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Performance-Based Wind
Engineering (PBWE) procedure
Background
ENVIRONMENT
Wind actions
Structural systems
Non environmental
actions
EXCHANGE ZONE
Site-specific Wind
Aerodynamic and aeroelasticphenomena
Wind site basic parameters
Environmental effects (like
waves)
Structural system as modified
by service loads
STRUCTURAL SYSTEM
Vm
Mean wind velocity profile
Vm+ v(t)
Turbulent wind velocity profileriv
er
Vm
Mean wind velocity profile
Vm+ v(t)
Turbulent wind velocity profileriv
erriv
er
ENVIRONMENT EXCHANGE ZONE
Ciampoli M, Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general procedure”, Structural Safety, 33 (6), 367-378. DOI: 10.1016/j.strusafe.2011.07.001.
Schematization of uncertainty in Wind Engineering (I)
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Types of uncertainties
ENVIRONMENT
Wind actions
Structural systems
Non environmental
actions
EXCHANGE ZONE
1. Aleatory
2. Epistemic
3. Model
Interaction
parametersStructural parameters
Site-specific Wind
Aerodynamic and aeroelasticphenomena
Wind site basic parameters
Intensity
measure
1. Aleatory
2. Epistemic
3. Model
1. Aleatory
2. Epistemic
3. Model
Environmental effects (like
waves)
Structural system as modified
by service loads
( )IM ( )IP ( )SP
STRUCTURAL SYSTEM
Ciampoli M, Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general procedure”, Structural Safety, 33 (6), 367-378. DOI: 10.1016/j.strusafe.2011.07.001.
Schematization of uncertainty in Wind Engineering (II)
( ) ( ) ( ) ( )SPPIMPSP,IMIPPSP,IP,IMP ⋅⋅=
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O
f(IM|O)
f(IM)f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysisStructural analysis Damage analysis Loss analysis
IM: intensity
measure
IP: interaction
parameters
EDP: engineering
demand param.DM: damage
measure
DV: decision
variable
Select
O, DO: location
D: design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural
system parameters
Structural
system
info
| | | ||||
Ciampoli M., Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general
procedure”, Structural Safety, 33 (6), 367-378
= progress with respect to the
Performance-Based Seismic Design
*
* *
Extension of the Performance-Based
Seismic Design procedure proposed by PEER Research
center
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30 35
P(Av > av*|Vm(zdeck))
Vm(zdeck) [m/s]
Ciampoli M., Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general
procedure”, Structural Safety, 33 (6), 367-378
EDP = Av - DM= max (av) [m/s2]
1.0
0.8
0.6
0.4
0.2
0
G(E
DP
)
0 1 2 3
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
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Preliminary studies:
Offshore Wind Turbines
(parked configuration)
University of Notre Dame , South Bend, IN, USAJune 19, 2012 – EMI/PMC Conference
Francesco Petrini, PhD, PE
x,x’
z’
y’
Waves
Current
P
(t)v P
(t)w P
(t)u P
Turbulent
windP
Mean
wind
Vm(zP)
z
yH
h
vw(z’)
Vcur(z’)
d
Terrain
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( ) ( ) ( ) ( )( )nfexpnSnSnS jkuuuuuu kkjjkj−⋅=
( )( ) 2
t0
0
u
2
u u1.75)log(zarctan1.16(n)dnS ⋅+⋅−== ∫∞
5.0
0
uu2
x
u200
300(x)dxRu
1L
⋅== ∫
∞z
x
z
The mean velocity magnitude varies with the height.
Me
an
con
trib
ution
Sto
ch
astic c
on
trib
utio
n
( )( )[ ]5/3
ju
ju2V
uu/z10,302fL1/2
/zfL6,686S
jj +=
( )j
j
zV2
zf = ( )
( )( ) ( )( )kj
2
kj
2
z
jkzVzV2
zzC
f+
−=
Autospectrum
where:
α
=
hub
hubz
zUzU )(
0.14=α
For normal wind condition
( )( )
−
−−
−
−=
2
5.0exp4
5
4
2
4
5exp
2
P
P
f
ff
Pf
ff
gfS
σγ
π
α
where f=2π/T is the frequency, fP=2π/TP is the peak frequency, α is the equilibrium coefficient, g is gravity acceleration, and γ parameters dependent from HS e TP
−=
−
R
yearHTST
FHSR
11
1
1max,,,
Extreme events analysis (Return period TR).
71
,)(
+⋅=
d
zdUzU refc
x
z
d
water mean level
Wind Current and waves
JONSWAP spectrum
Cross-spectrum
!
"#$
%&$
#'"(
)*+ ,
-.
/
0 1 2 3
0 4 5 6
EDP: )()( hgrhr rrm
p σ⋅+=)T(log2
577.0)T(log2g
winde
winder⋅
+⋅=η
η
1°1°1°1°
rp
1°1°1°1°
rp
7 8 9 : ; 9 <
7 8 9 : ; 9 =
7 8 9 : ; 9 7
7 8 9 : > 9 9
7 8 9 : > 9 77 8 : ; 9 ? 7 8 : ; 9 < 7 8 : ; 9 = 7 8 : ; 9 7 7 8 : > 9 9
@ A B C D E F G
HI
JK
LM
JI
JK
IN
OP
QR
ST
UV
WX
Y Z [ \ ] ^ _ [ ` a
b Z [ \ ] ^ _ [ ` a
Basis of the numerical modelingStructural response (EDP) in frequency domain
(parked configuration)
Peak along- and across- wind displacementsDavenport’s peak factor
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Previous studies: Numerical applicationUncertainties overview
(parked configuration)
Importance of SPs
as stochastic
parameters
Effects of the
interactions in the
environment
Effects of dominant
aeroelastic phenomena
1°1°1°1°
rp
1°1°1°1°
rp
EDP = peak
displacement at the rotor
[E
DP
]
EDP [m]
[ED
P]
EDP [m]
Comparison of mean annual frequencies [EDP] of
exceeding any value of the EDP:
Previous studies: Relevance of SP uncertainty Risk Including SP Uncertainty (Monte Carlo 5000 samples)
Barbato M., Ciampoli M., Petrini F. (2010). “Effects of Modelling Parameter Uncertainty on the Structural Response of Offshore Wind Turbines”, Proceedings of the 12th biennial ASCE Aerospace Division International Conference (Earth & Space 2010), Honolulu, USA, 14 – 17 March 2010. ISBN 978-0-7844-1096-7.
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Aerodynamic uncertainty characterization
by the meso-scale modeling
(Rotating Configuration)
Physics (1): Mean wind rotational sampling
Murtagh, P.J., Basu, B., Broderick, B.M., 2005. Along-wind response of a wind turbine tower with blade
coupling subjected to rotationally sampled wind loading. Eng. Struct. 27(8), 1209-1219
( ) ( ) ( )12 ddd zFzFF iii S
X
S
X
S
X −=∆
z1
Ω
z2
Ω
Time t2Time t1
Vm(z1)
Vm(z2)
Tributary
area
S
Ω
dFXS
Angular
rotational
velocity
hub
( ) ( ) ( )tFFtF ii
hub
i S
X
S
X
S
X ⋅⋅∆+= cosd2
1d
Additional peak in the wind force spectra
1.E-15
1.E-11
1.E-07
1.E-03
1.E+01
1.E+05
0.00001 0.001 0.1 10
Frequency [Hz]
Forc
e S
pec
tra
SF
XF
X
1
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Physics (2): Turbulent wind rotational samplingVariation of the turbulent force spectra with the blade position
during its rotational motion
The correlation of the turbulent wind field felt by the BE is a function of its rotational motion
t+
t
Halfpenny A. (1988). Dynamic Analysis of Both On and Offshore Wind Turbines in the Frequency Domain. Ph.D. thesis. University College London..
Connell J.R. (1988). “A PRIMER OF TURBULENCE AT THE WIND TURBINE ROTOR”, Solar Energy, 41 (3), 281-293
Auto-correlation CoherenceOrdinary wind spectra
Separation distance (is function of the motion)
R
ΩΩΩΩ
Vm(r)r
Vm(zhub)
u(r,t)
XY
Z
Aerodynamic actions by the BEM theoryWind velocities and reference systems
- Evaluate the relative angle of attack and the relative speed of the wind with respect to specific blade portions (BEs) at different locations
r(1+a’)
Y
X
DL
φφφφ
VmR(r)=
Vm(r)(1-a)W
Rotor
plane
u(r,t)
v(r,t)
’
FX= ½**Vm2 (cLcos+ cDsin)
aerodynamic force
reference system axis
wind velocity
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ENVIRONMENT
Structure
Non environmental solicitations
STRUCTURE
Structural (non-
environmental)
system
Site-specific
environment
Wind site basic
parameters
Other environmental
agents
Waves site basic
parameters
Wind, wave and current actions
Aerodynamic
and Aeroelastic
phenomena
Hydrodynamic
phenomena
1. Aleatoric
2. Epistemic
3. Model
Types of uncertainties
1. Aleatoric
2. Epistemic
3. Model
1. Aleatoric
2. Epistemic
3. Model
Propagation Propagation
Interaction parameters
Structural parametersIntensity Measure
( )IM ( )IP ( )SP
EXCHANGE ZONE
)10(01.0 1 mzVVcurr hourwind =⋅=
Wind generated currents
)164.00291.0221.0(2
110
2
10 +⋅−⋅= VVH s
Correlation data by Zaaijer, 2006, taking into account the Italy Waves Atlas.
ENVIRONMENT
Structure
Non environmental solicitations
STRUCTURE
Structural (non-
environmental) system
Site-specific
environment
Wind site basic
parameters
Other environmental
agents
Waves site basic
parameters
Wind, wave and current actions
Aerodynamic
and Aeroelastic phenomena
Hydrodynamic phenomena
1. Aleatoric
2. Epistemic
3. Model
Types of uncertainties
1. Aleatoric
2. Epistemic
3. Model
1. Aleatoric
2. Epistemic
3. Model
Propagation Propagation
Interaction parameters
Structural parametersIntensity Measure
( )IM ( )IP ( )SP
EXCHANGE ZONE
Uncertainties in Wind-Blade interactions
Vm
a, a’, cD,cL
r(1+a’)
Y
X
DL
φφφφ
VmR(r)=
Vm(r)(1-a)W
Rotor
plane
u(r,t)
v(r,t)
’
FX= ½**Vm2 (cLcos+ cDsin)
ENVIRONMENT
EXCHANGE
STRUCTURE ,
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32
1
M3
R1
Blade-hub
main reactionsX
Y
r
FSX
VmR(r)
u(r,t)
Numerical applicationMain features of the meso-scale problem
The blade considered in this study has a length of 38 meters and is made of glass fiber (elastic modulus E= 15000106 N/m2).
c
d e f g h i j k l m
n o m k c m m p
q h r c o n s p
t u t t v w x y w z u |
u ~ v w x z u
u v v x w z u t
u t t y x y u | ~
u ~ x w u
u x u
t u t t x w u
u ~ w x u |
u x y y u z z
u t t x w u t
u ~ x v t u |
u v x v t u
z t u t t x v t u |
z u ~ x w t u ~
z u v x v v t u
z u t t x t u
z u ~ w x w t u
z u x t u
t u t t x t u z |
u ~ x w t u z ~
u x y t u z
u t t x v t u z
u ~ w x t u
~ u w x t u
~ u z u t t u
Only the along-wind turbulent component has been considered to generate the drag and lift actions on the blade. The turbulent wind is modeled by an eight-variate Gaussian stochastic process with the wind acting in eight locations along the blade.
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1.E-13
1.E-09
1.E-05
1.E-01
1.E+03
1.E+07
0.0 0.1 1.0 10.0
1P 2P n13P n2 n3
Fo
rce
Sp
ectr
a S
R1
R1
[N
2/H
z]
Frequency [Hz]
1.E-12
1.E-08
1.E-04
1.E+00
1.E+04
1.E+08
0.0 0.1 1.0 10.0 n [Hz]Forc
e S
pec
tra
SR
1R
1 [N
2/H
z]
1P 2Pn1 3P n2 n3
Frequency [Hz]
Evaluation of the blade stress statePSD of the fluctuating component of the reaction R1
produced on the hub by the rotating blade - = 16 rpm
and = 20 rpm
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1012
1416
1820
2224
25
0.00
0.01
0.02
0.03
0.04
0.05
0.3
3
0.4
0.5
a
x [m]
Uncertainties affecting the meso-level problemStandard deviation of the blade tip displacement (x) in function of the rotating speed () and the induction coefficient (a)
( ) ( )( )hubm
hubmRhubm
hV
hVhVa
−=
Vm(hhub): mean wind velocity at the hub
height
VmR(hhub): mean wind velocity at the hub
height and at the rotor plane
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Open Issues for Life-Cycle Performance evaluation
• Identification of additional interaction parameters (IP) determining the uncertainty
in the response (e.g. parameters modeling
aeroelasticity)
• Appropriate probabilistic characterization of
these parameters (e.g. the relevance of the
mean wind field sampling depends on the
daily hours)
• Appropriate and efficient numerical methods to evaluate parameters of multimodal power
spectral densities (e.g. for fatigue
calculations)
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Analyses for investigating other
performances
1- SHIP IMPACT
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1. Tipi di imbarcazione 2. Parametri caratteristici
3. Forma della prua
4. Velocità d’impatto
v 4 - 8 nodi 2 - 4 m/s
SHIP IMPACT
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MODELLAZIONE
• 580 nodi
• 555 elementi Beam188
• 40 elementi Combin14
• 1 elemento
•Mass21Stro N
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TERRENO
• Volume di terreno
modellato: cubo di
lato 80m,
discretizzato con
elementi 2x2x2 m
• 5 sottostrati in
materiale elastico
lineare con modulo
di rigidezza variabile
Elementi SOLID
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Terreno modellato
con molle lineari
lungo x e y poste a
metà dei sottostrati
Costante k variabile
con la profondità in
proporzione al
modulo E del terreno
Molle + smorzatori
SCELTA DEI VINCOLI
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Molle + smorzatoriDai parametri relativi al 1° e 2° modo di vibrare ricavo una stima del
coefficiente di smorzamento critico
SCELTA DEI VINCOLI
VERIFICA• impongo uno spostamento in un punto significativo
• rilascio e monitoro l’andamento nel tempo equivalente/reale
eq = 5.30 % eq = 4.08%
2
3
4
1
nodo 144
Dynamic behavior
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nodo 168
Dynamic behavior
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Increase of damage from the reference baseline ULS configuration to the last equilibrium configuration
λλλλ = 1.44λλλλ = 1.00 λλλλ = 1.32λλλλ = 1.10
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2 - Tower Buckling under extreme winds
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.
Stiffening types of the cutout in tubular tower
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.
FE model
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.
Static pushover analysis
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal ofComputational and Nonlinear Dynamics. 10(4),041004-041004-9.
Incremental dynamic analysis
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.
Loss of shape Vs Elephant foot buckling
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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.
Dynamic vs Static