Civil Engineering Reference
In-Depth Information
Deformation demand model
The probabilistic deformation demand model is formulated in terms of the
natural logarithm of the drift demand defi ned as deformation demand at
the top of the tower,
, normalized by the hub height,
H
H
. The logarithmic
transformation is used to satisfy the homoskedasticity, normality, and addi-
tivity assumptions. Upon carrying out the model selection process, fi nal
probabilistic deformation demand model is written as:
Δ
S
H
W
⋅
T
⎛
⎜
⎞
⎟
+
⎛
⎜
⎞
⎟
ˆ
ˆ
(
)
=
(
)
++
(
)
+
d
s
n
D
xw
,,
q
d
xw
,
θθ
d
xw
,
θ
ln
θ
ln
δ
δ
δ
δ
1
δ
2
δ
δ
3
δ
4
H
H
H
2
K
K
K
K
⎛
⎜
⎞
⎟
+
⎛
⎜
⎞
⎟
+
t
t
+
θ
ln
θ
ln
σ ε
δ
5
δ
6
δ
δ
f
f
[26.9]
d
) is
available before conducting the virtual experiments, in the Bayesian
approach we used a non-informative prior in the form
p
(
Since no prior information on the unknown parameters
Θ
d
=
(
θ
d
,
σ
d
−
1
(Box
θ
d
,
σ
d
)
∝
σ
and Tiao, 1992). Table 26.4 gives the posterior statistics of
σ
d
). Also,
Fig. 26.3 shows a comparison between measured and predicted deformation
demands based on deterministic and probabilistic models. The points
inscribed in triangles represent the lower bound data, the others are the
equality data. The dashed lines in Fig. 26.3(b) delimit the region within one
standard deviation of the model. The fi gure clearly shows an improvement
in predicting the demand when using the proposed probabilistic demand
model rather than the deterministic model demand. The correction term
adjusts the bias inherent in the deterministic model and makes the proba-
bilistic model unbiased.
Θ
d
=
(
θ
d
,
Table 26.4
Posterior statistics of the parameters in the deformation demand
model
Correlation coeffi cient
Standard
deviation
Parameter
Mean
θ
d
1
θ
d
2
θ
d
3
θ
d
4
θ
d
5
θ
d
6
σ
d
θ
d
1
4.81
2.062
1.0
θ
−
0.50
0.104
−
0.01
1.0
d
2
θ
0.151
0.065
−
0.14
−
0.44
1.0
d
3
θ
0.078
0.111
0.06
−
0.66
0.05
1.0
d
4
θ
1.94
0.677
0.96
−
0.22
−
0.15
0.21
1.0
d
5
θ
0.153
0.053
0.94
−
0.26
−
0.13
0.22
0.99
1.0
d
6
σ
d
0.493
0.043
0.03
0.06
0.06
−
0.05
0.02
0.03
1.0
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