This document provides a summary of a doctoral thesis focused on uncertainty quantification in structural responses of offshore monopile wind turbines. The thesis contains six main parts: (1) introduction to the context, (2) stochastic vs. deterministic approaches, (3) aspects of the research, (4) results, (5) contributions to existing knowledge, and (6) conclusions and future agenda. Three papers are developed as part of the research, focusing on the influence of uncertainties in wave parameters, wind shear, and simulation length on extreme turbine responses. The research finds wave loading to be an important factor and develops methods to quantify sensitivity to input parameter uncertainties and flexible soil modeling.

1. UNCERTAINTY QUANTIFICATION IN STRUCTURAL RESPONSES OF
OFFSHORE MONOPILE WIND TURBINES
UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA MECÁNICA
ESCUELA CENTRAL DE POSGRADO
THESIS
SUBMITTED FOR THE DEGREE OF DOCTOR OF SCIENCE IN ENERGY
Presented by: David Barreto Lara

2. 2
Part I. Introduction to the Context
Part II. Stochastic vs. Deterministic
Part III. Aspects of the Research
Part IV. Results
Part V. Contributions to the Existent Knowledge
Part VI. Conclusions & Future Agenda
Content

3. Introduction to the Context
Part I
3

4. 4
WHY SHOULD WE PAY ATTENTION TO WIND ENERGY?

5. 5
WHY SHOULD WE PAY ATTENTION TO WIND ENERGY?

6.  Wind resource is abundant and more stable given the low roughness of the
sea.
 More energy per year can be produced , and larger and more powerful
wind turbines can be installed.
6
WHY OFFSHORE?

7. 7
BUT, WHAT IS THE
MAIN LIMITATION?
WHICH ARE THE MAIN
COSTS?

8. 8
FOUNDATIONS/ SUBSTRUCTURES

9. Stochastic vs. Deterministic
Part II
9

10. 10
DETERMINISTIC VS STOCHASTIC
Deterministic
Approach
Deterministic
System Response
Over/under-
designed System
Stochastic
Approach
Statistical
Properties of
System Response
Reliable System
Safety
Factor
Reliability-based
Design

11. 11
PROBABILITY-BASED DESIGN
Pf: Probability of
failure

12. 12
TREATMENT OF UNCERTAINTIES

13. 13
UNCERTAINTY QUANTIFICATION
“The process of quantifying uncertainties associated with model calculations of true,
physical quantities of interest (QOIs), with the goals of accounting for all relevant sources
of uncertainty and quantifying the contributions of specific sources to the overall
uncertainty”.
“…quantification of uncertainties is a critical and necessary aspect to facilitate the
reliability-based design of wind turbines. He based his conclusions on an extensive review
of the literature between the 1990s and 2017 on the subject of structural reliability
analysis of wind turbines”.
DEFINITION
IMPORTANCE
“…Uncertainty quantification become essential to advancing computational capabilities
while introducing innovations in the quest toward lower LCOE”
“…it is expected to improve the predictions of the loads/responses associated with
established return periods by controlling the level of uncertainty in the probabilistic
models.”

14. 14
UNCERTAINTY QUANTIFICATION
“…It is closely related to the achievement of a high-level objective within the offshore wind
industry, the lowering of the Levelized Cost of Energy (LCOE) . This is one of the main
issues that hinder the massive deployment of wind energy projects. The objective of
lowering the LCOE can be achieved by minimizing uncertainties in the design process that
could lead to excessive material consumption or reduced operational lifetime since large
uncertainties imply the use of high safety factors.”

15. Aspects of the Research
Part III
15

16. 16
SCOPE
ENERGY
RENEWABLES
NON-
RENEWABLES
SOLAR WIND WAVE TIDALHYDRO BIOMASS
ONSHORE OFFSHORE
BOTTOM-FIXED FLOATING
DETERMINISTIC
APPROACH
PROBABILISTIC
APPROACH

17. 17
SCOPE
PROBABILISTIC
APPROACH
STRUCTURAL
RELIABILITY
ENERGY
PRODUCTION
MACHINE
RELIABILITY
LOADS AND
RESPONSES
MATERIAL
RESISTANCE
EXTREME FATIGUE
SHORT-TERM LONG-TERM
ECONOMICS
RESOURCE
FORECASTING
ELECTRICAL SYSTEM
RELIABILITY
Uncertainty Quantification

18. 18
PROBLEM STATEMENT
“Sensitivity analysis of the effect of wind
characteristics and turbine properties on
wind turbine loads”
(Robertson et al.)
Wave loading Conditionality of
environmental
parameters
Effect of control
actionsLoad probability
distribution
Soil structure
interaction
Simulation
length
WSC
GAPS
GAPS
GAPS

19. 19
RESEARCH OBJECTIVES
RO: Evaluate the influence of uncertainties in input parameters on the extreme responses
of a monopile OWT.
SO1: Investigate the effects of wave parameters uncertainty on the dynamic responses of a
monopile OWT.
SO2: Study the influence of wind shear uncertainty on the dynamic responses of a
monopile OWT.
SO3: Evaluate the impact of uncertainty in the simulation length on the dynamic response
extrapolation process in a monopile OWT.
SO4: Assess the effect of soil-structure interaction uncertainty on the dynamic responses
of a monopile OWT.
MAIN RESEARCH OBJECTIVE (RO)
SPECIFIC OBJECTIVES (SO)

20. 20
CONSIDERATIONS FOR THE RESEARCH
NREL 5 MW
RESPONSE:
Forces
Moments
Displacements
Etc.
FX or FASF
MY or FABM

21. 21
CONSIDERATIONS FOR THE RESEARCH
TurbSim
FAST

22. 22
MAIN CHALLENGES
1.-AERO-HYDRO-SERVO-ELASTIC SIMULATIONS (COUPLED/INTEGRATED)
AERODYNAMICS
HYDRODYNAMICS
CONTROL ACTIONS
STRUCTURAL
DYNAMICS

23. 23
MAIN CHALLENGES
2.- ENVIRONMENTAL VARIABLES
𝑼 𝒘
𝑯 𝑺 𝑻 𝑷
𝜶

24. 24
MAIN CHALLENGES
3.-SURVIVAL STRATEGY OF WIND TURBINES
Power and thrust curves with respect to controller phases

25. 25
MAIN CHALLENGES
4.-ENVIRONMENTAL CONTOUR METHOD (TRADITIONAL & MODIFIED)
Return period = 50 years
Rosenblatt Transf.

26. 26
MAIN CHALLENGES
5.-EXTREME VALUE ANALYSIS
Maximun=
Max1
Max2
…
Max (n)
(mG,bG)
Gumbel Coefficients
Short-term distribution
Extrapolated Long-term
distribution

27. 27
MAIN CHALLENGES
6.-HIGH PERFORMANCE COMPUTING
7,800 sim. of 10-min (s)
11,700 sim. of 20-min (s)
1,200 sim. of 30-min (s)
2,400 sim. of 1-hour (s)

28. Results
Part IV
28

29. 29
PAPERS DEVELOPED

30. 30
SITUATION OF PAPERS
P1  It is already published and indexed in SCOPUS.
P2  It is already accepted, in process to be indexed (between Nov and Dec 2020).
P3  Planned to be submitted on December 2020.

31. 31
PAPER 1 (P1)
 The main purpose of this work is to investigate the impact in short-term
responses (variance propagation) when an uncertainty is introduced in
the wave parameters.
CONSIDERATIONS FOR THE ANALYSIS
 Seabed (Mudline) is considered the point which better reflects the
combined action of wind and wave.
 Only the results for the fore-aft shear force (Fx) and fore-aft bending
moment (My) at mudline are considered for the sensitivity analysis.

32. 32
SENSITIVITY METHOD: OAT (Once-at-a-time)
𝐻𝑠∗
= 𝐻𝑠 1 + 𝛿%
𝑇𝑝∗
= 𝑇𝑝 1 + 𝜀%
Derived Cases
(Uw, Hs, Tp)
Nominal Points
Baseline Case
(𝛿, 𝜀)
Uncertainties
introduced

33. 33
SENSITIVITY INDEX (S)
Baseline  Hs, Tp
Case 1  Hs*, Tp*
Case 2  …..
…
Case 11  ……
Case 12  Hs*, Tp*
𝑺(𝑪𝒂𝒔𝒆) =
𝝈 𝑿 𝒅𝒆𝒓𝒊𝒗𝒆𝒅
𝝈 𝑿 𝒃𝒂𝒔𝒆
− 𝟏 𝒙𝟏𝟎𝟎%
S: Sensitivity Index
𝝈: Standard deviation
Case: Hs, Tp, HsTp
X: Dynamic Response (e. g. Bending Moment at Mudline)

34. 34
RESULTS
Sensitivity plot of Fx for Uw=11.4 m/s
and sea state 4.
Sensitivity plot of My for Uw=25 m/s
and sea state 9.

35. 35
RESULTS
 Therefore, the sensitivity indexes can be modeled as:
𝐒 𝐇𝐬 = 𝐀 ∗ 𝛅
𝑺 𝑻𝒑 = 𝑩 𝟏 ∗ 𝜺 𝟐
+ 𝑩 𝟐 ∗ 𝜺
𝑺 𝑯𝒔𝑻𝒑 = 𝑪 𝟏 ∗ 𝜹 𝟐
+ 𝑪 𝟐 ∗ 𝜹
A, B1, B2, C1, C2 : Regression coefficients (SCF) to be determined.
𝜹, 𝜺 : uncertainties in the input data.
S(Hs), S(Tp), S(HsTp): Sensitivity indexes.

36. 36
RESULTS
 The coefficient of determination (r2) shows the goodness of the regression.
FX
MY

37. 37
RESULTS
Environmental Contour Line (ECL) : Dashed
Selected Environmental Conditions : Black points
 How about other sea states along the ECL?
 In order to develop a model which could predict any sensitivity coefficient in the
corresponding ECL, it is necessary to use a polynomial regression.

38. 38
RESULTS
 In our case, for the polynomial interpolation, we defined two vectors which reflect the
degree of the polynomial model.
X
Y
Z (A, B1, B2, C1, C2)

39. 39
RESULTS: Fore-Aft Shear Force

40. 40
RESULTS: Fore-Aft Bending Moment

41. 41
PAPER 2 (P2)
 The main purpose of this work is to find a relationship between the
variation of the wind shear exponent and the predicted long term
extreme response in a monopile wind turbine.
Wind Shear Exponent 𝜶
Long-TermExtreme
Response

42. 42
WIND SHEAR: ONSHORE VS OFFSHORE (AND TRANSITION ZONES)
SWL
~5 km
~150 m
Z01
Z02
Land Sea
H (m) H (m)
Marine atmospheric
boundary layer
(MABL)

43. 43
Wind Power-law

44. 44
PROCEDURE
WSC{i}
Uw
{k}
u{i,k}
Wind
power-law
HS
{i,j}
TP
{i,j}
N{i,k}
MECM
WSC{i}={ 0.06, 0.08, 0.10, 0.12, 0.14 }
Uw
{k}={10.0, 11.4,…,24.5, 25.0 }
Output: [WSC | UW | HS | TP]

45. 45
PROCEDURE
WSC{i}
Uw
{k}
TURBSIM
Wind random
seed
HS
{i,j}
TP
{i,j}
HYDRODYN
Wave random
seed
FAST
Output
Time series
Coupled
simulations

46. 46
RESULTS

47. 47
RESULTS

48. 48
RESULTS

49. 49
PAPER 3 (P3)
This paper focuses on two aspects:
 The first aspect is the study of the minimum simulation length required
to obtain accurate results when performing a statistical extrapolation
procedure.
 The second aspect deals with the study of the effect of considering a
flexible soil foundation, rather than the usual rigid connection, on
extreme responses.

50. 50
STOCHASTIC INDEPENDENCE
1 hour
10 min

51. 51
SOIL MODELING – IMPROVED APPARENT FIXITY METHOD(1)
(1) Developed by Løken et al. (2019)

52. 52
RESULTS - Independence

53. 53
RESULTS - Independence

54. 54
RESULTS - Independence

55. 55
RESULTS – SOIL FLEXIBLE VS RIGID

56. 56
RESULTS – SOIL FLEXIBLE VS RIGID

57. 57
RESULTS – SOIL FLEXIBLE VS RIGID

58. Contributions to the
Existent Knowledge
Part V
58

59. 59
CONTRIBUTIONS
The contributions of the present research are directly related to
the aspects introduced in the “PROBLEM STATEMENT” section (P0).
The study P0 was applied to an onshore wind turbine and
therefore waves were neglected. This aspect has been one of the first gaps
addressed in the present research.
 In the papers, joint probability distributions that consider both wind
(UW) and wave parameters (HS, TP) have been taken into account for all
the papers. In this case, conditionality among parameters means that
only certain combinations of environmental conditions are suitable to
be used in the simulations.
 In particular, the results of P1 confirmed the important participation of
waves to the system’s outputs. In the same way, it was observed in P2
that the FASF (FX) is mainly governed by the waves. Also, From the
results of P3, it was seen that the presence of waves particularly affects
long-term responses.

60. 60
A second gap identified at P0 was related to the fact that the
ultimate loads were estimated by averaging the absolute maximum values.
Also, authors only addressed to short term responses.
 Attending to this aspect, in papers P2 and P3, the Global Maxima
Method (GMM) was employed. Then, the data were fitted to a Gumbel
distribution to find the most probable value of extreme responses at
the mudline of the monopile. Thus, a more precise estimation of the
response was obtained to perform better comparisons.
 In this thesis also long-term loads were studied. relevance of this point
is related to the fact that at a long-term level the turbine control system
has a great influence on the extreme long-term load calculation. This
problem is bypassed in this research by including the Modified
Environmental Contour Method (MECM) .
 From the results obtained in P2 and P3, it was found that the critical EC
for FX is near 24 m/s and for MY is around 16mps. It was also found that
the location of the critical EC for FX is particularly affected by wind
shear whereas the location of this condition is unaffected for MY.
CONTRIBUTIONS

61. CONTRIBUTIONS
A third aspect addressed in the present research is referred to
the dynamic responses considered in P0. In that study, only the FABM was
taken into consideration, and not FASF. Since P0 did not consider wave
loading, conditionality on environmental parameters, or methods based on
extreme statistics, it was deemed necessary to examine the sensitivity of
the wind shear in more detail taking into consideration all these aspects.
61
 The results from P2 supported that MY was not very sensitive to wind
shear, but it was also found that FX was not sensitive to it. It is
important to mention that in P0 the responses were addressed only in
the short term. However, in this research, the analysis was made to
obtain the estimation of the 50-yr long-term responses.

62. CONTRIBUTIONS
Another important aspect that is often ignored during the
modelling of a bottom-fixed offshore wind turbine is the soil-structure
interaction. This aspect allows guaranteeing a high fidelity of the numerical
model of the offshore wind turbine. Within the literature, it is very
common to find that the foundation is modelled as a completely rigid
connection, as it was in done in P0. In an offshore context, the effects of
foundation flexibility may be important due to the combined loading
62
 To evaluate the effects that a flexible soil model can induce on the
extreme responses of an offshore wind turbine, the improved apparent
fixity (IAF) soil model was used in P3. From the results, it was observed
that the inclusion of the soil flexibility induced a particular effect on the
FABM. When a completely rigid foundation was considered, the critical
wind speed was 16.5 m/s. However, when the IAF model was employed
in simulations, this critical speed was shifted to 18 m/s. Also, the value
of the 50-yr long-term extreme response experienced a slight increase
in its value.

63. CONTRIBUTIONS
Another gap not directly related to limitations derived from P0
was also addressed. In P3, there was a literature review, and it was found
that there are on-going discussions about the suitability of adopting a
simulation length of 10-minutes for offshore wind energy applications. For
onshore, 10-min has been the standard for many years. However, since
offshore wind turbines are affected by wave loading, it is not entirely clear
whether 10-min can guarantee the stochastic independence.
63
 From the results of P3, the effects of simulation length were assessed.
It was found that a 10-minute simulation length gives acceptable results
for obtaining extrapolated extreme responses for the one hour level.
However, it does not provide adequate results for the extrapolation of
long-term extreme responses. This makes it necessary to use durations
longer than 30 minutes in the simulations.

64. Conclusions & Future
Agenda
Part VI
64

65. 65
CONCLUSIONS FROM P1
 It was found that there is a relationship between the sensitivity of the
outputs that can be well represented as a function of the uncertainties
in wave parameters.
 It was observed a linear behaviour when there was only uncertainty in
the wave height (HS). However, when uncertainty was introduced in the
wave period (TP), or both parameters, the effect in the response
exhibited a second-order relationship.
 It was found that the coefficients of the regression functions were fitted
with adequate precision using a third-order interpolation polynomial.

66. 66
CONCLUSIONS FROM P2
 It was found that 50yr long-term extreme responses are driven by
different environmental factors. In the case of FX, waves are the
environmental factor that governs its behaviour. In the case of MY, it
was observed a peak within the operational range, indicating that this
response is mainly governed by the wind.
 It was observed that the WSC influenced the identification of critical
wind speed for FX but not for MY.
 It was found that the long-term extreme responses associated with
monopile (FX, MY) have low sensitivity with respect to WSC.

67. 67
CONCLUSIONS FROM P3
 It was identified the need to explore the effects of lengths other than
that currently employed. In this regard, it was concluded that a 10-
minute simulation can estimate the distribution of one-hour extreme
responses with adequate accuracy, but it is not sufficient for long-term
responses with a return period of 50 years.
 From the results, it was found that the inclusion of soil flexibility on the
simulations does not have much impact on the one-hour extreme
response. However, when a return period of 50 years is considered, the
critical condition found with the MECM for MY is shifted, and the
extreme response increases by 2.96%. In the case of FX, the inclusion of
soil does not produce a significant variation in the long-term extreme
response.

68. 68
FUTURE RESEARCH AGENDA
 Inclusion of higher-order wave kinematics e.g. Stokes 5th order waves,
Stream function wave theory, and others. Also, inclusion of higher-order
loading models to capture the effects that nonlinear wave kinematics
can induce on the structure e.g. FNV, Rainey, M&M, and others.
 Evaluation of including more complete and advanced soil models e.g.
coupled springs, distributed springs, among others.
 Addressing the combined effect of all types of uncertainties will be
important to understand how they are interrelated and what is their
respective influence on the dynamic responses of interest.
 Evaluation of the effects that ringing and springing can produce on the
aero-hydro-servo-elastic simulations must be addressed as they can
cause extreme loads to increase considerably.

69. 69
FUTURE RESEARCH AGENDA
 The inclusion of more environmental variables in the joint probability
distributions and their influence on the environmental contour method
as well as the dynamic responses should be explored. These include the
turbulence intensity, wind veer, wind shear, coherence spectrum
parameters, and many others.
 It is important to study the propagation of uncertainty on the dynamic
responses under different working conditions e.g. parked, idling, in
installation, with faults, and others
 Fatigue analysis is also an important aspect in the verification of the
criteria fulfilment that ensures the reliability of the structure. These
types of analysis should be studied in more detail in future research.

70. 70
FUTURE RESEARCH AGENDA
 Larger turbines need to be studied. The NREL has recently released the
FAST simulation model for a 15 MW wind turbine, so further research is
expected to be carried out using this model for the near future

71. ACKNOWLEDGEMENTS
Thank you for the attention¡
71
FONDECYT - CONCYTEC
Dr Madjid Karimirad and Dr. Arturo Ortega
Dr Jaime Luyo and Mrs Laura Parillo
Dr Alberto Coronado
my family, my doctoral colleagues, and
everyone who has given me any kind of help during the development of this
thesis