Dissertation in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE WITH A MAJOR IN WIND POWER
PROJECT MANAGEMENT
Uppsala University
Department of Earth Sciences, Campus Gotland
Frauke Wilberts
30 December 2017
Dissertation in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE WITH A MAJOR IN WIND POWER
PROJECT MANAGEMENT
Uppsala University
Department of Earth Sciences, Campus Gotland
Approved by:
Supervisor, Karl J. Nilsson Co-Supervisor, Wout Weijtjens Examiner, Heracles Polatidis
30 December 2017
Abstract
The installed capacity of offshore wind turbines in Europe is increasing with the mono- pile being the most common type of foundation. During its lifetime an offshore wind turbine is exposed to high dynamic loads which eventually can result in the fatigue of the substructure. This thesis will show how the linear damage accumulation approach based on the Miner’s rule can be used to estimate the damage induced on the substruc- ture of an offshore wind turbine using measurements from strain gauges. Furthermore, the most important environmental influences will be illustrated and the different stress concentration factors and the size effect introduced in the industry guideline DNVGL- RP-C203 will be analysed towards their effect on the calculated lifetime.
Acknowledgements
I would first like to thank my thesis supervisor Wout for sharing his knowledge about fatigue analysis, offshore wind turbines and foundations and so much more based on experience and enthusiasm for this field of research. I received invaluable ongoing support and Wout always showed the patience to answer every question, read my drafts and discuss about my work.
Furthermore, I would also like to thank my home university supervisor Kalle for giving valuable input on the progress of my thesis from an outside perspective. His persever- ance kept me on track.
Thanks to everyone in the Acoustics and Vibration Research Group at the Vrije Uni- versiteit Brussel for being open and curious researchers and giving me the chance to work within their field of expertise as a visiting master student.
I also received continuous support from my fellow students of the Wind Power Project Management class in Visby which I highly appreciate.
Special thanks go out to Raphaël, Tim, Simone and Antonio for their friendship and ongoing moral support during the time I spent in Brussels.
Last but not least I would like to thank my parents and especially my mum for always encouraging me in pursuing my university education. This accomplishment would not have been possible without the support of my family.
Table of Contents
Abstract I
Acknowledgements II
List of Tables V
List of Figures VI
List of Acronyms VIII
1 Introduction 1
1.1 Background . . . . 1
1.2 Aim . . . . 1
1.3 Research Questions . . . . 2
1.4 Outline . . . . 2
2 Fatigue Assessment of OWT Foundations – State of the Art 3 2.1 Introduction . . . . 3
2.2 Design of Offshore Monopile Foundations . . . . 3
2.3 Regulations for the Design of Offshore Foundations concerning Fatigue 5 2.4 Fatigue Monitoring and Assessment . . . . 7
2.5 Summary . . . . 14
3 Methodology 15 3.1 Overview . . . . 15
3.2 Measurement and processing from Strains to Stresses . . . . 15
3.3 Calculation of Damage . . . . 20
3.4 Extrapolation in Time . . . . 21
3.5 Case Definitions . . . . 22
3.6 Introduction of Sensitivity Analysis of Correction Factors . . . . 23
3.7 Summary . . . . 24
4 Case Study Results & Discussion 25 4.1 Sensitivity Analysis of Stress Correction Factors . . . . 25
4.2 Available Data for the Fatigue Analysis . . . . 28
4.3 Analysis of Environmental Influences on the Damage . . . . 29
4.4 Analysis of Damage Results . . . . 39
5 Conclusion 44
Literature 46
List of Tables
Table 2.1: Design Fatigue Factor & Material Safety Factor . . . . 10
Table 3.1: Case Definitions for V112 . . . . 23
Table 3.2: Properties used for the Sensitivity Analysis . . . . 23
Table 4.1: Measurement Data used for the Fatigue Assessment . . . . 29
Table 4.2: Properties used for the Fatigue Assessment . . . . 29
List of Figures
Figure 2.1: Offshore Wind Turbine with Monopile Foundation . . . . 4
Figure 2.2: Loads and Bending Moment on Offshore Wind Turbine with Monop- ile Foundation . . . . 5
Figure 2.3: S-N Curve for Steel in an Air Environment Type B1, C1 & D . . . . . 9
Figure 2.4: Geometric sources of local stress concentrations . . . . 11
Figure 2.5: Parameters for the Calculation of the Stress Concentration Factor for Thickness Transitions . . . . 12
Figure 2.6: Parameters for the Calculation of the Stress Concentration Factor for Conical Transitions . . . . 12
Figure 2.7: Rainflow Counting Method . . . . 13
Figure 2.8: Damage Accumulation Process and resulting Damage Contributions 13 Figure 3.1: Flowchart from Measurement Data to remaining useful Lifetime (RUL) 15 Figure 3.2: Overview of Belgian OWFs and Wind Turbine Positions . . . . 16
Figure 3.3: Convergence of Damage depending on Number of Bins used for RFC 18 Figure 3.4: Results for the RFC for different Ranges of Bins . . . . 19
Figure 3.5: Fatigue Spectra induced by Mtland Mtnand Sensor Locations . . . . 21
Figure 4.1: Stress Concentration Factors for Concentricity, Center Eccentricity and Out of Roundness . . . . 25
Figure 4.2: Stress Concentration Factor for Thickness Transitions . . . . 26
Figure 4.3: Stress Concentration Factor for Conical Transitions . . . . 27
Figure 4.4: Size Effect for different S-N Curves in Sea Environment based on RP-C203(2016) . . . . 28
Figure 4.5: Fatigue Spectra induced by Mtland Mtn, corrected & extrapolated . 30 Figure 4.6: Relation of Wind Speed to Wave Height . . . . 31
Figure 4.7: Thrust Loads of the Vestas V112 3.0 MW . . . . 32
Figure 4.8: Relation of Bending Moments to Wind Speed . . . . 32
Figure 4.9: Influence of Wind Speed on Damage Equivalent Load . . . . 33
Figure 4.10: Influence of Wind Speed and Wave Height on the DEL . . . . 34
Figure 4.11: Influence of Wind and Wave Misalignment on the DEL . . . . 35
Figure 4.12: Influence of Wind Direction and Wind Speed on the DEL for Mtn . . 36
Figure 4.13: Influence of Wind Direction and Wind Speed on the DEL for Mtl . . 37
Figure 4.14: Turbulence Intensity in relation to Wind Speed and Wind Direction . 38 Figure 4.15: Influence of Turbulence Intensity and Wind Speed on the DEL . . . 39
Figure 4.16: Design Wind Speed and Wind Direction Probabilities . . . . 40
Figure 4.17: Extrapolated Damages for 20 Years for all Cases . . . . 41
Figure 4.18: Extrapolated Damages for 20 Years for operational Cases . . . . 42
Figure 4.19: Extrapolated Damages for 20 Years for idle Cases . . . . 43
List of Acronyms
DEL damage equivalent load
DFF design fatigue factor
DNVGL Det Norske Veritas Germanischer Lloyd MSF material safety factor
OWF offshore wind farm
OWT offshore wind turbine
RFC rainflow counting
RUL remaining useful lifetime
SCADA supervisory control and data acquisition SCF stress concentration factor
SE size effect
SHM structural health monitoring
1 Introduction
1.1 Background
The capacity of installed offshore wind farms in Europe has been constantly increasing over the last years. In 2016 there were 48 MW capacity installed which means a growth of 15.4 % compared to 2015 with 41.6 MW. In total, the installed capacity in Europe now amounts for 12.631 MW. Among the existing offshore wind farms (OWFs) the most common type of foundation is the monopile with a share of 80.8 % (Ho and Mbistrova, 2017). During the lifetime of an offshore wind turbine (OWT) the substructure, i.e. the monopile and the transition piece, faces between 107to 108load cycles in 20 to 25 years of operational lifetime (Bhattacharya, 2014). Offshore foundations are designed in a way that they survive without maintenance and inspection as a big part of the substructure is either hard to access or completely inaccessible. Nevertheless, it is desirable to monitor and assess the structural health. This is done in order to be able to plan maintenance works or to decide if a substructure is fit for repowering activities or a lifetime extension.
One approach for the structural health monitoring (SHM) of the substructure is to install strain gauges and thus indirectly measure the loads that act on the OWT. Afterwards, the strain data is evaluated giving the consumed lifetime and a resulting remaining lifetime (Weijtjens et al., 2016).
1.2 Aim
This thesis aims to develop an algorithm in MATLAB that uses measurement data from three strain gauges of one OWT. This data is used to assess the fatigue life at the point of measurement but also enable the extrapolation in location and time to cover the whole substructure of the wind turbine and the whole operational life. Furthermore, the influence of the stress concentration factors (SCFs) and the size effect on the overall lifetime as introduced in the industry guideline DNVGL-RP-C203 (DNV GL, 2016a) will be investigated.
1.3 Research Questions
How can strain measurements be used for a lifetime assessment?
What are the influencing environmental factors on the fatigue loads of the substructure?
What are the most critical events for the fatigue of the substructure?
1.4 Outline
In Chapter 2 the theoretical background and relevant literature in connection to the topic of fatigue assessment for OWTs is introduced. The results of the literature study lead to the methodology (Chapter 3) used for the lifetime assessment based on strain measurements. It starts with describing the measurement setup and continues by introducing the steps to handle the data and what calculations are necessary to obtain the resulting damage to the substructure. Moreover, the sensitivity analysis of the correction factors from the industry guideline DNVGL-RP-C203 will be introduced. In Chapter 4 results of the aforementioned sensitivity analysis are presented folllowed by the results of the fatigue assessment and the overall damaging influence of the different environmental factors, e.g. the wind speed, are discussed. Chapter 5 sums up the results and gives an outlook for future work in this field of research.
2 Fatigue Assessment of OWT Foundations – State of the Art
2.1 Introduction
The state of the art provides a summary of offshore foundation design with regards to fatigue life and identifies the relevant research that has already been conducted con- cerning the fatigue monitoring and assessment of an offshore wind turbine (OWT) in operation.
First of all, the design criteria for fatigue of offshore foundations will be explained to determine the relevance of the fatigue on the whole design process. Moving on from the design process to the actual OWT in operation, an overview of the most common fatigue monitoring systems is provided. Afterwards, there will be an introduction into the linear damage accumulation method, the strengths and limitations. In the last part of this chapter the research contributions are summarised and the research questions of this thesis will be put into context with the current state of the art.
2.2 Design of Offshore Monopile Foundations
In the first place, it is essential to know how the foundation of an OWT is designed and how the fatigue limit is accounted for. The most common type of foundation is the monopile (Ho and Mbistrova, 2017). The tower of the OWT is connected with the monopile by the transition piece (Figure 2.1) (Kallehave et al., 2015). The transition piece and the monopile together are defined as the substructure (Vorpahl et al., 2013).
When designing a substructure it is important to consider its fatigue life. Fatigue is a physical phenomenon where a material cracks after bearing a certain number of load cycles whereas a single load of the same magnitude would not have caused a failure (Schijve, 2003). According to Bhattacharya (2014), fatigue is a driver for the design of offshore substructures. Aiming for lower costs, the challenge is to reduce the material used for the substructure but still ensure a sufficient fatigue life. As the foundation of an OWT accounts for up to 34 % of the overall costs of the turbine, reducing the material costs has a significant impact on the overall costs. Kallehave et al. (2015) state that two of the main design parameters are the wall thickness and the monopile diameter which
Figure 2.1: Offshore Wind Turbine with Monopile Foundation, adapted from Kallehave et al. (2015) and Ziegler, Schafhirt et al. (2016)
are predominantly influenced by the fatigue life calculations. They further claim that for the British OWF Walney an extension of up to 40 % in lifetime might be possible due to the unused optimisation potential.
The loads the structure has to bear during operation determine the fatigue life of an OWT. They can be classified as static and dynamic loads. The static loads derive from the weight of the parts and can easily be determined in the design process. On the other hand there are four different types of dynamic loads which have an impact on the fatigue life (Figure 2.2). The first load is caused by turbulent flow through the rotor which results in a lateral movement. Secondly, the substructure gets hit by the waves at sea level. The third and fourth type of dynamic loads are caused by vibrations of the rotor and the tower respectively. In contrast to the static loads, the dynamic loads cannot be expressed in a single number but have to be modelled in probability functions. There are different simulation models and statistical data for the site involved to calculate the expected loads on the substructure (Bhattacharya, 2014). Moreover, the complexity of the simulations grows when different operational situations are considered. One significant difference is whether the OWT is turning or idling. Kallehave et al. (2015) predict that in future design processes it will become more important to estimate the amount of idle hours of an OWT as these severely contribute to fatigue damage. The reason is that during operation the turning rotor provides aerodynamic damping in fore-aft direction which damps the share of wave loads not aligned with the wind direction. During standstill the wave loads are not damped in any direction (Gengenbach et al., 2015).
Figure 2.2: (a) Loads and resulting Bending Moment on OWT with Monopile Foundation, adapted from Ziegler, Smolka et al. (2017) and Bhattacharya (2014), (b) resulting Bending Moments Mtn(Normal Tower Moment) and Mtl (Lateral Tower Moment), adapted from IEC (2015)
2.3 Regulations for the Design of Offshore Foundations concerning Fatigue
Based on common practice and experiences from offshore applications of the oil and gas industry there is one recommended practice which mainly determines how an OWT foundation is designed concerning fatigue. It is called ’Fatigue design of offshore steel structures’ and is issued by the classification society Det Norske Veritas Germanischer Lloyd (DNVGL). The latest edition got published in April 2016 (DNV GL, 2016a).
Following this industry standard for design, after assessing all loads that act on the OWT, the lifetime can be calculated by using a so-called S-N curve. This is a material specific curve which shows below which number of cyclic loads (N) and a corresponding stress (S) the material will with a probability of 97.7 % not fail. These curves were determined empirically. S-N curves are established using constant amplitude loading. In real-world conditions the amplitude of the load will vary and different load cycle sizes will need to be combined. Therefore, the simulated cyclic loads with varying amplitudes have to be aggregated in two numbers, one for the stress and one for the number of load cycles respectively. This is done by using the linear damage accumulation rule published by Pålmgren in 1923 and later adopted by Miner which nowadays is commonly known as
Miner’s rule. The Miner’s rule (Equation 2.1) is a mathematical simplification to predict the fatigue life (Schijve, 2003).
D=
∑k i=1
ni Ni =
¯a11
∑k i=1
ni· (∆σi)m1≤η : N≤107
1
¯a2
∑k i=1
ni· (∆σi)m2≤η : N>107
(2.1)
with D as accumulated fatigue damage, ¯a as intercept of the design S-N curve with the log N axis, m as negative inverse slope of the S-N curve, k as the number of stress blocks, nias the number of stress cycles in stress block i, Ni as number of cycles to failure at constant stress range∆σi and the usage factor η. The usage factor is most of the times set to η=1 which means that the fatigue life is reached once the damage D=1 (DNV GL, 2016a).
There have been several attempts to develop a more accurate model based on new know- ledge about crack propagation but so far no other model has been widely accepted as an alternative. Fatemi and Yang (1998) give an extensive review of various life prediction methods but also summarise that although the Miner’s rule has a lot of shortcomings it is still the state of the art of fatigue assessment. Schijve (2003) remarks that to account for the uncertainty caused by the simplification of fatigue life prediction with the linear damage accumulation in the design requirements different safety factors are introduced (e.g. the material safety factor (MSF) in DNVGL-RP-C203 (DNV GL, 2016a)). These factors however probably lead to overly conservative assumptions in the design process thus limiting the possibilities for an optimisation concerning the material as discussed earlier (Brennan and Tavares, 2014).
Adedipe et al. (2016) mention three major gaps the classical S-N curve approach does not cover. First of all the steel used today has more advanced properties due to improved fabrication processes than the material used in the tests on which the S-N curves are based. Secondly, the S-N curve method does not allow to consider sequence effects.
There is evidence that the load history has an influence on if and how fast a crack grows.
Therefore, the order of the different load cycles should be taken care of which cannot be done with the linear damage accumulation. The last gap identified by Adedipe et al.
(2016) is that cracks have the ability to heal if they are subject to negative loads. This can also not be considered in the S-N curves. Moreover, the standards which are used for the fatigue design of offshore structures like an OWT are based on the experiences made in the oil & gas platform industry. They might be inappropriate because for an oil or gas platform the load is characterised by a big the vertical static contribution, in contrast to an OWT which is prone to strong horizontal loads from wind and waves (Brennan and Tavares, 2014). Nevertheless, the Miner’s rule is still used as a state of the art method for fatigue assessment although the weaknesses are known Schijve (2003).
Concerning design the calculation of the fatigue life of an OWT is a key factor and is widely accounted for. It is however not guaranteed that the conditions during the operation match the simulations from the design process. Therefore, a structural health monitoring system can ensure the substructure stays within the permissible limits for the loads. Moreover, it provides measurement data which can be used to validate simu- lation models and improve future designs and also to assess the current state of fatigue.
The following section will give an overview of the most common fatigue monitoring strategies and fatigue assessment methods.
2.4 Fatigue Monitoring and Assessment
There are some challenges involved in the offshore foundation monitoring as the sensors might be difficult to access once the OWT is installed. A premature failure has to be prevented as the replacement might not be feasible later on or take a lot of time during which the measurements cannot be continued (Wymore et al., 2015).
Söker (1996) introduced a methodology with the measurement of strains and the rainflow counting (RFC) method for the fatigue assessment of an onshore wind turbine already more than 20 years ago. The main goal of the measurements was to improve the design to make it more economic. The measurement setup consisted of four strain gauges.
The concept had been proven by a measurement campaign of nine months in a wind farm with wind turbines of about 500 kW nominal power. Due to constraints in the available computational possibilities to store large amounts of data, the strain measure- ments were immediately processed with a rainflow counting (RFC) algorithm which categorises the data in bins (see also Chapter 2.4.4). Afterwards, it was however im- possible to link the time-domain data like wind speed measurements with the strain data.
Weijtjens et al. (2016) also use the measurement data of strain gauges to determine fatigue loads and extrapolate them from two equipped OWTs in the Belgian Northwind wind farm to the remaining 70 wind turbines. The idea is called the fleet leader concept and uses a simplified model based on site specific parameters, e.g. the water depth and soil properties, to calculate the remaining useful lifetime (RUL) of the non-equipped OWTs in the wind farm. Although it would be more reliable, it is not economically feasible to equip all of the OWTs. The strain data is stored as the results of a RFC method but in much smaller intervalls (10 min average) than it was possible for Söker (1996). Keeping the results of the RFC algorithm in intervals of 10 minutes allows for a comparison with other data like the wind speed or the wind direction which is collected by the supervisory control and data acquisition (SCADA).
In contrast to measuring the strain of an OWT, Ziegler, Schafhirt et al. (2016) follow an approach to reassess the lifetime by updating the original design model. The adjusted model is based on environmental, structural and operational parameters and the dif- ference between those used in design and measured during operation. The analysis is however solely based on simulation data and estimated variabilities of the environ- mental, structural and operational conditions. There is no case study or measurement data which serves as a basis for the fatigue assessment.
There are approaches for fatigue assessment of OWTs in operation which use simulated loads for the fatigue assessment. On the other hand, the mentioned measurement methods with strain gauges show that it is possible to measure strains in wind turbine substructures and that simulations are not needed in case there are measurements available. The next step is the analysis of the data, as the simulations of the load or the measurements on their own do not allow for a fatigue assessment. The following part will introduce the linear damage accumulation model and how it is used for the fatigue assessment.
2.4.1 S-N Curves
S-N curves are the basis of the linear damage accumulation method. They are a function of the number of stress cycles N and the corresponding stress σ. Their result is the fatigue life which is the number of cycles which a material for a given stress value can survive under a dynamic load (Equation 2.2) (DNV GL, 2016a). In welded structures the welds are the weak spot of the structure as the heat during the welding process changes the microstructure and the mechanical properties of the material. Therefore, welds are locations where a fatigue crack is likely to begin (Adedipe et al., 2016).
log N=
( log a1−m1log∆σ : N≤107
log a2−m2log∆σ : N>107 (2.2) with N fatigue life, log a intercept of log N axis, m negative slope of S-N curve on log N−log S plot and∆σ stress range in MPa as given in DNVGL-RP-C203 (DNV GL, 2016a).
For offshore applications there are three different categories of S-N curves for welded joints depending on the environment the steel is placed in: air, water or free corrosion.
The S-N curves for the air environment have the highest fatigue life, the water environ- ment (splash zone) has lower fatigue lives and the free corrosion environment (under the water level) is predicted to have the shortest fatigue life because of the corrosive environment which fosters fatigue damage. In total there are 14 different S-N curves per environment and curve B1 represents the maximum stress range. For the fatigue
assessment the appropriate S-N curve has to be picked. It depends on the structural detail which is going to be analysed. Monopile and transition piece sections are classified as hollow sections according to Appendix A.9 in DNVGL RP-C203 DNV GL (2016a). The joint type is typically a circumferential two-sided butt weld. From this information the type of S-N curve can be determined. The two S-N curves applying to hollow sections are type C1 and D (Figure 2.3). The difference between the two is that for type C1 to be applicable the weld has to be machined or ground flush during the fabrication. It is allowed to use the more advantageous S-N curve in this case as the treatment after the welding improves the fatigue life (DNV GL, 2016a).
Figure 2.3: S-N Curve for Steel in an Air Environment Type B1, C1 and D, adapted from DNV GL (2016a)
2.4.2 Safety Factors
There are two safety factors which are applied in the design of an OWT. The first one is the material safety factor (MSF) which depends on the design fatigue factor (DFF) (Table 2.1). The DFF is selected according to the location of the structural detail (atmospheric, splash, submerged, scour or below scour zone) which is analysed and to what extend
regular inspections can and are planned to be carried out (DNV GL, 2016b).
Table 2.1: Design Fatigue Factor and corresponding Material Safety Factor (DNV GL, 2016b)
DFF MSF Zone
1 1.0 with inspections (check for cracks every 13 years):
atmospheric, splash and submerged zone
2 1.15 with inspections (check for cracks every 7 years):
atmospheric, splash and submerged zone
3 1.25 no inspections: atmospheric, splash and submerged zone;
always: scour, below scour zone
The second safety factor is the size effect SE. It accounts for differences in the geometry of the test specimen of the S-N curves and the actual geometry. The size effect depends on the wall thickness tw, as a thick section is more likely to fail than a very thin section used in the S-N curves. A thickness exponent k which depends on the fatigue strength is given for every S-N curve within a range of 0 to 0.25 (Equation 2.3). The reference thickness of tre f =25 mm is applicable for all welded connections (DNV GL, 2016a).
SE= tw tre f
k
(2.3)
2.4.3 Stress Concentration Factor
The S-N curves are based on tests of specimen with a uniform stress distribution. When using the S-N curve for a structural detail which does not have a uniform stress dis- tribution but evoke a local stress concentration, changed local stresses are accounted for by the multiplication of the normal stress with the SCF. Such structural details which can occur as part of the substructure of an OWT are thickness transitions, center eccentricities, concentricity, out of roundness (ovality) and conical transitions from one section to the other (Figure 2.4).
Figure 2.4: Geometric sources of local stress concentrations (DNV GL, 2016a)
The general equation for the SCF Equation 2.4 can be used for all sources of local stress concentration at the same time (except for the conical transition). The thickness transition is selected as the most common case for the substructure among the different sources.
For the thickness transition the equation can be simplified as shown in Equation 2.7. The geometric parameters (δt, δm, δ0, T, t, L and D) can be determined using Figures 2.4b) and 2.5.
SCF=1+6(δt+δm+δ0)
t · 1
1+ Ttβ
·e−α (2.4)
with α= 1.82 L√
Dt · 1 1+ Ttβ
(2.5)
and β=1.5− 1
log Dt + 3
log Dt2 (2.6)
for thickness transition: SCF=1+6 δt
t · 1
1+ Ttβ
·e−α (2.7)
Figure 2.5: Parameters for the Calculation of the Stress Concentration Factor for Thickness Transitions (DNV GL, 2016a)
For the conical transition (Figure 2.6, which also is a common structural detail in OWT substructures, there is a different approach of calculation used (Equation 2.8, simplified assuming the wall thickness stays constant). The parameters are the diameter of the cylindrical part at the junction Dj, the wall thickness t and the slope angle α.
Figure 2.6: Parameters for the Calculation of the Stress Concentration Factor for Conical Transitions (DNV GL, 2016a)
SCF=1+ 0.6 tp Dj·2t
t2 tan α (2.8)
2.4.4 Rainflow Counting
The first steps of picking the applicable S-N curve and correct it by the safety factors and a stress concentration factor of the weld detail have been explained. In order to be able to use the S-N curve for the fatigue assessment the two unknowns which are the number of cycles N and the corresponding stress range σ have to be determined. This is done using a method called rainflow counting. The name derives from the basic idea of counting rain drops which fall from rooftop to rooftop (Figure 2.7 (b)). Rychlik (1987) adopted the method which was developed by M. Matsuishi and T. Endo in 1968. His work is the basis of the later used MATLAB toolbox WAFO (Chapter 3.2.1) (A. Brodtkorb et al., 2011). The idea of the RFC is to use the strain signal (Figure 2.7 (a)) which shows a dynamic load with varying amplitudes over time and convert it into countable stress cycles. This is illustrated by turning the graph of the signal by 90° and then pretending to let rain flow down from the start of the signal to the end (Figure 2.7 (b)). There are fixed rules as to when a raindrop is stopping or how far it is falling. The horizontal arrows mark the amplitude of the strain and by counting how many times a certain
strain amplitude is occurring a histogram of number of times per strain amplitude is calculated. Thus the result of a RFC algorithm is a bin count, in this case number of cycles per strain range.
Figure 2.7: Rainflow Counting Method (a) for a Strain Signal and (b) illustrated as a Rainflow over Rooftops, adapted from Rychlik (1987)
2.4.5 Miner’s rule
The core idea of the linear damage accumulation lies within the Miner’s rule (Equation 2.1): it is assumed that all damage contributions of single stress cycles which occur a given number of times can be summed up to one damage value.
Figure 2.8: (a) Damage Accumulation Process (adapted from DNV GL (2016a)) and (b) resulting Damage Contributions
In Figure 2.8 (a) the damage accumulation process is demonstrated. It shows on the left-hand side the fatigue spectrum resulting from the RFC and the applicable S-N curve.
The two graphs can be used to determine the values for ni and Nifor every stress bin σi. From the curve of the fatigue spectrum, the number of cycles to failure Nican be read by
the contributions of each stress bin to the overall damage. With the vertical line at d=1, the fatigue limit is shown. Comparing the two graphs (Figure 2.8 (a) and (b)), it can be seen that a low number of very high stress cycles causes a higher damage than a high number of low stress cycles.
2.4.6 Damage Equivalent Load
The damage equivalent load (DEL) is a measure which enables the comparison of different fatigue load spectrums. The slope of the S-N curve m and the number of cycles Neq are getting fixed. From the damage calculated it can then be determined which constant amplitude would have generated the same amount of damage based on the fixed parameters, k as the number of stress blocks and Nias number of cycles to failure at constant stress range (Hendriks and Bulder, 1995).
DEL=
∑k i=1
(Niσ)m Neq
!m1
(2.9)
2.5 Summary
From this state of the art overview it can be seen that the fatigue is a design driver for OWT substructures. Although the classical S-N curve approach with a linear damage accumulation has shortcomings which are based on the one hand on the old data used for the curves and on the other hand on the method of summing up damages which does not allow for accounting sequence effects and crack retardation there is not an adequate substitute which can be applied this universally. Therefore, the linear damage accumulation model will also be used during the following analyses.
In contrast to the majority of fatigue analyses which are based on simulation models and determining the design fatigue life, the method used in this thesis is focussing on measurement data. Another focus in addition to the fatigue assessment itself is a look at different operational cases and how they influence the lifetime of an OWT rather than collecting data isolated from the load scenario. There is evidence that an idling OWT experiences higher fatigue loads than being in operation (Vorpahl et al., 2013).
The last addition to the current fatigue assessment method is a separate sensitivity analysis of the geometric properties (wall thickness, diameter and slope angle) of a weld of the monopile and how they influence the correction factors according to the recent guidelines for design (DNVGL RP-C203).
3 Methodology
3.1 Overview
Figure 3.1: Flowchart from Measurement Data to remaining useful Lifetime (RUL) This chapter provides a description of the methodology from the measurement data to the determination of the remaining useful lifetime (RUL) (Figure 3.1) and a sensitivity analysis of the different stress correction factors and how they vary with the different geometrical properties of the substructure. All calculation steps are carried out in a MATLAB script developed for this specific methodology.
3.2 Measurement and processing from Strains to Stresses
All measurement data used is collected from one instrumented Vestas V112 OWT in the Northwind wind farm (Figure 3.2) which is situated 37 km off the Belgian coast (Parkwind NV, 2017). At the moment there are two other operational wind farms and a third one expected to be completed by the end of 2017. For the SHM three optical fibre strain gauges have been welded to the transition piece of the OWT at the edge of the wind farm at a height of 4 m from the lowest astronomical tide (LAT). The three sensors are positioned at 90°, 210° and 330° respectively.
The measurements obtained the from strain gauges are the axial strains εz. They are stored in time series with one value for every ten minutes and every sensor. In order to be able to use the S-N curve later, the strain data εz is converted into stresses σ using Hook’s law with the Young’s modulus E and the Poisson coefficient ν (Equation 3.1) for the stresses in three directions σx, σyand σz. Since the measurement location is above the sea level the stress components for the hydrostatic load σxand σyare 0 and the relation
Figure 3.2: Overview of Belgian OWFs and Wind Turbine Positions of Northwind, adapted from OffshoreWIND.biz (2017) and Renewable Energy Base Oostende (REBO) (2017)
εz= 1
E σz−ν(σx+σy) (3.1)
σx=0, σy=0
⇒σz=E εz (3.2)
So far the stresses are still given in three separate signals for the different sensors which are positioned 120° apart. In order to align them with the coordinate system of the nacelle the first step is to calculate the resulting stresses in North-West direction. To begin with, the geometry of the measurement location is used to calculate the normal force FN and the bending moments Myand Mz. The inner and outer radius (Ri, Ro) of the measurement location are needed to calculate the cross-sectional area A (Equation 3.3) as well as the area moment of inertia Ic(Equation 3.4). The general equation for the normal stress σzin cylindrical coordinates (Equation 3.5) can be rewritten into a more specific form with one equation for every sensor (Equation 3.6) with the position of the sensor given by the angle θ. Solving the equation gives the normal load FNand the two bending moments Myand Mz. The moments Myand Mz are oriented towards North and West. In order to direct the stresses towards North and West the equation for normal stresses in cartesian coordinates is used (Equation 3.7).
A=π(R2o−R2i) (3.3) Ic= π
4(R4o−R4i) (3.4)
σz= FN A + Ri
Ic (Mysin θ−Mzcos θ) (3.5)
σz1 σz2 σz3
=
1 A
Ri
Ic sin θ1 −RIi
c cos θ1
1 A
Ri
Ic sin θ2 −RIi
c cos θ2
1 A
Ri
Ic sin θ3 −RIi
c cos θ3
FN My Mz
(3.6)
σNorth=MyRi
Ic, σWest=MzRi
Ic (3.7)
In the last step the stresses are rotated from the North-West orientation towards a Fore- Aft and Side-Side orientation depending on the yaw angleΨ by multiplying the stress values with the rotation matrix R (Equation 3.8). It puts the values into the nacelle’s frame of reference which always follows the current wind direction (Equation 3.9).
R=
"
cos(−Ψ+180◦) sin(−Ψ+180◦)
−sin(−Ψ+180◦) cos(−Ψ+180◦)
#
(3.8)
σMtl=σNorth·R, σMtn=σWest·R (3.9)
3.2.1 Rainflow counting
In order to obtain the number of cycles per stress level the stresses are counted with the rainflow counting algorithm (Chapter 2.4.4). A MATLAB toolbox called WAFO, provided by the Centre for Mathematical Sciences at Lund University, is used for the rainflow counting (P. Brodtkorb et al., 2000). The research by Rychlik (1987) is the basis for this MATLAB toolbox. The steps are (1) find the turning points of the stress signals, (2) do the rainflow count, (3) transfer the bins ranges to amplitudes and (4) store the results of the RFC as histogram data. In contrast to the default method provided by WAFO, stress cycles that are below the lowest stress bin are included in the lowest bin.
Otherwise they would be excluded from the count.
The number of bins and the range of the bins which are used during the RFC directly influence the result of the damage calculation as they determine which stress level a cycle is assigned to. Recommended is the use of at least 20 bins (DNV GL, 2016a). Figure 3.3 shows the convergence of the calculated damage with a higher amount of bins used for the RFC for a total range of 104 to 108 and 104 to 109. Due to the convergence the number of bins used for the RFC is 500. The example was calculated with measurement
data of one day using the S-N curve D in air environment from DNVGL-RP-C203(2016) (DNV GL, 2016a).
Figure 3.3: Convergence of Damage depending on Number of Bins used for Rainflow Counting with a Bin Range of 104to 108and 104to 109
Figure 3.4 shows the different results of the rainflow count for the two different bin ranges. For a fixed amount of 500 bins, the width of a single bin for the higher bin range (red crosses) is bigger than for the lower bin range (blue circles). Therefore, the results have the same overall shape but they are slightly shifted in the number of cycles per
stress bin.
Figure 3.4: Results for the Rainflow Count for different Ranges of Bins from 104to either 108or 109
3.2.2 Extrapolation of Location
Up to this point the data of the stresses is only available for the measurement location.
In order to analyse different locations of the substructure the stresses have to be extrapol- ated. The necessary geometry and material parameters of the different cross sections can be extracted from the design documents. The relevant parameters are the wall thickness tw, the outer diameter doand the distance from the hub z. At first the bending moment at the measurement position is calculated from the stress bins (Equation 3.10). The wall thickness tw and outer diameter do can also be expressed as the inner radius Ri. The thrust force at hub height FHubis assumed as the main force which causes the bending moment Mband can be calculated following the lever principle with the known distance from the hub to the measurement location (Equation 3.11). Afterwards, the extrapolated bending moment Mb,extcan be calculated using the distance from the hub to the location in question zloc(Equation 3.12). Using the bending theory again (Equation 3.10), the extrapolated stress σextcan directly be calculated from the extrapolated bending moment Mb,ext. A second transformation of Equation 3.13 however leads to an equation for the
ment location and the desired location (Equation 3.14). In a final step these parameters are summarised in a static extrapolation factor SEF which can be used to transfer the stress bins of the measurement location to any other location of the substructure via static extrapolation (Equation 3.15).
Mb=σ Ic
do−2tw =σ Ic
Ri (3.10)
FHub= Mb
z (3.11)
⇒Mb,ext=FHub·zloc= Mb
z ·zloc (3.12)
σext=Mb,extRi,loc
Ic,loc =Mb·zloc z ·Ri,loc
Ic,loc (3.13)
⇒σext=σ· Ic
Ic,loc · Ri,loc Ri ·zloc
z (3.14)
⇒SEF= Ic
Ic,loc · Ri,loc Ri ·zloc
z (3.15)
3.2.3 Calculation of Correction Factors
The stress bins resulting from the RFC are directly based on the measured strains and have so far been adjusted to match the frame of reference of the nacelle and afterwards been extrapolated statically. There are however two other corrections which have to be applied to them. First of all there are two different safety factors according to DNV GL (2016a) and DNV GL (2016b) (Chapter 2.4.2). These are the MSF and the size effect (SE).
Furthermore, there is the SCF which adjusts the stress induced and measured in the clean section to the weld detail by adjusting it to the local expected stress (Chapter 2.4.3).
Depending on the structural detail and the geometry the methods for the calculation differ among the welds of the substructure. For the case study a fictitious weld between two monopile segments with different wall thicknesses will be analysed. There the simplified equation (Equation 2.7) can be used. The corrected stress is calculated by multiplying the stress bins with the MSF, SE and SCF (Equation 3.16).
σcorr=σext·MSF·SE·SCF (3.16)
3.3 Calculation of Damage
After the RFC there are two counts for the stress bins, one induced by the bending moment Mtland one induced by Mtn. They can now be used to determine how high the damaging impact on the substructure at the desired location is. For the sake of
one resulting damage value for the whole detail the counts of the stresses induced by two bending moments need to be summarised in one resulting count. A conservative approach is chosen to cover all cycle counts of both bending moments: for each stress bin the respective maximum value of the count of the two counts is used to form the resulting cycle count. Compared to the statistical method of using the mean value of both counts, the conservative approach covers the whole range of cycle counts over all stress ranges (Figure 3.5).
100 101 102 103 104 105 106 107
Number of cycles
Stress in MPa
Fatigue spectrum TP_WFBG_LAT04_Mtl_CycleCount & TP_WFBG_LAT04_Mtn_CycleCount
Mtl Mtn Sensor 90°
Sensor 210°
Sensor 330°
Mean Max
Figure 3.5: Fatigue Spectra induced by Mtl and Mtnand for the Sensor Locations Afterwards, the accumulated damage is calculated according to Miner’s rule (Equation 2.1) with the resulting stress bin count for N, the stress bin range for σ and the paramet- ers of the applicable S-N curve. The DEL is calculated to be able to compare different damage calculations on the basis of an S-N slope of m=3 and a number of Neq =107 equivalent load cycles according to (Equation 2.9).
3.4 Extrapolation in Time
The result of the earlier steps is the induced damage for the measurement period. It can be set in relation to a combination of a certain wind speed coming from a certain wind direction. For the extrapolation of the damage to the whole operational period the wind conditions used for the design are applied to the calculated damage. That way, the strain measurement data gets long-term corrected because the design wind conditions are based on long-term corrected wind measurements. The two parameters for the wind conditions are the annual average wind speed and the wind direction. The first are given as Weibull distributions per 30◦in wind direction which results in 12 different probability distributions. In addition, there are the probabilities for a wind direction
occurring during a year. Multiplying the calculated damage with the probabilities for a given wind speed from a given wind direction gives the expected damage for those wind conditions. The sum of all individual damages results in the total expected damage for the measurement period. By multiplying the expected damage with a time factor to reach the total operational time the total expected damage over the lifetime of the OWT can be calculated.
Dexp=∑D90(wd, ws) ·Probability(wd, ws) (3.17) In contrast to the design wind conditions in the strain measurement data not every combination of wind speed and wind direction has occurred during the measurements.
This means that there is no damage value for those empty bins although there is a probability that this wind condition might occur at some point during the lifetime of the OWT. To assign damages to the empty bins an estimation has to be made as to how high the damage would be for that wind condition. This is done by taking the maximum value among the damages calculated for the full bins. By multiplying them with the probabilities of the design wind conditions a comparatively high damage for a very unlikely wind condition gets corrected.
Assuming that with a damage of Dexp = 1 the material would fail, the RUL can be calculated (Equation 3.18) using the corresponding time frame texpof the extrapolation.
RUL= texp
Dexp −texp (3.18)
3.5 Case Definitions
As Kallehave et al. (2015) state there’s a difference of damage being induced for an OWT in operation or during stand-still. In order to be able to analyse differences in the damage calculations, the strain measurements get classified according to 10 different cases which are determined by the wind speed ws, the revolutions per minute (rpm), the pitch angle ϕand the power output P (Table 3.1). Cases marked "caseless" cannot be categorised ac- cording to the mentioned parameters. They are connected to either an abnormal turbine behaviour (during curtailment/downrating), or indicate a transition in the behaviour of the turbine (e.g. rotor start and stop). All of the parameters can be extracted from the SCADA system of the wind turbine. Cases that are marked with yellow are summarised
