Civil Engineering Reference
In-Depth Information
ˆ
k
(
x
,
w
) to capture any pos-
sible under- or over-estimation of the deterministic models. To capture
possible dependence of residuals on foundation, environment and earth-
quake parameters, which are not properly included in the deterministic
model, additional explanatory functions are also considered. Table 26.1
shows candidate explanatory functions for the demand models. To charac-
terize the infl uence of wind and wave parameters,
h
k
3
-
h
k
6
are selected as
normalized functions of the mean wind speed, turbulence intensity, signifi -
cant wave height, and wave peak period, respectively. The explanatory
functions
h
k
7
-
h
k
13
are considered to incorporate the infl uence of the mag-
nitude and frequency content of the ground motion. In addition,
h
k
14
is
considered to capture the possible infl uence of the rotor diameter. Finally
we consider
h
k
15
-
h
k
18
to capture the possible infl uence of the foundation
stiffness, which is not included in the deterministic model. A Bayesian infer-
ence is then used to estimate the unknown model parameters
that is independent of
x
and
w
, and
h
k
2
(
x
,
w
)
=
k
. Owing to
the lack of available data needed to conduct the statistical analysis required
to estimate the model parameters, we generate a database of virtual experi-
θ
Table 26.1
Explanatory functions for demand models
Explanatory
function
Formula
Parameters
h
k
1
1
k
=
d
,
v
or
m
d
ˆ
k
d
ˆ
k
h
k
2
deterministic deformation, shear or
moment demand
=
h
k
3
ln(
W
s
⋅
T
n
/
H
H
)
W
s
=
mean wind speed;
H
H
=
hub height
T
n
natural period of the support
structure
=
h
k
4
ln(
IT
w
)
IT
w
=
wind turbulence intensity
h
k
5
ln(
H
s
/
H
H
)
H
s
=
signifi cant wave height
h
k
6
ln(
T
s
/
T
n
)
T
p
=
wave peak period
h
k
7
ln(
S
a
/
g
)
S
a
=
spectral acceleration;
g
=
ground
acceleration
h
k
8
ln(
S
d
/
H
H
)
S
d
=
spectral displacement
h
k
9
ln(
PGA
/
g
)
PGA
=
peak ground acceleration
h
k
10
ln(
PGV
⋅
T
n
/
H
H
)
PGV
=
peak ground velocity
h
k
11
ln(
PGD
/
H
H
)
PGD
=
peak ground displacement
h
k
12
ln[2
π
PGV
/(
PGA
⋅
T
n
)]
h
k
13
ln[2
π
PGD
/(
PGV
⋅
T
n
)]
h
k
14
ln(
RD
/
H
H
)
RD
=
rotor diameter
h
k
15
ln(
C
s
/
C
smax
)
C
s
shear wave velocity of the soil;
C
s
max
=
=
194.594 m/s
h
k
16
ln(
C
soil
/
E
soil
)
C
soil
=
soil cohesion
h
k
17
ln[tan(
ϕ
soil
)]
ϕ
soil
=
soil friction angle
h
k
18
ln(
K
t
/
K
f
)
K
t
=
tower stiffness;
K
f
=
foundation
stiffness
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