652.9 -1796353 0.48 13 2 3 2.91

228 658739.6 -1780903 0.48 11 2 3 2.70

229 670890.1 -1758924 0.48 9 2 3 2.62

230 604632.1 -1754818 0.48 7 2 3 2.90

231 664450.5 -1752461 0.48 5 2 3 2.64

232 1156607 -2071247 0.96 13 2 3 1.79

233 1235475 -2067803 0.96 11 2 3 1.67

234 1268011 -2040172 0.96 9 2 3 1.61

235 1238002 -1956027 0.96 7 2 3 1.58

236 1191201 -1895102 0.96 5 2 3 1.59

237 1718319 -2379813 1.44 13 2 3 1.38

238 1827149 -2383601 1.44 11 2 3 1.30

239 1835630 -2440058 1.44 9 2 3 1.33

240 1758145 -2226344 1.44 7 2 3 1.27

241 1615586 -2098366 1.44 5 2 3 1.30

242 1776972 -2265579 1.6 5 2 3 1.27

243 2614372 -2800456 2.24 13 2 3 1.07

244 2703334 -2701412 2.24 9 2 3 1.00

245 2389019 -2503730 2.24 5 2 3 1.05

246 3086239 -3187870 2.88 13 2 3 1.03

247 3053551 -2926217 2.88 9 2 3 0.96

248 2888585 -2621536 2.88 5 2 3 0.91

249 879030 -2543408 0 NaN 2 3 2.89

250 933090.3 -2074591 0 NaN 2 3 2.22

169

251 426777 -2142662 0 NaN 2 3 5.02

252 476986.1 -1835575 0 NaN 2 3 3.85

253 225452.6 -1793923 0 NaN 2 3 7.96

254 295113.4 -1702012 0 NaN 2 3 5.77

255 2309764 -2690353 2 9 2 3 1.16

256 2138609 -2573030 2 12 2 3 1.20

257 730860.9 -2278687 1 6 2 4 3.12

258 1132102 -2267319 1 8 2 4 2.00

259 1364002 -2519483 1 10 2 4 1.85

260 1915999 -2679841 2.5 8 2 4 1.40

261 1946489 -2667717 2.5 10 2 4 1.37

262 1996938 -2624892 2.5 12 2 4 1.31

263 2022169 -2686599 2.5 14 2 4 1.33

264 2191152 -2937212 4 10 2 4 1.34

265 1397024 -2497986 2.5 8 2 4 1.79

266 717955.1 -2027835 2.5 10 2 4 2.82

267 562230.6 -1932326 2.5 12 2 4 3.44

268 214539.4 -1826398 0.5 9 2 3 8.51

269 888591.3 -2154504 2 9 2 3 2.42

270 1724300 -2677422 3.5 12 2 3 1.55

271 212890.1 -2636496 0.5 9 2 3 12.38

272 251675.1 -2676025 0.5 12 2 3 10.63

273 724572 -2887265 1.5 12 2 3 3.98

274 207083.8 -1921897 1.5 12 2 5 9.28

275 70296.34 -1749271 1.5 12 2 5 24.88

277 2466295 -3065968 4 12 2 4 1.24

288 149398.9 -1548410 4 10 2 5 10.36

291 364805.7 -1792705 8.4 13 1 5 4.91

regular = 3

irregular = 4

survival = 5

170

Appendix 7

Simulation Model – Peak and Load Statistics

Wave Ht(m)

Wave Pd(s)

RMS Load

Max Load

Mean Load

A100 A10 A3 Number of Peaks

0.5 3 2520011 2569466 2534623 2566253 2556359 2547272 233

0.5 4 2521921 2570460 2530851 2570460 2557460 2547948 100

0.5 5 2527809 2599280 2530726 NaN 2582165 2564676 32

0.5 6 2561014 2599280 2532694 NaN 2599280 2591023 15

0.5 7 2594519 2815371 2537357 NaN 2815371 2696845 16

0.5 8 2643985 2848313 2544047 NaN 2848313 2775452 19

0.5 9 2649995 2789925 2542860 NaN 2789925 2742432 19

0.5 10 2695887 3085854 2549020 NaN 3085854 2875823 18

0.5 11 2694225 3112638 2563160 NaN 3083118 3039484 23

0.5 12 2676641 3172704 2566367 NaN 3104500 2928284 33

0.5 13 2675668 3149524 2569471 NaN 3106663 3057529 20

0.5 14 2681171 3233747 2579059 NaN 3136181 2986511 38

1 4 2535871 2648407 2538292 NaN 2619835 2588482 74

1 5 2543211 2758648 2539919 NaN 2698275 2628087 28

1 6 2580909 2855616 2547139 NaN 2855616 2835971 13

1 7 2618427 2872700 2548414 NaN 2872700 2767854 19

1 8 2668264 3069794 2581124 NaN 3049307 2953360 39

1 9 2663372 3286005 2582937 NaN 3259100 3067692 24

1 10 2696294 3259287 2596913 NaN 3244469 3110764 37

1 11 2688408 3256369 2604862 NaN 3238620 3166604 38

1 12 2663667 3390833 2595753 NaN 3368928 3240834 25

1 13 2641541 3598085 2598578 NaN 3594129 3307112 21

1 14 2638683 3467098 2620377 NaN 3451492 3402782 30

1 15 2643031 3501718 2635966 NaN 3495259 3416837 43

1 16 2606885 3544118 2639026 NaN 3514345 3399976 50

1 17 2615189 3528087 2662891 NaN 3486332 3422602 40

1.5 5 2554641 3528087 2596112 NaN 3499272 3373180 28

1.5 6 2590391 3528087 2605368 NaN 3499272 3389238 24

1.5 7 2623121 3528087 2609401 NaN NaN 3499272 6

1.5 8 2663313 3528087 2630387 NaN 3474888 3375217 32

1.5 9 2651764 3528087 2621253 NaN 3499272 3367035 25

1.5 10 2671620 3678234 2648791 NaN 3675511 3546652 33

1.5 11 2654018 3704150 2655250 NaN 3704150 3647359 19

1.5 12 2669064 3704172 2637331 NaN 3614260 3430504 41

1.5 13 2659917 3685022 2683195 NaN 3664448 3588782 48

1.5 14 2651905 3648875 2691852 NaN 3621727 3590928 39

1.5 15 2642833 3613062 2677888 NaN 3588744 3529857 38

1.5 16 2606733 3613062 2689373 NaN 3604288 3575513 45

1.5 17 2612939 3575382 2718271 NaN 3561390 3543184 60

171

2 6 2602699 3555525 2634935 NaN 3553095 3507773 38

2 7 2630676 3555525 2644635 NaN 3553791 3533635 29

2 8 2645177 3727436 2668143 NaN 3725002 3583303 27

2 9 2646375 3722567 2687371 NaN 3722567 3660391 19

2 10 2679675 3672569 2693413 NaN 3661590 3602767 44

2 11 2635125 3712815 2713714 NaN 3673416 3642577 36

2 12 2653436 3810069 2761880 NaN 3715168 3658507 54

2 13 2650757 3740045 2756670 NaN 3704166 3638053 53

2 14 2666318 3691047 2798838 NaN 3666408 3611982 78

2 15 2650745 3688583 2791258 NaN 3651527 3609430 59

2 16 2624609 3687799 2809328 NaN 3628972 3586957 66

2 17 2629219 3687799 2771405 NaN 3626182 3582374 65

2.5 6 2609238 3687799 2705579 NaN 3648210 3589722 37

2.5 7 2622423 3687799 2727948 NaN 3661421 3604581 29

2.5 8 2654059 3687799 2755722 NaN 3683803 3644268 30

2.5 9 2651251 3700773 2789026 NaN 3694761 3662977 42

2.5 10 2684719 3715317 2812793 NaN 3706591 3662692 70

2.5 11 2662962 3708967 2825912 NaN 3682232 3645964 68

2.5 12 2667372 3740140 2856355 NaN 3688818 3643250 78

2.5 13 2680697 3704588 2888122 NaN 3681718 3636972 87

2.5 14 2657021 3700175 2872531 NaN 3646931 3616984 78

2.5 15 2662068 3661172 2867164 NaN 3637286 3596359 81

2.5 16 2655748 3667260 2854874 NaN 3638681 3590565 77

2.5 17 2646981 3642304 2875501 NaN 3607435 3566596 90

3 6 2620918 3636663 2783218 NaN 3618443 3569937 39

3 7 2631555 3636663 2806149 NaN 3635805 3586538 28

3 8 2655980 3694462 2857270 NaN 3683445 3652173 51

3 9 2653574 3790383 2865493 NaN 3773004 3702097 44

3 10 2688234 3823552 2951779 3823552 3750810 3694426 101

3 11 2701050 3724746 3010283 3724746 3707129 3661608 117

3 12 2674913 3818686 2981671 3818686 3748204 3673580 105

3 13 2685745 3801719 3029335 3801719 3746233 3681693 107

3 14 2667688 3795879 3007625 NaN 3715676 3647458 98

3 15 2689050 3715663 2988318 3715663 3669558 3611426 104

3 16 2654647 3715663 2998749 3715663 3666752 3609308 103

3 17 2632061 3715663 2992707 NaN 3648699 3594947 96

3.5 7 2657824 3829244 2913986 NaN 3692951 3604955 77

3.5 8 2675316 3813726 2949558 NaN 3779821 3717675 97

3.5 9 2677419 3812150 3006387 3812150 3750973 3712823 109

3.5 10 2732337 3846320 3134475 3846320 3756029 3685649 139

3.5 11 2727309 3785856 3114953 3785856 3726811 3673043 135

3.5 12 2721175 3785856 3134430 3785856 3739235 3682274 124

3.5 13 2708983 3808170 3158393 3808170 3721922 3656453 146

3.5 14 2668927 3804094 3126843 3804094 3724839 3652459 115

3.5 15 2688692 3804094 3093476 3804094 3742243 3650894 125

172

3.5 16 2675017 3847795 3116546 3847795 3759329 3661829 112

3.5 17 2649389 3804094 3099411 NaN 3719608 3647253 99

4 8 2699426 3894951 3071514 3894951 3838214 3736322 128

4 9 2692668 3905611 3111549 3905611 3803893 3714791 109

4 10 2772425 3829495 3227998 3829495 3783300 3693796 165

4 11 2764023 3856294 3261981 3856294 3739597 3676373 171

4 12 2750418 3883561 3229576 3883561 3751360 3665419 142

4 13 2745205 3825330 3240613 3825330 3735993 3670939 156

4 14 2736040 3898286 3280618 3898286 3753073 3659210 178

4 15 2710610 3776560 3270964 3776560 3728262 3668220 142

4 16 2702887 3807547 3266263 3807547 3745386 3667220 151

4 17 2710343 3943448 3245153 3943448 3753881 3662122 128

4.5 9 2696612 3871694 3269214 3871694 3826896 3727355 149

4.5 10 2797328 3886359 3295870 3886359 3763361 3694243 188

4.5 11 2822392 3845992 3407669 3845626 3756856 3675377 211

4.5 12 2787156 3881007 3414135 3880844 3797161 3681380 201

4.5 13 2814450 3882093 3369658 3872799 3764818 3665600 206

4.5 14 2761501 3970824 3387679 3970824 3804703 3699712 178

4.5 15 2741620 3973283 3403357 3973283 3811689 3706319 167

4.5 16 2762729 3796832 3368467 3796832 3751620 3677576 163

4.5 17 2720779 3808254 3365514 3808254 3766128 3698906 151

5 10 2845094 3911742 3404977 3882047 3804803 3705651 222

5 11 2855680 3883289 3428023 3862608 3769068 3676877 215

5 12 2852351 3845508 3455498 3845382 3753066 3660644 237

5 13 2839930 3845256 3478915 3829076 3763388 3656226 208

5 14 2818608 3885905 3462252 3885905 3791133 3698400 182

5 15 2788649 3918571 3462323 3918260 3770380 3673849 201

5 16 2774951 3873717 3444938 3873717 3774942 3692487 187

5 17 2759669 3879551 3442739 3879551 3801250 3713810 179

5.5 10 2863828 4021836 3426026 3937767 3793507 3692956 231

5.5 11 2886621 4007429 3496904 4006292 3839803 3716818 251

5.5 12 2907429 3917940 3477871 3916985 3781046 3682344 256

5.5 13 2872010 3925140 3451334 3924559 3771325 3661483 257

5.5 14 2896855 3955033 3477567 3954560 3765930 3670206 250

5.5 15 2837605 3945685 3487107 3945218 3873256 3747028 230

5.5 16 2807650 4002351 3464362 3963165 3775715 3687469 227

5.5 17 2785454 3923978 3412970 3884612 3773813 3672107 205

6 11 2931426 3878512 3400633 3849810 3771587 3659115 259

6 12 2955258 3890056 3485575 3883228 3782294 3684341 268

6 13 2888610 3791233 3447201 3790632 3748179 3661054 263

6 14 2868277 3997424 3442155 3997371 3848138 3699760 225

6 15 2851590 4015979 3446892 4014667 3801627 3674830 242

6 16 2868860 3873419 3432769 3872825 3769193 3662399 260

6 17 2835377 3932779 3390779 3914891 3771407 3654739 241

6.5 12 2945466 4025487 3436168 4003000 3808749 3662411 269

173

6.5 13 2995268 3965232 3458769 3950320 3787270 3679740 305

6.5 14 2971548 3961036 3430652 3960331 3782861 3661457 278

6.5 15 2926347 3986397 3429331 3981978 3790440 3675745 241

6.5 16 2900740 3922685 3471776 3922418 3829491 3730782 266

6.5 17 2875775 3916497 3428384 3894845 3785079 3683392 263

7 12 3011079 3949321 3404490 3945385 3767556 3651167 288

7 13 3035284 3990567 3468868 3990538 3803631 3700526 282

7 14 2984967 4050576 3440373 4049546 3850661 3702995 276

7 15 2953446 4027331 3429228 3976320 3799455 3685317 269

7 16 2941110 4040061 3434795 4040052 3816058 3692499 281

7 17 2921236 3973969 3441881 3973873 3839448 3730765 246

7.5 12 3054688 4046951 3475039 4042312 3851388 3704202 293

7.5 13 3029974 4179908 3396851 4179822 3816912 3667429 286

7.5 14 3032548 4179908 3429299 4145335 3835645 3674625 277

7.5 15 3067314 3968861 3483369 3954184 3853162 3734583 324

7.5 16 2990835 4019146 3424070 4019057 3859566 3707448 287

7.5 17 3000191 4019146 3457184 3982999 3817329 3701014 254

174

Appendix 8

Simulation Model – Fatigue Loads

Wave Ht(m)

Wave Pd(s)

Damage Design Life (s)

Equivalent Load (N)

Max Load (N)

Life Time Damage

0.5 3 8.99E+22 175316.2 48662.37 51903.79 3.15E+28

0.5 4 5.15E+24 175316.2 113113.4 105155.1 1.81E+30

0.5 5 4.20E+26 175316.2 283000.5 239097.8 1.47E+32

0.5 6 2.59E+27 175316.2 413467 306164.1 9.10E+32

0.5 7 2.10E+28 175316.2 639272.4 600623.6 7.37E+33

0.5 8 2.12E+28 175316.2 640201 502726.4 7.42E+33

0.5 9 6.50E+28 175316.2 808937.8 752928.8 2.28E+34

0.5 10 1.70E+29 175316.2 988816.4 835935 5.98E+34

0.5 11 1.96E+29 175316.2 1017887 880865.1 6.87E+34

0.5 12 1.69E+29 175316.2 986569.6 757351.7 5.91E+34

0.5 13 2.44E+29 175316.2 1065811 830817.8 8.57E+34

0.5 14 2.33E+29 175316.2 1055498 878040.9 8.18E+34

1 4 8.19E+26 175316.2 325154.4 252741.5 2.87E+32

1 5 4.00E+28 175316.2 730932.5 611910.7 1.40E+34

1 6 1.52E+29 175316.2 966061.9 685904.6 5.35E+34

1 7 4.57E+29 175316.2 1214395 925525.8 1.60E+35

1 8 9.55E+29 175316.2 1415688 1034293 3.35E+35

1 9 1.72E+30 175316.2 1600277 1100396 6.03E+35

1 10 2.57E+30 175316.2 1740124 1209032 9.01E+35

1 11 2.82E+30 175316.2 1774629 1201699 9.90E+35

1 12 3.01E+30 175316.2 1798576 1203440 1.06E+36

1 13 2.87E+30 175316.2 1780514 1226024 1.01E+36

1 14 3.05E+30 175316.2 1803675 1145658 1.07E+36

1 15 2.52E+30 175316.2 1733694 1139798 8.85E+35

1 16 2.91E+30 175316.2 1785156 1194763 1.02E+36

1 17 2.58E+30 175316.2 1741280 1144492 9.04E+35

1.5 5 3.25E+29 175316.2 1131082 902634 1.14E+35

1.5 6 1.23E+30 175316.2 1491341 1134123 4.30E+35

1.5 7 2.98E+30 175316.2 1795050 1217621 1.05E+36

1.5 8 6.25E+30 175316.2 2093922 1394847 2.19E+36

1.5 9 7.48E+30 175316.2 2173921 1370339 2.62E+36

1.5 10 9.67E+30 175316.2 2293324 1380907 3.39E+36

1.5 11 8.95E+30 175316.2 2256953 1399434 3.14E+36

1.5 12 7.73E+30 175316.2 2188696 1353369 2.71E+36

1.5 13 8.59E+30 175316.2 2237558 1329472 3.01E+36

1.5 14 8.44E+30 175316.2 2229274 1295763 2.96E+36

1.5 15 8.37E+30 175316.2 2225190 1289960 2.93E+36

1.5 16 6.78E+30 175316.2 2130110 1257011 2.38E+36

1.5 17 6.77E+30 175316.2 2129120 1258423 2.37E+36

175

2 6 5.46E+30 175316.2 2036105 1442955 1.92E+36

2 7 1.02E+31 175316.2 2319711 1468545 3.58E+36

2 8 1.46E+31 175316.2 2497820 1462142 5.11E+36

2 9 1.60E+31 175316.2 2546713 1440869 5.61E+36

2 10 1.54E+31 175316.2 2528391 1456220 5.42E+36

2 11 1.60E+31 175316.2 2548239 1383479 5.62E+36

2 12 1.50E+31 175316.2 2512650 1420297 5.26E+36

2 13 1.52E+31 175316.2 2518962 1448700 5.32E+36

2 14 1.36E+31 175316.2 2460365 1406941 4.75E+36

2 15 1.28E+31 175316.2 2431655 1386100 4.49E+36

2 16 1.15E+31 175316.2 2375971 1379325 4.02E+36

2 17 1.09E+31 175316.2 2349253 1352834 3.81E+36

2.5 6 1.18E+31 175316.2 2390482 1509660 4.14E+36

2.5 7 2.07E+31 175316.2 2686136 1544618 7.24E+36

2.5 8 2.33E+31 175316.2 2754976 1494337 8.18E+36

2.5 9 2.58E+31 175316.2 2813283 1532807 9.04E+36

2.5 10 2.37E+31 175316.2 2764153 1521290 8.31E+36

2.5 11 2.42E+31 175316.2 2776615 1501824 8.49E+36

2.5 12 2.39E+31 175316.2 2770262 1462704 8.40E+36

2.5 13 2.26E+31 175316.2 2736806 1478234 7.92E+36

2.5 14 1.86E+31 175316.2 2628031 1509343 6.52E+36

2.5 15 1.86E+31 175316.2 2628797 1502744 6.53E+36

2.5 16 1.69E+31 175316.2 2576905 1477574 5.93E+36

2.5 17 1.59E+31 175316.2 2543234 1419113 5.57E+36

3 6 2.08E+31 175316.2 2691443 1597876 7.31E+36

3 7 3.10E+31 175316.2 2924193 1563852 1.09E+37

3 8 3.58E+31 175316.2 3012345 1564033 1.26E+37

3 9 3.55E+31 175316.2 3007548 1571171 1.25E+37

3 10 3.64E+31 175316.2 3022218 1647225 1.28E+37

3 11 3.27E+31 175316.2 2956616 1568779 1.15E+37

3 12 2.93E+31 175316.2 2889378 1751365 1.03E+37

3 13 2.87E+31 175316.2 2876932 1590828 1.01E+37

3 14 2.45E+31 175316.2 2783847 1565670 8.60E+36

3 15 2.46E+31 175316.2 2786075 1536571 8.63E+36

3 16 2.29E+31 175316.2 2743495 1534766 8.01E+36

3 17 2.05E+31 175316.2 2682201 1502332 7.19E+36

3.5 7 4.24E+31 175316.2 3119658 1690509 1.48E+37

3.5 8 4.35E+31 175316.2 3137575 1604461 1.53E+37

3.5 9 4.30E+31 175316.2 3129102 1663402 1.51E+37

3.5 10 4.79E+31 175316.2 3201029 1631754 1.68E+37

3.5 11 4.06E+31 175316.2 3092443 1731572 1.42E+37

3.5 12 4.17E+31 175316.2 3110293 1745445 1.46E+37

3.5 13 3.93E+31 175316.2 3070668 1633493 1.38E+37

3.5 14 3.26E+31 175316.2 2953908 1691612 1.14E+37

3.5 15 3.05E+31 175316.2 2912772 1653016 1.07E+37

176

3.5 16 2.65E+31 175316.2 2829589 1690216 9.30E+36

3.5 17 2.45E+31 175316.2 2782744 1643427 8.58E+36

4 8 5.81E+31 175316.2 3332027 1815277 2.04E+37

4 9 5.36E+31 175316.2 3277060 1802578 1.88E+37

4 10 5.80E+31 175316.2 3330866 1808856 2.03E+37

4 11 5.38E+31 175316.2 3278659 1693614 1.89E+37

4 12 4.75E+31 175316.2 3195147 1744279 1.67E+37

4 13 4.85E+31 175316.2 3208645 1768407 1.70E+37

4 14 3.96E+31 175316.2 3075696 1668170 1.39E+37

4 15 3.67E+31 175316.2 3027572 1755879 1.29E+37

4 16 3.42E+31 175316.2 2983435 1673277 1.20E+37

4 17 3.03E+31 175316.2 2910244 1615998 1.06E+37

4.5 9 6.83E+31 175316.2 3446756 1788642 2.40E+37

4.5 10 6.02E+31 175316.2 3357021 1999881 2.11E+37

4.5 11 6.07E+31 175316.2 3362135 1909437 2.13E+37

4.5 12 5.58E+31 175316.2 3303878 1812260 1.96E+37

4.5 13 5.30E+31 175316.2 3268607 1821087 1.86E+37

4.5 14 4.83E+31 175316.2 3206435 1903633 1.69E+37

4.5 15 4.54E+31 175316.2 3164875 1873088 1.59E+37

4.5 16 3.81E+31 175316.2 3051704 1735275 1.34E+37

4.5 17 3.58E+31 175316.2 3012549 1829720 1.26E+37

5 10 6.50E+31 175316.2 3411112 1908979 2.28E+37

5 11 6.70E+31 175316.2 3432240 1918492 2.35E+37

5 12 6.02E+31 175316.2 3357367 1855598 2.11E+37

5 13 5.96E+31 175316.2 3349350 1860601 2.09E+37

5 14 5.68E+31 175316.2 3315936 1957461 1.99E+37

5 15 4.94E+31 175316.2 3220906 1889076 1.73E+37

5 16 4.59E+31 175316.2 3172422 1827537 1.61E+37

5 17 4.06E+31 175316.2 3091575 1740066 1.42E+37

5.5 10 8.18E+31 175316.2 3578084 2062940 2.87E+37

5.5 11 7.86E+31 175316.2 3548526 1991349 2.76E+37

5.5 12 7.54E+31 175316.2 3518120 1963859 2.64E+37

5.5 13 6.09E+31 175316.2 3364759 1928862 2.13E+37

5.5 14 6.69E+31 175316.2 3430947 2017713 2.34E+37

5.5 15 6.09E+31 175316.2 3365270 1851928 2.14E+37

5.5 16 5.36E+31 175316.2 3277175 1819964 1.88E+37

5.5 17 5.00E+31 175316.2 3229667 1799924 1.75E+37

6 11 7.05E+31 175316.2 3469029 2044681 2.47E+37

6 12 7.84E+31 175316.2 3546849 2059712 2.75E+37

6 13 6.99E+31 175316.2 3463096 2060087 2.45E+37

6 14 6.22E+31 175316.2 3379263 2074375 2.18E+37

6 15 6.11E+31 175316.2 3366779 1946630 2.14E+37

6 16 5.91E+31 175316.2 3344514 1894331 2.07E+37

6 17 4.97E+31 175316.2 3225584 1902361 1.74E+37

6.5 12 7.26E+31 175316.2 3490741 2136422 2.55E+37

177

6.5 13 7.02E+31 175316.2 3466031 2012973 2.46E+37

6.5 14 6.37E+31 175316.2 3396966 2040505 2.23E+37

6.5 15 7.06E+31 175316.2 3470549 2036656 2.48E+37

6.5 16 5.79E+31 175316.2 3329087 1934637 2.03E+37

6.5 17 5.92E+31 175316.2 3345315 1957378 2.08E+37

7 12 7.84E+31 175316.2 3546837 2100619 2.75E+37

7 13 8.13E+31 175316.2 3573208 2113408 2.85E+37

7 14 7.18E+31 175316.2 3482830 2014255 2.52E+37

7 15 6.94E+31 175316.2 3457586 2070176 2.43E+37

7 16 6.19E+31 175316.2 3375980 2024795 2.17E+37

7 17 6.23E+31 175316.2 3380748 1899807 2.18E+37

7.5 12 8.52E+31 175316.2 3608938 2197367 2.99E+37

7.5 13 8.81E+31 175316.2 3633674 2141771 3.09E+37

7.5 14 7.95E+31 175316.2 3556597 2123656 2.79E+37

7.5 15 8.37E+31 175316.2 3595654 2107735 2.94E+37

7.5 16 7.83E+31 175316.2 3545479 2112099 2.74E+37

7.5 17 5.72E+31 175316.2 3321358 2022865 2.01E+37

178

Appendix 9

Additional Objectives

In early May, the following deliverables were added in the list under the topic Load Case

Analysis,

A. For each sea state, a saved time series of the loads, the position and accelerations listed below

5

a. F_wire_lateral

b. F_wire_vertical

c. F_trans

d. F_WS

e. A_buoy_heave

f. A_buoy_surge

g. A_buoy_sway

h. A_buoy_pitch

i. A_buoy_roll

j. D_rack

k. V_rack

l. A_rack

B. Analyzed data based on these time series for each sea state:

a. Scatter plot of A_buoy_heave vs D_rack [TANK, Simulink, OrcaflexTM]

b. Scatter plot of A_buoy_surge vs D_rack [TANK, Simulink, OrcaflexTM]

c. Scatter plot of A_buoy_sway vs D_rack [TANK]

d. Scatter plot of A_buoy_pitch vs D_rack [TANK]

e. Scatter plot of A_buoy_roll vs D_rack [TANK]

f. Scatter plot of A_buoy_yaw vs D_rack [TANK]

g. Resultant acceleration in XY plane [TANK]

C. Accelerations

a. Max Acceleration value detected [A_heave; A_surge, A_sway_A_pitch, A_roll] with the

corresponding rack position at the event of the MAX acceleration value

[D_rack_maxheave; D_rack_max_surge; D_rack_max_sway; D_rack_max_pitch;

D_rack_max_roll] for each sea state

b. Min Acceleration value [A_heave; A_surge, A_sway_A_pitch, A_roll] with the

corresponding rack position at the event of the MIN acceleration value

[D_rack_min_heave; D_rack_min_surge; D_rack_min_sway; D_rack_min_pitch;

D_rack_min_roll] for each sea state. (MIN-values needed to capture most negative

acceleration, alternatively give only absolute IIA_MAXII)

D. ROD/tether [F_wire]

b. Scatter plot of F_wire_lateral & F_wire_vertical vs D_rack in each sea state

c. F_wire_lateral_max recorded from all sea states for the full range of rack positions, for

instance given with 0,1-m bins for the rack, e.g. F_wire_lateral_max for D_rack[0,1: 0,2;

180

0,3 …. 7;0m] Vector with Sea_State_name[Hs,Tp];Time[s] for the max event recorded.

(so that one can easily go back to the time series and find the Max_event)

d. Distribution plot showing number of load cycles of each Load bin for each sea state

e. Table showing total number of load cycles of each Load bin over 20 years in our 6 target

sites (plot from above multiplied with site scatter)

E. WAVESPRING [F_WS]

a. Scatter plot of F_WS vs D_rack in each sea state.

b. F_WS _max recorded from all sea states for the full range of rack positions, for instance

given with 0,1-m bins for the rack, e.g. F_WS _max for D_rack[0,1: 0,2; 0,3 …. 7;0m]

Vector with Sea_State_name[Hs,Tp];Time[s] for the max event recorded. (so that one

can easily go back to the time series and find the Max_event)

c. Distribution plot showing number of load cycles of each Load bin for each sea state

d. Table showing total number of load cycles of each Load bin over 20 years in our 6 target

sites (plot from above multiplied with site scatter)

F. Transmission [F_trans]

a. Scatter plot of F_trans vs D_rack in each sea state .

b. F_trans_max recorded from all sea states for the full range of rack positions, for

instance given with 0,1-m bins for the rack, e.g. F_WS _max for D_rack[0,1: 0,2; 0,3 ….

7;0m], Vector with Sea_State_name[Hs,Tp];Time[s] for the max event recorded. (so that

one can easily go back to the time series and find the Max_event)

c. Distribution plot showing number of load cycles of each Load bin for each sea state

d. Table showing total number of load cycles of each Load bin over 20 years in our 6 target

sites (plot from above multiplied with site scatter)

G. Number of WS-cut-off events in each sea state (D_Rack >2.5 || after zero crossing)

H. Number of slack events in each sea state

181

Appendix 10

Peak Identification MatlabTM Code

Algorithm 1 inspired by work done by US Navy in Peak Identification MethodsXXXI

% US Navy Algorithm % % inputfilename=input('dataset_2_KT.mat','s'); clear all close all clc

directory = 'D:\corpower\All Files'; % IDENTIFY FOLDER

FilesNames=dir(directory); NumFiles=length(FilesNames)-2; disp('Number of Files: '); disp(NumFiles); % IDENTIFY NUMBER OF FILES

n1 = 1; %COUNTER FOR PEAK STORAGE MATRIX n2 = 1; m = 24+(n2-1)*2; %START VALUE OF ROW NUMBER IN RUNLIST

filename = 'runList.xlsx'; Q = xlsread(filename); % INSERT RUNLIST FILE HERE

%Start automation for i = n2:0.5:NumFiles % LOOP FOR PICKING ONE FILE AT A TIME)

ExperMatlab = FilesNames(1+2*i).name % FILE SEQUENCE SELECTOR load([directory '\' ExperMatlab]); input = data;

time=data.time; dt = time(5)-time(4);

Fc = mean(data.F_subsea(1:10));

T1 = Q(m,4); T2 = Q(m,3);

%Upper gg = max(find(abs(time-Q(m,4))<=2*dt)); %Lower pp = max(find(abs(time-Q(m,3))<=2*dt));

ID = ExperMatlab(3:6) ID1 = str2num(ID) % g=9.81; % inputfilename = 'time_series_0.5_03.mat';

182

% load time_series_0.5_03.mat; % time in first column, data of interest in

second column % A=data.time;

raw_data=-1*data.F_subsea(:,1); L=length(raw_data(pp:gg)); % length of time history T=time(L); % max time Fs=(L-1)/(T-time(1)); %sampling frequency; assumes evenly spaced data

raw_data = raw_data(pp:gg); time = time(pp:gg);

figure(1) plot(time,raw_data) xlabel('Time (s)') ylabel('Force (N)') title('Raw data') axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Initial Data.jpg' ])

NFFT = 2^nextpow2(L); % Next power of 2 from length of rawdata Y = fft(raw_data,NFFT)/L; f = Fs/2*linspace(0,1,NFFT/2+1);

% Plot single-sided amplitude spectrum. figure(2) plot(f,2*abs(Y(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of y(t)before processing') xlabel('Frequency (Hz)') ylabel('|Y(f)|') axis([0 50 0 1]) saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_AmplitudeSpectrum_initial.jpg' ])

%% Filtering % filter_type=input('Select filter type; [0] unfiltered, [1] Butterworth, [2]

Kaiser: [3] idealfilter'); filter_type = 1;

if filter_type==0 % No filtering filtered_data=raw_data; filterstr=sprintf('Unfiltered');

elseif filter_type==1 % Butterworth lowpass filter % Details of this filter block can be found on the Mathworks website:

http://www.mathworks.com/help/toolbox/signal/butter.html % cutoff=input('Enter desired cutoff frequency in Hz [10 recommended]:

');

183

% butterorder=input('Enter desired order for Butterworth filter [at least

3 recommended]: '); cutoff = 2.5; butterorder = 9; Wn=cutoff/(Fs/2); [b,a]=butter(butterorder,Wn,'low'); filtered_data=filtfilt(b,a,raw_data); %use filtfilt rather than filter

for 0 phase shift % Plot raw and filtered data figure(3) plot(time,[raw_data,filtered_data]) xlabel('Time (s)') ylabel('Force (N)') if butterorder==1 filterstr = sprintf('Filtered at %.1f Hz with a %.fst order

Butterworth lowpass filter',[cutoff,butterorder]); elseif butterorder==2 filterstr = sprintf('Filtered at %.1f Hz with a %.fnd order

Butterworth lowpass filter',[cutoff,butterorder]); elseif butterorder==3 filterstr = sprintf('Filtered at %.1f Hz with a %.frd order

Butterworth lowpass filter',[cutoff,butterorder]); else filterstr = sprintf('Filtered at %.1f Hz with a %.fth order

Butterworth lowpass filter',[cutoff,butterorder]); end title(filterstr); legend('Raw data','Filtered data') axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Filtered Data.jpg' ])

elseif filter_type==2 % Kaiser lowpass filter % Details of this filter block can be found on the Mathworks website:

http://www.mathworks.com/help/toolbox/signal/kaiserord.html % Further information can also be found in the FILTER.m routine by

Charlie Weil at CCD passband=input('Enter desired upper frequency for pass band in Hz [10

recommended]: '); stopband=input('Enter desired lower limit to stop band in Hz [12

recommended]: '); % passripple=input('Enter allowable passband ripple [0.05 recommended]:

'); % stopatten=input('Enter stopband attenuation [0.01 recommended]: '); passripple = 0.05; stopatten = 0.01; [n,Wn,beta,ftype]=kaiserord([passband stopband],[1 0],[passripple

stopatten],Fs); hh=fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale'); filtered_data=filtfilt(hh,1,raw_data); %use filtfilt rather than filter

for 0 phase shift % Plot raw and filtered data figure(3) plot(time,[raw_data,filtered_data])

184

xlabel('Time (s)') ylabel('Force (N)') filterstr = sprintf('Filtered at %.1f Hz passband and %.1f Hz stopband

with a Kaiser lowpass filter',[passband stopband]); title(filterstr); legend('Raw data','Filtered data') axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Filtered Data.jpg' ])

elseif filter_type==3 %idealfilter passbandPos = [0.001 2.5]; passband = passbandPos(1); stopband = passbandPos(2); idealinput = timeseries(raw_data,time); posfiltR = idealfilter(idealinput,passbandPos,'pass'); filtered_data=posfiltR.data; % Plot raw and filtered data figure(3) plot(time,[raw_data,filtered_data]) xlabel('Time (s)') ylabel('Force (N)') filterstr = sprintf('Filtered at %.1f Hz passband and %.1f Hz stopband

with an idealfilter',[passband stopband]); title(filterstr); legend('Raw data','Filtered data') axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Filtered Data.jpg' ])

else fprintf('You must select a filter type by entering either 0 for

unfiltered, 1 for Butterworth, or 2 for Kaiser.\n'); break end

RMS_filtered=sqrt(var(filtered_data)+(mean(filtered_data))^2);

% time_threshold=input('Enter desired time threshold in seconds [0.5

recommended; use 0 to denote manual entry of conditions]: '); time_threshold = 1;

if time_threshold==0 Vk=input('Enter craft speed in knots: '); heading_deg=input('Enter heading in degrees [any value from 0 to 360,

following seas=0, head seas=180]: '); wper=input('Enter wave period in seconds: '); Vc=Vk*0.514444; % speed in m/s $$$$$$ heading=heading_deg*pi/180; %heading in radians w=2*pi/wper; k=w^2/g; %assume deep water we=w-Vc*k*cos(heading);

185

te=2*pi/we; if te<0 fprintf('You were overtaking the waves! This algorithm will use the

absolute value of encounter frequency.\n'); end time_threshold=abs(te/2); end

peaks_counter=0; for i=ceil(time_threshold*Fs):L-ceil(time_threshold*Fs) if filtered_data(i)>filtered_data(i-1) &&

filtered_data(i)>=filtered_data(i+1) peaks_counter=peaks_counter+1; peaks_time(peaks_counter)=time(i); peaks(peaks_counter)=filtered_data(i); peaks_i(peaks_counter)=i; end end % peaks = -1*peaks; % This step implements the RMS and time thresholds final_peaks_counter=0; for i=2:peaks_counter-1 if peaks(i)>RMS_filtered && peaks_time(i+1)-peaks_time(i)>time_threshold

&& peaks_time(i)-peaks_time(i-1)>time_threshold final_peaks_counter=final_peaks_counter+1; final_peaks(final_peaks_counter)=peaks(i); final_peaks_time(final_peaks_counter)=peaks_time(i); elseif peaks(i)>RMS_filtered keep=0; for j=1:ceil(time_threshold*Fs) if peaks(i)>filtered_data(peaks_i(i)-j) &&

peaks(i)>=filtered_data(peaks_i(i)+j) keep=1; else keep=0; break end end if keep==1 final_peaks_counter=final_peaks_counter+1; final_peaks(final_peaks_counter)=peaks(i); final_peaks_time(final_peaks_counter)=peaks_time(i); end end end

% Plot time history showing all peaks, all peaks meeting thresholds, and

filtered time history figure(4) %plot(time,filtered_data,'k-

',peaks_time,peaks,'gx',final_peaks_time,final_peaks,'ro') plot(final_peaks_time,final_peaks,'r-o') xlabel('Time (s)') ylabel('Force (N)') title('Peak extraction') if filter_type==0

186

legend('Unfiltered data','All peaks','Peaks meeting thresholds') else legend('Filtered data','All peaks','Peaks meeting thresholds') end axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Identified Peaks.jpg' ])

%% Sort peaks and do statistics sorted_peaks=sort(final_peaks,'descend'); A100=sum(sorted_peaks(1:floor(final_peaks_counter/100)))/floor(final_peaks_co

unter/100); A10=sum(sorted_peaks(1:floor(final_peaks_counter/10)))/floor(final_peaks_coun

ter/10); A3=sum(sorted_peaks(1:floor(final_peaks_counter/3)))/floor(final_peaks_counte

r/3); figure(5) plot(sorted_peaks,'ro') xlabel('Peak Number'); ylabel('Peak Force (N)'); peaksstr = sprintf('%.f sorted peaks',final_peaks_counter); title(peaksstr); axis tight saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Sorted Peaks.jpg' ])

sss = round(final_peaks_counter/10); ttt = sorted_peaks(1:sss); ttt = ttt';

NFFT = 2^nextpow2(final_peaks_counter); % Next power of 2 from length of

rawdata Y = fft(peaks,NFFT)/final_peaks_counter; f = 0.01*linspace(0,1,NFFT/2+1);

% Plot single-sided amplitude spectrum. figure(6) plot(f,2*abs(Y(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of y(t)') xlabel('Frequency (Hz)') ylabel('|Y(f)|') saveas(gcf,[ 'Results\Figs\SubseaPeaksEXP\' genvarname([ 'Exp'

ExperMatlab(3:6)]) '_Single Side Amplitude Spectrum_Final.jpg' ])

% axis([0 50 0 1])

%% Store this information to an output file % outputfilename='fefe.txt'; % fid = fopen(outputfilename, 'w'); % fprintf(fid,'This file yields output of the Combatant Craft Division Small

Craft Procedure: Standard g\n');

187

% fprintf(fid,'Standard g was developed by Mike Riley, Tim Coats, Kelly

Haupt, and Don Jacobson\n'); % fprintf(fid,'This script, and heading/speed/wave dependent time

thresholding, written by Leigh McCue\n'); % fprintf(fid,'\n'); % fprintf(fid,'Input file: %s\n',inputfilename); % fprintf(fid,filterstr); % fprintf(fid,'\n'); % fprintf(fid,'Vertical threshold at RMS= %.4f\n',RMS_filtered); % fprintf(fid,'Horizontal threshold at %.3f s\n',time_threshold); % fprintf(fid,'Record length= %.2f s\n',T); % fprintf(fid,'\n'); % fprintf(fid,'npeaks= %g\n',final_peaks_counter); % fprintf(fid,'A_1/100= %.3f g\n',A100); % fprintf(fid,'A_1/10= %.3f g\n',A10); % fprintf(fid,'A_1/3= %.3f g\n',A3); % fprintf(fid,'Average= %.3f g\n',mean(final_peaks)); % fprintf(fid,'Max= %.3f g\n',max(final_peaks)); % fprintf(fid,'\n'); % fprintf(fid,'Sorted Peak Values (g)\n'); % for i=1:final_peaks_counter % fprintf(fid,'%.3f\n',sorted_peaks(i)); % end % fprintf(fid,'\n'); % fprintf(fid,'Chronological Peak Values\n'); % fprintf(fid,'Time Accel \n'); % fprintf(fid,'(sec) (g) \n'); % for i=1:final_peaks_counter % fprintf(fid,'%.3f %.3f \n',[final_peaks_time(i),final_peaks(i)]); % end % fclose(fid);

Results(n1,1) = ID1; %Wave Ht % Results(n1,2) = ID2; %Wave Period Results(n1,3) = RMS_filtered; %Vertical Threshold Results(n1,4) = time_threshold; %Horizontal Threshold Results(n1,5) = max(final_peaks); Results(n1,6) = mean(final_peaks); Results(n1,7) = A100; Results(n1,8) = A10; Results(n1,9) = A3; Results(n1,10) = final_peaks_counter; %Number of Peaks Results(n1,11) = Fc; Results(n1,12) = max(final_peaks) + abs(Fc);

n1 = n1 + 1; m = m + 1; close all

end

188

Algorithm 2 inspired by work done on Peak Identification by Mikael RazolaXXX

clear all close all clc

% load ID0022.mat

% filename = 'runlist.xlsx'; % Q = xlsread(filename); % INSERT RUNLIST FILE HERE % A=data.time; % dt = A(5)-A(4); %Upper % m = 24; % gg = max(find(abs(A-Q(m,4))<=dt)) %Lower % pp = max(find(abs(A-Q(m,3))<=dt))

% zz = 0.05; %percentage of data that is to be discarded at start % zz1 = 0.05; %percentage of data that is to be discarded at end % size = size(data.time); % t1 = pp; % t2 = gg; % t = data.time(t1:t2); % XX = data.F_wire_filt(:,1); % X = XX(t1:t2);

load dataset_2_KTH.mat X = a; X1 = a;

figure(1) plot(t,X,'r') title('Raw Data for Heave Acceleration') xlabel('time (s)') ylabel('Heave Acceleration (m/s^2)') % hold on options = [1.25,0.25,1.25,0.25]; mphDiff = options(1); mpdDiff = options(2); mphAcc = options(3); mpdAcc = options(4); Wn = 5;

dt = t(2)-t(1); % Time step fs = 1/dt; % Sampling frequency

if fs~=Wn [b,a] = butter(9,Wn/((fs/2)+0.1),'low'); Xn = filter(b,a,X); Xn = wrev(filter(b,a,wrev(Xn))); % Remove phase shifts from filtering X = Xn; end

figure(2)

189

plot(t,X1,'r') title('Filtered Data after 9th Order Butterworth Filter') xlabel('time (s)') ylabel('Heave Acceleration (m/s^2)') hold on plot(t,X,'g')

Xdiff = diff(X)./diff(t);

XdiffMod = Xdiff; %XdiffMod(XdiffMod<0) = 0; XdiffMod(XdiffMod==inf) = 0;

ttt = t(1:length(XdiffMod)); figure(3) plot(ttt,XdiffMod,'r') title('Differentials of Heave Acceleration') xlabel('time (s)') ylabel('Heave Acceleration Differential (m/s^3)')

mphDiff = std(XdiffMod)*mphDiff; [~,locs] = findpeaks(XdiffMod,'minpeakheight',mphDiff);

mpdDiff = round(mean(diff(locs))*mpdDiff); acclocs = zeros(1,length(locs));

for i = 1:length(locs) w = min([mpdDiff length(X)-locs(i)]); % Check so that not

searching beyond end of array [~, index] = max(X(locs(i):(locs(i) + w))); % Find max within window acclocs(i) = index + locs(i) - 1; % Find corresponding

index end

mphAcc = std(X)*mphAcc; acclocs = acclocs(X(acclocs)>mphAcc); acclocs = unique(acclocs); peaks1 = X(acclocs); % % figure(4) % plot(acclocs,peaks1,'g-x')

hold on i = 1; mpdAcc = mean(diff(acclocs))*mpdAcc; sW = round([0:mpdAcc]); count = 0; locs = []; while i<=length(acclocs) if i~=length(acclocs) count = count + 1; dAcc = sW + acclocs(i); dAcci = ismember(acclocs,dAcc);

190

nP = sum(dAcci); [~,index3] = max(peaks1(dAcci==1)); index4 = acclocs(dAcci==1); index3 = index4(index3); locs(count) = index3; i = i + nP; else break end end

peaks = X(locs);

figure(4) plot (locs,peaks, 'r-o') title('Final Acceleration Time Series') xlabel('time (s)') ylabel('Heave Acceleration (m/s^2)') % rrr = length(locs); sorted_peaks=sort(peaks,'descend'); figure(5) plot(sorted_peaks,'ro') xlabel('Peak Number'); ylabel('Heave acceleration (m/s^2)'); peaksstr = sprintf('%.f sorted peaks for Heave Acceleration',rrr); title(peaksstr); axis tight

A100=sum(sorted_peaks(1:floor(rrr/100)))/floor(rrr/100) A10=sum(sorted_peaks(1:floor(rrr/10)))/floor(rrr/10) A3=sum(sorted_peaks(1:floor(rrr/3)))/floor(rrr/3)

sss = round(rrr/10); ttt = sorted_peaks(1:sss)

NFFT = 2^nextpow2(rrr); % Next power of 2 from length of rawdata Y = fft(peaks,NFFT)/rrr; f = 100/2*linspace(0,1,NFFT/2+1);

%Plot single-sided amplitude spectrum. figure(6) plot(f,2*abs(Y(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of y(t)') xlabel('Frequency (Hz)') ylabel('|Y(f)|') axis([0 50 0 5])

191

Appendix 11

Equivalent Load Estimation for Fatigue MatlabTM Code % function [Leq, MaxLoad, LifeTimeDamage,DamageHere, TLife, T2] =

ExRainflow(data,gg,pp,ExperMatlab)

%INITIALIZATION clear all close all clc

directory = 'E:\corpower\1'; % IDENTIFY FOLDER

FilesNames=dir(directory); NumFiles=length(FilesNames)-2; disp('Number of Files: '); disp(NumFiles); % IDENTIFY NUMBER OF FILES

n1 = 1; %COUNTER FOR PEAK STORAGE MATRIX n2 = 1; m = 24 +(n2-1)*2; %START VALUE OF ROW NUMBER IN RUNLIST

%Start automation for i = n2:0.5:NumFiles % LOOP FOR PICKING ONE FILE AT A TIME)

ExperMatlab = FilesNames(1+2*i).name % FILE SEQUENCE SELECTOR load([directory '\' ExperMatlab]); input = data;

% Lower Limit of useful data pp = max(find(abs(data.time)==30)); % Upper Limit of useful data gg = max((find(abs(data.time)==data.time(end))));

% Extraction of wave parameters from filename ID = ExperMatlab(13:15); ID1 = str2num(ID);

ID = ExperMatlab(17:18); ID2 = round(str2num(ID));

% Requires WAFO toolbox: http://code.google.com/p/wafo/ initwafo;

scale = 16;

force0 = data.F_wire(:,1); Fs = 1/(data.time(3)-data.time(2));

I=pp:gg;

force = (-1*force0(I));

192

t = data.time(I);

%% -------------------------------------- % Turning Points & Rainflow filter

tp0 = dat2tp([t force]); % No RFC-filter figure(1) plot(t,force) title('Subsea Force on Tether Time Series') xlabel('time(s)') ylabel('Subsea Force (N)') xlim([0 2100]) % % hold on figure(2) plot(tp0(:,1),tp0(:,2),'r-*'), xlabel('Time (s)') ylabel('Force (N)') title('Turning Points') axis tight % % hold off % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_TurningPoints.jpg' ])

% % LOL = (max(force) - min(force))/2; for jj = 1:0.1:6 LOL = (max(force)-min(force))/jj tp = rfcfilter(tp0,LOL); % RFC-filter figure(3) plot(tp(:,1),tp(:,2),'g-*') xlabel('Time (s)') ylabel('Force (N)') title('Turning Points after filtration of adjacent peaks') axis tight % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_TurningPoints_Filtered.jpg' ])

% whos; % How much reduction in cycles?

%% How much loss in damage?

beta = 4.8; % Damage exponent (constant for a material except stress

concentrations)

dam0 = cc2dam(tp2rfc(tp0,'CS'),beta); dam = cc2dam(tp2rfc(tp,'CS'),beta); % [dam dam0]; % Damage CCC = dam/dam0 % Relative damage [length(tp0)];% Length of original turning points [length(tp)]; % Lenth of rainflow filtered turning points PPP = [length(tp0)/length(tp)] % Relative length

193

%% -------------------------------------- % Calculate rainflow cycles

rfc = tp2rfc(tp0,'cs'); figure(4) ccplot(rfc); xlabel('Cycle Crests') ylabel('Cycle Troughs') title('Rainflow Cycle Distribution') axis tight % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_RainflowCycles.jpg' ])

% Load spectrum (Rainflow amplitudes) amp = cc2amp(rfc);

ls=[sort(amp) ones(length(amp),1)]; figure(5) lsplot(ls) title('Rain Flow Cycle Amplitude vs Frequency of Occurance') axis tight % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_LoadSpectrum.jpg' ])

% Level crossings lc = cc2lc(rfc); figure(6) lcplot(lc) title('Rain Flow Cycles and Number of Upcrossings') % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_LevelCrossings.jpg' ])

figure(7), semilogx(lc(:,2),lc(:,1)) title('Rain Flow Cycles and Number of Upcrossings in Log scale') xlabel('Number of Upcrossings in log scale') ylabel('Rain Flow Cycles') % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_LevelCrossingsSemiLog.jpg' ])

%% -------------------------------------- % Calculate rainflow matrix

n = 50; % Number of discrete levels param = [-10000000 10000000 n]; % Define discretization u = levels(param); % Discrete levels

RFM = cc2cmat(param,rfc,0);

194

figure(8) cmatplot(u,u,RFM,3) xlabel('Rainflow Cycle Trough Value') ylabel('Rainflow Cycle Crest Value') title('Contour of Rainflow Cycle Occurance') axis tight

figure(9) cmatplot(u,u,RFM,4) xlabel('Rainflow Cycle Trough Value') ylabel('Rainflow Cycle Crest Value') title('Contour of Rainflow Cycle Occurance') axis tight % saveas(gcf,[ 'Results\Figs\Fatigue\' genvarname([ 'Exp'

ExperMatlab(13:18)]) '_RainFlowMatrix.jpg' ])

%% -------------------------------------- % Calculate Equivalent Load

% Input data & parameters beta = 4.8; % damage exponent beta=5 T = t(end)/3600; % Mesured time in hrs Tlife = 20*8765.81; % Target life 20 years N0 = 1e6; % Number of Target equivalent cycles

% Measured pseudo damage d = cc2dam(rfc,beta);

%% -------------------------------------- % Equivalent load amplitude %% INCLUDE SCALING FACTOR FOR TIME % Extrapolation factor T2 = T; d2 = d; K = Tlife/T2;

% Pseudo damage extrapolated to target life LifeTimeDamage = K*d2;

Leq = (K*d2/N0)^(1/beta); MaxLoad = ((max(tp(:,2))-min(tp(:,2)))/2);

G1(n1,5) = Leq; %Equivalent Load G1(n1,6) = MaxLoad; %Max Load or Peak Value in signal G1(n1,7) = LifeTimeDamage; G1(n1,8) = T2; G1(n1,1) = ID1; G1(n1,2) = ID2; G1(n1,3) = d2; %damage G1(n1,4) = Tlife; G1(n1,9) = CCC;

195

G1(n1,10) = PPP;

n1 = n1+1; close all clear dam clear dam0

end

end

196

Appendix 12

Wave Interference and production of Irregular waves

When we take two waves, Wave A and Wave B and mix them, we observe interference

between the waves and what we get is an irregular wave system Wave AB.

Now if we add one more component to this system, Wave C, then we get a new system of

irregular waves, Wave ABC.

This is how irregular waves were simulated in OrcaflexTM for simulating a buoy.

Picture Source: http://www.antrimdesign.com/wave-action---how-and-why-waves-behave-

as-they-do.html

197

www.kth.se

198

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VII [VII]M.F.P. Lopes, J. Hals, R.P.F.Gomes, T. Moan, L.M.C. Gato, and A.F.deO. Falc ao. Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter. 2009.

VIII [VIII]commons.wikimedia.org

IX [IX]Andrew M. Cornett. A global wave energy resource assessment.

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Renewable and Sustainable Energy Reviews 14 (2010), page 899918, 2009.

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