Civil Engineering Reference
In-Depth Information
where
h
[
t
)] represents the pseudo-acceleration response of a single-
degree-of-freedom linear oscillator subject to a unit impulse and is formu-
lated as
−
τ
,
λ
(
τ
()
ωτ
ζτ
[
()
]
=
f
[
−
() ()
−
(
)
]
ht
−
ττ
,
l
exp
ζτωτ
t
τ
f
f
()
1
−
2
f
⎣
()
()
−
(
)
⎦
×
sin
ωτ
1
−
ζ
2
τ
t
τ
τ
≤
t
[26.6]
f
f
=
0
otherwise
where
τ
=
the time of the pulse,
ω
f
(
τ
)
=
natural frequency, and
ζ
f
(
τ
)
=
damping ratio of the fi lter.
The unknown parameters of the process
α
=
(
α
1
,
α
2
,
α
3
,
T
0
) and
λ
(
t
j
)
=
)] are assessed by matching the properties of generated and refer-
ence ground motions. The modulating function parameters (
[
ω
f
(
τ
),
ζ
f
(
τ
α
3
) are
related to ground motion time history variables (
¯
a
,
D
5-95
,
t
mid
), where
¯
a
α
1
,
α
2
,
=
expected Arias intensity (Arias, 1970) of the acceleration process,
D
5-95
=
time interval between the instants at which the 5% and 95% of the expected
Arias intensity are reached, and
t
mid
time at which 45% of the expected
Arias intensity is reached. The fi lter parameters [
=
)], which control
the evolving predominant frequency and bandwidth of the process, are
assessed based on their relations to the rate of zero-level up-crossings and
the cumulative number of negative maxima and positive minima of the
acceleration process. More details on the assessment of the unknown
parameters of this process are presented in Rezaeian and Der Kiureghian
(2010).
In case of a seismic event, a base acceleration time history is responsible
for the resulting forces in the structure. FAST does not accept an accelera-
tion time history as an input. Therefore we apply a time history of force,
F
(
t
), to the platform. Using an artifi cially large mass for the support plat-
form, the force
F
(
t
)
ω
f
(
τ
),
ζ
f
(
τ
a
(
t
) produces the desirable acceleration
a
(
t
) at the
base of the turbine support structure, where
=
μ
μ
is the total mass of the
support platform and the wind turbine.
26.3.2 Model correction
θ
k
) is intended to adjust for the bias inherent
in the deterministic model. We use the linear form presented in Eq. (26.2)
for the correction term, where for each demand of interest
k
,
The correction term
γ
k
(
x
,
w
,
θ
k
=
[
θ
ki
] and
1, . . . ,
p
, are, respectively, unknown model parameters and
selected explanatory functions. Also, in this chapter,
k
h
ki
(
x
,
w
),
i
=
d,
v
or
m
, for the
deformation, shear, or moment demand, respectively. Ideally, explanatory
functions should be selected from laws of mechanics and structural dynam-
ics. We select
h
k
1
(
x
,
w
)
=
=
1 to capture potential constant bias in the model
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