Wind Tunnels and Experimental Fluid Dynamics Research Part 12 ppt

20
A Computer-assisted Wind Load Evaluation
System for the Design of Cladding of Buildings:
A Case Study of Spatial Structures
Yasushi Uematsu
Tohoku University
Japan
1. Introduction
Thin sheet metal and/or membrane are often used for roof cladding of spatial structures
because of their strength and lightness (Noguchi et al., 2003). Being light and flexible, such
roofing materials are vulnerable to dynamic wind actions. Since wind pressures acting on
spatial structures vary spatially as well as in time, the design wind loads should be
determined based on the dynamic characteristics of wind pressures. Fatigue of cladding
elements, such as roofing material and its fixings, may play an important role in the wind
resistant performance of cladding systems, although it is seldom considered in the design.
Roof cladding is usually designed based on the worst peak pressure coefficients irrespective
of wind direction. The conventional codification provides a single peak design pressure
coefficient for each roof zone considering a nominal worst-case scenario. Neither the
probability distribution of the peak pressure coefficients nor the peaks other than the largest
one are considered. Hence, they are not suitable for fatigue and risk-consistent designs.
Building design has recently shifted to a performance-oriented one. Therefore, it is hoped to
develop a new methodology that provides the peak pressure coefficients according to
predetermined risk levels and the loading sequence for estimating the fatigue damage to
roof cladding and its fixings. Computer simulation of wind pressure time series may be
useful for this purpose.
Kumar and Stathopoulos (1998, 1999, 2001) proposed a novel simulating methodology that
generates both Gaussian and non-Gaussian wind pressure fluctuations on low building
roofs. Despite its simple procedure, the technique is successfully applied to fatigue analysis
as well as to the evaluation of extreme pressures in a risk-consistent way. Therefore, this

technology is used in this chapter and a simplification of this method is discussed. Gaussian
and non-Gaussian pressure fluctuations can be simulated from the statistics of wind
pressures, i.e. the mean, standard deviation, skewness, kurtosis and power spectrum. These
statistical values change with location as well as with many factors related to the structure’s
geometry and the turbulence characteristics of approach flow. For such a complicated
phenomenon, in which a number of variables involve, artificial neural networks (simply
neural networks or ANN’s) can be used effectively. Artificial neural networks can capture a
complex, non-linear relationship via training with informative input-output example data
pairs obtained from computations and/or experiments. Among a variety of artificial neural

Wind Tunnels and Experimental Fluid Dynamics Research

430
networks developed so far, Cascade Correlation Learning Network (Fahlman and Lebiere,
1990) is applied to the present problem. It is a popular supervised learning architecture that
dynamically grows layers of hidden neurons of a fixed non-linear activation (e.g. sigmoid),
so that the topology (size and depth) can also be efficiently determined.
This chapter proposes a computer-assisted wind load evaluation system for the design of roof
cladding of spatial structures. Focus is on spherical domes and vaulted roofs, as typical shapes
of spatial structures. The composition of the system is schematically illustrated in Fig. 1. This
system provides wind loads for the design of cladding and its fixings without carrying out any
additional wind tunnel experiments. An aerodynamic database, artificial neural network and
time-series simulation technique are employed in the system. Finally, applications of the
system to risk-consistent design as well as to fatigue design are presented.


Fig. 1. Wind load evaluation system for the roof cladding of spatial structures
The wind load evaluation system proposed here is based on our previous studies (Uematsu
et al., 2005, 2007, 2008). It can be applied not only to spherical domes and vaulted roofs but
also to any other structures. However, such a system may be more useful for designing the

cladding of spatial structures because of its sensitivity to dynamic load effects of fluctuating
wind pressures. The spatial variation of statistical properties and the non-normality of
pressure fluctuations on spherical domes and vaulted roofs are less significant than those on
flat and gable roofs. Therefore, an ANN and a time-series simulation technique can be used
more efficiently for these structures. This is the reason why we focus on the cladding of
spherical domes and vaulted roofs in this chapter.
2. Aerodynamic dadabase
2.1 Wind tunnel experiments
Two series of wind tunnel experiments were carried out; one is for spherical domes and the
other is for vaulted roofs. The experimental conditions are somewhat different from each
other. The outline of the experimental conditions is presented here.
2.1.1 Spherical dome
The experiments were carried out in a closed-circuit-type wind tunnel with a working
section 18.1 m long, 2.5 m wide and 2.0 m high. Two kinds of turbulent boundary layers
simulating natural winds over typical open-country and urban terrains were generated;
these flows are respectively referred to as Flows ‘II’ and ‘IV’ in this chapter. The geometric
Wind pressure
loading cycles
Probability of peak values
RISK-CONSISTENT DESIGN
A
RTIFICIAL NEURAL NETWORK
TECHNIQUE
Wind pressure
loading cycles
FATIGUE DESIGN
Extreme value analysis
Probabilit
y
of

p
eak values
A
PPLICATIONS
Rainflow count method
DATABASE OF
WIND PRESSURE
TIME SERIES
DATABASE OF
STATISTICS OF
PRESSURE COEFFICIENTS
WIND LOADS FOR CLADDING
DESIGN (conventional method)
A
RTIFICIAL NEURAL NETWORK
TIME SERIES SIMULATION
TECHNIQUE
WIND TUNNEL
EXPERIMENTS
STATISTICAL VALUES
OF WIND PRESSURES
ROOF SHAPE,
FLOW CONDITION
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

431
scale of these flows ranges from 1/400 to 1/500, judging from the longitudinal integral scale
of turbulence.
The geometry of the wind tunnel model is schematically illustrated in Fig. 2(a). The

rise/span ratio (f/D) is varied from 0 to 0.5, while the eaves-height/span ratio (h/D) from 0
to 1. The span D of the wind tunnel model is 267 mm and the surface of the model is
nominally smooth. Each model is equipped with 433 pressure taps of 0.5 mm diameter, as
shown in Fig. 2(b). The pressure taps are connected to pressure transducers in parallel via 80
cm lengths of flexible vinyl tubing of 1 mm inside diameter. The compensation for the
frequency response of this pneumatic tubing system is carried out by using a digital filter,
which is designed so that the dynamic data up to approximately 500 Hz can be obtained
without distortion. The signals from the transducers are sampled in parallel at a rate of 1
kHz on each channel for a period of approximately 33 seconds. All measurements are made
at a wind velocity of U
ref
= 10 m/s at a reference height of Z
ref
= 267 mm. The velocity scale is
assumed 1/5. The wind velocity U
top
at the level of rooftop ranges from 5.3 to 10.2 m/s; the
corresponding Reynolds number Re, defined in terms of D and U
top
, ranges from
approximately 9.4 × 10
4
to 1.8× 10
5
. The turbulence intensity I
u,top
at the level of rooftop
ranges from 0.13 to 0.20 for Flow II and from 0.12 to 0.27 for Flow IV.

f/D = 0, 0.05, 0.10, 0.20, 0.50
h/D = 0, 1/16, ･･･, 16/16

WIND
WIND
f
h
z
y
O
D = 267mm
x
y
O

(a) Geometry (side view) (b) Location of pressure taps (top view)
Fig. 2. Wind tunnel model and coordinate system (spherical domes)
2.1.2 Vaulted roof
The experiments were carried out in a closed-circuit-type wind tunnel with a working
section 18.9 m long, 2.6 m wide and 2.1 to 2.4 m high. Two kinds of turbulent boundary
layers similar to those used for spherical domes were generated; these flows are respectively
referred to as Flows ‘II’’ and ‘IV’’ in this chapter.
The geometry of the wind tunnel model is schematically illustrated in Fig. 3(a). The
rise/span ratio (f/D) is varied from 0.1 to 0.4, while the eaves-height/span ratio (h/D) from
1/30 to 20/30. The span D of the wind tunnel model is 150 mm and the length W is 300mm.
Each model is equipped with 228 pressure taps of 0.5 mm diameter, as shown in Fig. 3(b).
The turbulence intensity I
u,H
at the mean roof height H is approximately 0.16 for Flow II’ and

approximately 0.19 for Flow IV’.
The experimental procedure is the same as that for spherical domes except that the wind
direction is varied from 0 to 90
o
at a step of 5
o
.

Wind Tunnels and Experimental Fluid Dynamics Research

432


y
z
O
D = 150mm
W
= 300mm
f
h
0
o
90
o
f/D = 0.1, 0.2, 0.4
h/D = 1/30, 10/30, 20/30
x
y
O

(a) Geometry (side view) (b) Location of pressure taps (top view)
Fig. 3. Wind tunnel model and coordinate system (vaulted roofs)
2.2 Database of the statistics of wind pressures
The data from the simultaneous pressure measurements are stored on a computer in the
form of pressure coefficient; the pressure coefficient C
p
is defined in terms of the velocity
pressure q
H
(= 1/2
ρ
U
H
2
, with
ρ
and U
H
being the air density and the wind velocity at the
mean roof height H, respectively). Then, the statistical values of pressure coefficients, i.e.
mean
p
C , standard deviation '
p
C , maximum and minimum peaks, C
pmax
and C
pmin
, during

a full-scale period of 10 min, skewness S
k
, kurtosis K
u
and power spectrum S
p
(f), with f being
the frequency, are computed. In the spherical dome case, the distributions of
p
C ,
'
p
C
, C
pmax
,
C
pmin
, S
k
and K
u
in the circumferential direction are smoothed by using a cubic spline
function. Furthermore, the values at two points that are symmetric with respect to the
centreline parallel to the wind direction are replaced by the average of the two values, which
makes the distribution symmetric with respect to the centreline. In the case of vaulted roofs,
the distributions along the roof’s periphery are smoothed by using a cubic spline function.
Such a smoothing procedure may eliminate noisy errors included in the experimental data.
Sample results on
p

C are shown in Figs. 4 and 5. The smoothed data for all the cases tested
are stored in the database, together with the coordinates (x, y) of pressure taps, the values of
geometric parameters (i.e. f/D and h/D), and the turbulence intensity I
uH
of approach flow at
the mean roof height H and the wind direction (only for vaulted roofs).
The power spectrum S
p
(f) is approximated by the following equation:

11 22
2
()
exp exp
p
HH
p
Sf
fDH fDH
ac ac
UU
σ

=− +−



(1)
where
σ

p
is the standard deviation of pressure fluctuation; a
1
and a
2
are the position
constants and c
1
and c
2
are the shape constants. The first and second terms of the right-hand
side of Eq. (1) control the position and shape of S
p
(f)/
σ
p
2
at lower and higher frequencies,
respectively. Similar representation was used by Kumar and Stathopoulos (1998) for
pressures on low building roofs. In the above equation, however, the frequency f is reduced
A Computer-assisted Wind Load Evaluation System
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433
by DH , not by H. This is related to a three-dimensional effect of the flow around the roofs.
The values of the four constants are determined based on the least squares method applied
to the experimental data.


Fig. 4. Distributions of

p
C on a spherical dome (f/D = 0.1, h/D= 4/16, Flow II)


Fig. 5. Distributions of
p
C on a vaulted roof (f/D = 0.1, h/D= 1/30, Flow IV’)
In the spherical dome case, the general shape of S
p
(f)/
σ
p
2
changes only slightly in the x-
direction (Noguchi and Uematsu, 2004). Therefore, focus is on the variation of S
p
(f)/
σ
p
2
only
in the y-direction. The values of a
1
, a
2
, c
1
and c
2
at the pressure taps on the dome’s centreline

are computed for all the cases tested and stored in the database. In the wind load evaluation
system, we use the values of the four constants at a point on the centreline that gives a y-axis
value closest to that of the target point (evaluation point). Fig. 6 shows sample results of
comparison between experiment and formula for the power spectra at two points on a
spherical dome. The experimental results are plotted by the circles and the empirical
formula is represented by the solid line. It is seen that the approximation by Eq. (1) is
generally satisfactory.
In the vaulted roof case, the wind pressures are affected by the wind direction. Hence, the
power spectra are calculated for all pressure taps and wind directions. Fig. 7 shows sample
results of comparison between experiment and formula for the power spectra at two points
on a vaulted roof. Again, the agreement is generally good.
-
1
.
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0
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2
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0
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2
(a) Before smoothing
(
b

)
After smoothin
g
C.L.
W
C.L.
90
o

90
o

W
-1.2
-1.2
-0.4
-0.4
-0.6
-0.6
-1.0
-1.0
-0.4
-0.4
-0.4
-
1
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0
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6

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(a) Before smoothing
(
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)
After smoothin
g
W

Wind Tunnels and Experimental Fluid Dynamics Research

434

0.0001

0.001

0.01

0.1

1

0.001

0.01 0.1 1 10
Experiment
Formula

0.0001
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10
Experiment
Formula
WINDWIND
WINDWIND
2
()
p
p
Sf
σ
H
f
HD
U
⋅
(a) Windward region (b) Leeward region
Fig. 6. Wind pressure spectra for a spherical dome (f/D = 0.1, h/D = 4/16, Flow II)

0.00001
0.0001
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10
Experiment
Formula
2
()
p
p
Sf
σ
H
f
HD
U
⋅
0.00001
0.0001
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10
Experiment
Formula
～

～
～
～
30
o
C.L.
～
～
～
～
0
o
C.L
(a) Windward region (b) Leeward region
Fig. 7. Wind pressure spectra for a circular arc roof (f/D = 0.1, h/D = 1/30, Flow IV’)
3. Artificial neural network
3.1 Spherical dome
Although the wind pressures were measured simultaneously at several hundreds points in the
wind tunnel experiments, spatial resolution may be still limited from the viewpoint of cladding
design. Cladding or roofing cover is sensitive to the spatial variation and fluctuating character
of the time-dependent wind pressures. The turbulence of approach flow also affects the wind
pressures significantly. Hence, an artificial neural network based on Cascade Correlation
Learning Network (CCLN, Fahlman and Lebiere, 1990) is used to improve the resolution.
Fig. 8 illustrates the network architecture, which has a layered structure with an input layer,
an output layer and a hidden layer between the input and output layers. The input vector
consists of five parameters, that is, two geometric parameters of the building (f/D and h/D),
the coordinates (x, y) of measuring point, and the turbulence intensity I
uH
of the approach
flow at the mean roof height H; the coordinate system is defined as shown in Fig. 2. There is

also a bias unit, permanently set to +1. Each network is constructed for each of the four
parameters,
p
C , '
p
C , S
k
and K
u
.
The quickprop algorithm (Fahlman, 1988) is used to train the output weights. Training
begins with no hidden units. As the first step, the direct input-output connections are
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

435
trained as well as possible over the entire training set. The network is trained until either a
predetermined maximum number of iterations is reached, or no significant error reduction
has occurred after a certain number of training cycles. If the error is not acceptable after the
first step, a new hidden unit is added to the network to reduce this residual error. The new
unit is added to the network, its input weights are frozen, and all the output weights are
once again trained. This cycle repeats until the error becomes acceptably small.



h/D
f/D
x
y
I

uh
Input Layer
or
or
or
Output Layer
Hidden
Cp
mean
Cp
rms
Skewness
Kurtosis
Bias-Unit
+1
h/D
f/D
x
y
I
uh
Input Layer
or
or
or
Output Layer
Hidden
Cp
mean
Cp

rms
Skewness
Kurtosis
Bias-Unit
+1
p
C
'
p
C

Fig. 8. CCLN for the statistics of wind pressures on spherical domes
Well-distributed representative data are required for training the network. In the above-
mentioned database, pressure data at 230 locations are stored each for five f/D ratios,
seventeen h/D ratios and two kinds of turbulent boundary layers (open-country and urban
exposures). Note that the h/D ratio is varied from 1/16 to 1 in the flat roof case (f/D = 0).
Therefore, the number of data set is 38,640 (= 2
× (16+17×4) ×230 = 168×230). Ten typical
cases of experimental conditions are selected from these 168 cases. Forty-six locations are
randomly selected from the 230 points for testing. Therefore, the number of test data is 460
(= 10×46). The other data are used for training the network.
The sigmoid function represented by the following equation is used to process the net input
signals and provide the output signals at hidden nodes:

max min
min
()
1
s
SS

f
sS
e
−
−
=+
+
(2)
where S
max
and S
min
represent the upper and lower limits of the output from the neuron.
Appropriate values of S
max
and S
min
depend on the output vector. In the training phase of
the network using the quickprop algorithm, three empirical terms, i.e. learning rate
η
,
maximum growth factor
μ
, and weight decay term
λ
, are introduced to improve the
convergence of training and the stability of computation. Appropriate values of these terms
are determined by trial and error, considering the behaviour of the mean square error that
the network produces. The weights are initialised to random numbers between +1.0 and –
1.0. The number of epochs also affects the convergence of training, which is again

determined by trial and error. Table 1 summarizes the values of
η
and the numbers of

Wind Tunnels and Experimental Fluid Dynamics Research

436
epochs for
p
C , '
p
C , S
k
and K
u
, together with the values of the error index I
E
in the training
phase; the error index is defined by the following equation:

()
2
1
1
N
kk
k
E
TO
N

I
σ
=
−
=

(3)
where T
k
and O
k
represent the target value and the actual output for training pattern k,
respectively; N = number of training patterns; and
σ
= standard deviation of the target data.
Because the values of S
k
and K
u
change over a wide range, these values are divided by some
factors.

Statistical value
η
Number of epochs I
E
(training phase)
p
C
0.5 100 0.144

'
p
C

0.5 50 0.333
S
k

0.02 200 0.478
K
u

0.2 300 0.421
Table 1. Characteristics of the neural network for spherical domes


Fig. 9. Comparison between experiment and ANN prediction for
p
C , '
p
C , S
k
and K
u

-2
-1.5
-1
-0.5
0

0.5
-2 -1.5 -1 -0.5 0 0.5
Experimental value
Predicted value by ANN
Prediction
Target+0.26
Target-0.26
0
0.2
0.4
0.6
0 0.2 0.4 0.6
Experimental value
Predicted value by ANN
Prediction
Target+0.07
Target-0.07
-2
-1
0
1
-2 -1.5 -1 -0.5 0 0.5
Experimental value
Predicted value by ANN
Prediction
Target+0.2
Target-0.2
-1
0
1

2
3
4
5
-1135
Experimental value
Predicted value by ANN
Prediction
Target+0.63
Target-0.63
(a)
p
C
(b) '
p
C
(c) S
k
(d) K
u

A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

437
Fig. 9 shows comparisons between experiment and prediction by ANN for
p
C , '
p
C , S

k
and
K
u
, respectively; 460 data are plotted in each figure. The solid lines in the figures represent
permitted limits, which are tentatively chosen as a standard deviation of the experimental
values. Regarding
p
C and '
p
C , the agreement is generally good. Regarding the skewness
and kurtosis, on the other hand, the agreement is somewhat poorer than that for
p
C and
'
p
C , although the ANN captures the general trend of the experimental data. This is because
the skewness and kurtosis exhibit large values in magnitude in relatively small areas.
Furthermore, their variation in these areas is also remarkable. However, as will be described
later, the effects of S
k
and K
u
on the simulated time-series of wind pressures are relatively
small. This feature implies that the neural networks constructed for S
k
and K
u
can be used in
the practical applications.

To discuss the application of the ANN to practical situations, a comparison is made between
the prediction by the ANN and the experimental data for Nagoya Dome (Fig. 10). The
geometry of this building is as follows: i.e. span D = 187.2 m, rise f = 32.95 m, eaves-height h =
30.7 m (f/D = 0.18, h/D = 0.16). This dome is constructed in the suburb of Nagoya City, Japan.
The wind tunnel experiment was carried out with a 1/500 scale model in a turbulent boundary
layer with a power law exponent of
α
= 0.25 and the turbulence intensity of 0.19 at the level of
rooftop. The actual situation in the circular area with a radius of 450 m around the dome was
modeled exactly. The experimental data on
p
C and '
p
C were provided by Takenaka
Corporation that had carried out the wind tunnel experiment. Fig. 11 shows comparisons
between the ANN prediction and the experimental data for
p
C and '
p
C . The agreement is
relatively good, particularly for
p
C . The ANN somewhat overestimates the values of '
p
C .
However, such a difference up to about 0.1 may be acceptable in plactical applications.


Fig. 10. Nagoya Dome (provided by Takenaka Corporation)

Wind Tunnels and Experimental Fluid Dynamics Research

438

Fig. 11. Comparison between ANN and experiment for the
p
C and '
p
C distributions
3.2 Vaulted roof
Fig. 12 shows the ANN architecture for vaulted roofs. In this case, the wind direction
θ
is
considered in the input vector. The network is trained in the same manner as that for
spherical domes. Eighteen typical cases of experimental conditions are selected from the 342
cases. Forty-five locations are randomly selected from the 228 points for testing. The number
of test data is 810 (= 18×45). The other data are used for training the network. Table 2
summarizes the characteristics of the network obtained.
Fig. 13 shows comparisons between experiment and prediction by ANN for
p
C , '
p
C , S
k
and
K
u
, respectively; 810 data are plotted in each figure. The behaviour of the networks for
vaulted roofs is similar to that for spherical domes shown in Fig. 9. However, the ANN
prediction is somewhat poorer than that for spherical domes. This may be related to a wider

variation of the characteristics of wind pressures with many parameters in the vaulted roof
case.



f/D
h/D
x
y
I
uH
Input Layer
or
or
or
Output Layer
Hidden
Cp
mean
Cp
rms
Skewness
Kurtosis
Bias-Unit
+1
cos
θ
s
in
θ

f/D
h/D
x
y
I
uH
Input Layer
or
or
or
Output Layer
Hidden
Cp
mean
Cp
rms
Skewness
Kurtosis
Bias-Unit
+1
cos
θ
s
in
θ
p
C
'
p
C

Fig. 12. CCLN for the statistics of wind pressures on vaulted roofs

WIND WIND
(a)
p
C
Wind tunnel experiment ANN prediction
(b) '
p
C
WIND WIND
Wind tunnel experiment ANN prediction
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

439
Statistical value
η
Number of epochs I
E
(training phase)
p
C
0.2 150 0.229
'
p
C
0.5 150 0.378
S

k

0.2 300 0.446
K
u

0.2 500 0.827
Table 2. Characteristics of the neural network for vaulted roofs


Fig. 13. Comparison between experiment and ANN prediction for
p
C , '
p
C , S
k
and K
u

4. Time series simulation of wind pressures
4.1 Outline of the procedure
First, the application of the Kumar and Stathopoulos’s method (1999, 2001) to the present
problem is discussed. The flow chart for the simulation is described in Fig. 14. The approach
is based on an FFT Algorithm. The Fourier amplitude is constructed from the power
spectrum S
p
(f) of pressure fluctuations, which is represented by Eq. (1). The values of the
four coefficients involved in the equation are obtained from the database. The spike features
inducing the non-Gaussian character to the pressure fluctuations are achieved by preserving
the target skewness and kurtosis given by the ANN and the database. A simple stochastic

model with a single parameter b has been suggested for the simulation of phase. The
(a)
p
C
(b) '
p
C
(c) S
k
(d) K
u

-2.5
-1.5
-0.5
0.5
-2.5 -1.5 -0.5 0.5
Experimental value
Predicted value by ANN
Prediction
Target+0.31
Target-0.31

0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1

Experimental value
Predicted velue by ANN
Prediction
Target+0.09
Target-0.09

-4
-2
0
2
-4 -3 -2 -1 0 1 2
Experimantal value
Predicted value by ANN
Prediction
Target+0.34
Target-0.34

-1
1
3
5
7
9
-1 1 3 5 7 9
Experimental value
Predicted value by ANN
Prediction
Target+1.2
Target-1.2

Wind Tunnels and Experimental Fluid Dynamics Research

440
computation of b is accomplished by minimizing the sum of the squared errors in skewness
and kurtosis. In practice, changing the value of b from 0 to 1 with a small increment (e.g.
0.01), the skewness S
k
and kurtosis K
u
of the simulated time series are computed. The sum of
the squared errors (SSE) in S
k
and K
u
are calculated for each value of b and the value giving
the least SSE is chosen as the optimum one.


PHASE
Generate phase
signal
Generate exponential
random numbers
Y
t
= 0, with probability b
E
t
, with probability 1-b
t

E
Generate skeleton signal
t
Y
k
φ
1
0
1
0
sin(2 / )
arctan
cos(2 / )
n
t
t
k
n
t
t
Yktn
Yktn
π
φ
π
−
=
−
=
−⋅

=
⋅


()
k
πφ π
−≤ <
Generate Fourier
amplitude
k
I
()
kmk
InSff=Δ
AMPLITUDE
Simulate
t
Z
1
12/
0
k
n
i
iktn
tk
k
Zn Iee
φ

π
−
−
=
=

PHASE
Generate phase
signal
Generate exponential
random numbers
Y
t
= 0, with probability b
E
t
, with probability 1-b
t
E
Generate skeleton signal
t
Y
k
φ
1
0
1
0
sin(2 / )
arctan

cos(2 / )
n
t
t
k
n
t
t
Yktn
Yktn
π
φ
π
−
=
−
=
−⋅
=
⋅


()
k
πφ π
−≤ <
PHASE
Generate phase
signal
Generate exponential

random numbers
Y
t
= 0, with probability b
E
t
, with probability 1-b
t
E
Generate skeleton signal
t
Y
k
φ
1
0
1
0
sin(2 / )
arctan
cos(2 / )
n
t
t
k
n
t
t
Yktn
Yktn

π
φ
π
−
=
−
=
−⋅
=
⋅


()
k
πφ π
−≤ <
Generate Fourier
amplitude
k
I
()
kmk
InSff=Δ
AMPLITUDE
Generate Fourier
amplitude
k
I
()
kmk

InSff=Δ
AMPLITUDE
Simulate
t
Z
1
12/
0
k
n
i
iktn
tk
k
Zn Iee
φ
π
−
−
=
=

Simulate
t
Z
1
12/
0
k
n

i
iktn
tk
k
Zn Iee
φ
π
−
−
=
=



Fig. 14. Schematic of the generation of non-Gaussian wind pressure time series (Kumar and
Stathopoulos, 1999, 2001)
4.2 Toward simplification of the procedure
The most troublesome and time-consuming procedure is the determination of the optimum
value of b. Fig. 15 shows sample results on the variation of S
k
and K
u
with b. Note that the
ordinate of the figure for kurtosis is represented by K
u
–3, considering that K
u
= 3 for
Gaussian processes. Because the skewness and kurtosis are related to each other, both S
k

and
K
u
show similar behavior. They increase monotonically with an increase in b. When the
value of b is relatively small, such as b < 0.6, for example, the variation is quite small. On the
other hand, they increase significantly with increasing b for larger values of b. In practice,
the optimum value of b is not so large and the values of S
k
and K
u
are less sensitive to b.
Therefore, the variation of S
k
and K
u
can be approximated by a simple function of b with a
small number of data points in the practical range. The cubic spline function is used here.
Using such a function, the optimum value of b can be calculated easily.


0
5
10
15
20
0.0 0.5 1.0
b
Skewness , Kurtosis
−
3

Skewness
Kurtosis-3
WIND

Fig. 15. Variation of S
k
and K
u
with b for a spherical dome (f/D = 0.1, h/D = 0.25, Flow II)
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

441
4.3 Results and discussion
A comparison of the wind pressure time series between experiment and simulation is
shown in Fig. 16. The spike features of pressure fluctuations are simulated well. Tables 3
and 4 summarize comparisons between experiment and simulation for the statistics of the
wind pressures at two typical points on a spherical dome and a vaulted roof, respectively.
Note that the averaging time for evaluating the peak pressure coefficients is 1 sec and the
values in the table are all the ensemble averages of the results from six consecutive runs. A
good agreement between experiment and simulation is seen for both points. Similar
comparisons are made for ninety-two points shown in Fig. 17 (points on the solid lines).
The results for C
pmax
and C
pmin
are plotted in Fig. 18. The agreement is relatively good.
Approximately 95 % of the simulated results is within a range of the target value
±
0.1 for

C
pmax
and ± 0.2 for C
pmax
. These results indicate that the method proposed here can be used
for evaluating the design wind loads by combining the database of the statistics of wind
pressures and the ANN.


Fig. 16. Experimental and simulated time series of wind pressure coefficient at a point near
the leeward edge of a spherical dome (f/D = 0.2, h/D = 4/16, Flow II)


-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 240 480 720 960 1200 1440 1680 1920 2160 2400 2640 2880 3120 3360
Time (s)
Cp


-1.2
-1.0

-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 240 480 720 960 1200 1440 1680 1920 2160 2400 2640 2880 3120 3360
Time (s)
Cp
(a) Experiment
(b) Simulation

Wind Tunnels and Experimental Fluid Dynamics Research

442
Statistics
p
C
C
pmax
C
pmin

S
k
K
u

Tap location
(a) Point 1

Experiment 0.226 -0.394 -1.872 -0.385 3.065
Simulation 0.211 -0.395 -1.685 -0.436 3.057
Error 0.015 0.001 -0.187 0.051 0.008
(b) Point 192

Experiment 0.126 0.208 -0.742 -0.647 4.225
Simulation 0.120 0.154 -0.732 -0.661 4.212
Error 0.006 0.054 -0.010 0.014 0.013
Table 3. Comparison between experiment and simulation for the statistics of wind pressures
on a spherical dome (f/D = 0.2, h/D = 0.25, Flow II)

Statistics
p
C
C
pmax
C
pmin

S
k
K
u
Tap location
(a) Point 1
Experiment 0.475 -0.437 -3.188 -1.367 3.302
Simulation 0.437 -0.386 -3.084 -1.188 2.852

Error 0.038 -0.051 -0.104 -0.179 0.450
(b) Point 210
Experiment 0.206 0.115 -1.209 -0.884 2.708
Simulation 0.190 0.066 -1.142 -0.852 2.332
Error 0.016 0.049 -0.067 -0.032 0.376
Table 4. Comparison between experiment and simulation for the statistics of wind pressures
on a vaulted roof (f/D = 0.3, h/D = 10/30, Flow II
’)


WIND
92
点

Fig. 17. Tap locations where the time series of pressure fluctuations is simulated (92 points
on the solid lines)
#1
WIND
#1
WIND
#192
WIND
#210
WIND
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

443

Fig. 18. Comparison between experimant and simulation for a spherical dome (f/D = 0.2,

h/D = 4/16, Flow II)


Fig. 19. Effects of S
k
and K
u
on the simulated value of C
pmin
for a spherical dome (f/D = 0.2,
h/D = 9/16, x/D = 0, y/D = –1/4)
As mentioned above, the accuracy of the ANN prediction for S
k
and K
u
is not so high,
compared with that for
p
C and '
p
C . Then, the effects of S
k
and K
u
on the simulated results
are investigated. The time series is simulated by changing either S
k
or K
u
from the optimum

value. Fig. 19(a) shows the variation of the change of C
pmin
(
Δ
C
pmin
) with the change of S
k

(
Δ
S
k
) from the optimum value. A similar result for K
u
is shown in Fig. 19(b). It is found that
the simulated results are not sensitive to the variation of S
k
and K
u
. In practice, the simulated
result of C
pmin
changes some 5 percent when the values of S
k
or K
u
change by 50 percent.
5. Application of the wind load evaluation system to wind resistant design
The wind load evaluation system proposed here can provide peak pressure coefficients

according to a predetermined risk level by combining the extreme value analysis. Fig. 20
shows the probability of non-exceedence for C
pmin
at a windward edge point of a spherical
dome. The thick solid line shows the result calculated from a set of 200 extremes that the
evaluation system predicted. For comparative purpose, the results predicted from 33 sets of
six extremes by using BLUE (Lieblein, 1974) are represented by thin solid lines. These
results exhibit a considerable scatter around the 200 data curve. The result predicted from

-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
Experimental result
（
Target
）
Simulated result
Simulation
Target
Target±0.1

-2
-1.5
-1
-0.5
-2 -1.5 -1 -0.5
Experimental result

（
Target
）
Simulated result
Simulation
Target
Target±0.2
(a)
p
C
(b) '
p
C

0
1
2
3
4
5
-100 -50 0 50 100
Δ
S
k

(
％）
|
Δ
C

p min
/C
p min
| (%)
(a) Skewness (b) Kurtosis

0
2
4
6
8
10
-100 -50 0 50 100
Δ
K
u
(%)
|
Δ
C
p min
/C
p min
| (%)

Wind Tunnels and Experimental Fluid Dynamics Research

444
the six experimental data is also quite different from the 200 data curve. Such a difference
implies that we need a lot of data for predicting the probability of non-exceedence precisely.

It takes a long time to collect so much data in a wind tunnel experiment. By comparison, the
proposed wind load evaluation system can provide much data more easily. This is one of
the advantages of the system over the wind tunnel experiment.


0.0
0.2
0.4
0.6
0.8
1.0
0.5 1.0 1.5
-C
pmin
Probability of non-excedence
Experiment
（
N = 6
）
Simulation
（
N = 200
）
Simulation
（
N
= 6
）
・

Fig. 20. Probability of non-exceedence for C
pmin

(Spherical dome; f/D = 0.2, h/D = 4/16,
Flow II)
Furthermore, by introducing a load cycle counting method, such as the rainflow count
method, the system can provide the wind load cycles for fatigue design. Fig. 21 shows a
sample result on the frequency distribution of wind pressure coefficient fluctuations,
represented as a function of mean and amplitude of fluctuation at the center of a dome. By
combining such a result with the influence coefficients, we can easily compute the stresses
or strains induced in the cladding and its fixings, which are used for evaluating the fatigue
damage.


-1.95
-1.45
-0.95
-0.45
0.025
0.525
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Mean
Amplitude

Relative
frequency

・

Fig. 21. Number of load cycles (Spherical dome; f/D = 0.2, h/D = 4/16, Flow II)
6. Concluding remarks
A computer-assisted load evaluation system for the design of roof cladding of spatial
structures using an aerodynamic database, artificial neural network and time-series
simulation technique has been proposed. Focus is on spherical domes and vaulted roofs as
typical roof shapes used for spatial structures. The proposed methodology is capable of
WIND
A Computer-assisted Wind Load Evaluation System
for the Design of Cladding of Buildings: A Case Study of Spatial Structures

445
providing peak pressure coefficients according to pre-determined risk levels by combining
the extreme value analysis; this can generate risk consistent and more economical design
wind loads for the roof cladding. Furthermore, by introducing a load cycle counting
method, such as the rainflow count method, the system can provide the wind load cycles to
be used for fatigue design.
This chapter describes the components of the load evaluation system proposed by the
author. Although there are some problems to be investigated further, the results presented
here indicate that the proposed system is promising. In this chapter the subject is limited to
spherical domes and vaulted roofs. However, it is possible to apply the proposed method to
the cladding of any buildings, once the database of the statistics of wind pressures has been
constructed based on a wind tunnel experiment and/or CFD computations.
7. Acknowledgment
A part of the study is financially supported by Nohmura Foundation for Membrane
Structure’s Technology. The authors are much indebted to Dr. Takeshi Hongo of Kajima

Technical Research Institute and Dr. Hirotoshi Kikuchi of Shimizu Corporation for
providing them the wind tunnel test data. Thanks are also due to Mr. Raku Tsuruishi, Ms.
Miki Hamai and Chihiro Sukegawa, who were then graduate students of Tohoku
University, for assistance in constructing the neural networks.
8. References
Fahlman, S.E. (1988). Faster-learning variations on back-propagation: an empirical study,
Proceedings of the 1988 Connectionist Models Summer School, Morgan Kaufmann.
Fahlman, S.E. & Lebiere, C. (1990). The cascade-correlation learning architecture, Advances in
Neural Information Processing Systems, Vol. II, Morgam Kaufmann, pp. 524-532.
Kumar, K.S. & Stathopoulos, T. (1998). Fatigue analysis of roof cladding under simulated
wind loading, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 77&78,
pp. 171-184.
Kumar, K.S. & Stathopoulos, T. (1999). Synthesis of non-Gaussian wind pressure time series
on low building roofs, Engineering Structures, Vol. 21, pp. 1086-1100.
Kumar, K.S. and Stathopoulos, T. (2001). Generation of local wind pressure coefficients for
the design of low building roofs, Wind and Structures, An International Journal, Vol.
4, No. 6, pp. 455-468.
Lieblein, J. (1974). Efficient methods of extreme-value methodology, National Bureau of
Standards, U.S. Department of Commerce, NBSIR 74-602.
Nogchi, M.; Uematsu, Y. & Sone, T. (2003). Structural characteristics and wind resistant
design of spatial structures constructed in Japan, Eleventh International Conference on
Wind Engineering, pp. 1595-16002, Lubbock, Texas, USA, June 2-5, 2003.
Nogchi, M. & Uematsu, Y. (2004). Model of fluctuating wind pressures on spherical domes
for load estimation of cladding, Proceedings of the 18th National Symposium on Wind
Engineering, December 1-3, 2004, Tokyo, Japan, pp. 353-358 (in Japanese).
Uematsu, Y., Araki, Y., Tsuruishi, R. & Hongo, T. (2005). Wind load evaluation system for
cladding of spherical domes using aerodynamic database, neural network and
simulation, Proceedings of the 6th Asia-Pacific Conference on Wind Engineering, 12-14
September, 2005, Seoul, Korea (CD-ROM).

Wind Tunnels and Experimental Fluid Dynamics Research

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Uematsu, Y., Tsuruishi, R., Hongo T. & Kikuchi, K. (2007). A computer-assisted wind load
evaluation system for the design of cladding of spatial structures, Proceedings of the
11th International Conference on Civil, Structural and Environmental Engineering
Computing, 18-21 September, 2007, St. Julians, Malta (CD-ROM).
Uematsu, Y. & Tsuruishi, R. (2008). Wind load evaluation system for the design of cladding
of spatial structures, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 96,
pp. 2054-2066.
21
Monitoring of Soil Surface under Wind and
Water Erosion by Photogrammetry
Shigeoki Moritani et al.
*

Arid Land Research Center, Tottori University,
Japan
1. Introduction
Soil degradation resulting from accelerated water and wind-induced erosion is a serious
problem in drylands, and will remain so throughout this century. The detachment and
transport of soil particles degrade the fertility of agricultural land and consequently reduce its
productivity (Lyles and Tartako 1986 ).Many of the particles involved in soil erosion processes,
such as raindrops, wind velocity, soil aggregates, sediment, and siltation have characteristic
dimensions on the millimeter scale (Huang 1998). The addition of organic matter increases the
connection between aggregate by physical and chemical bounding. The strongly bonding
aggregation induces the increase of soil porosity and permeability, which result the decrease of
water erosion. The bigger aggregate also decrease the wind erosion due to their heaviness.
The modeling and quantification of such processes require detailed measurements of the
physical, chemical, and biological properties of soils (Soil Conservation Service 1976).

However, these measurements are too slow, tedious, and expensive for routine or regular
monitoring.
Several researchers have already used aerial photography to assess soil erosion. A precise
form of this photography, photogrammetry, has the advantage of very efficiently and cost
effectively providing detailed information about a large area. Together with aerial
photography, the use of remotely sensed data forms the basis for land use mapping and
change detection (Pellikka et al. 2004). In particular, for inaccessible areas, photogrammetry
is far superior to traditional ground surveys. The subsequent convergence in recent years of
photogrammetry and digital imaging technology has led to an increase in the use of digital
elevation models (DEMs) in modern studies involving the monitoring of landscape changes
(Prosser and Aberneathy 1996; DeRose et al. 1998).
The areas measured experimentally in microtopographical studies of soil erosion range from
1 to approximately 20 m
2
. In general, the DEMs used for analysis have grid resolutions of 1
to 15 mm (Elliot et al. 1997; Darboux and Huang 2003). A variety of instruments and
methods are used by soil scientists to acquire measurement coordinates, including
mechanical point gauges (Elliot et al. 1997) that make contact with the soil surface,

*
Tahei Yamamoto, Henintsoa Andry, Mitsuhiro Inoue, Taku Nishimura, Haruyuki Fujimaki,
Reiji Kimura and Hirotaka Saito
Arid Land Research Center, Tottori University, Japan

Wind Tunnels and Experimental Fluid Dynamics Research

448
optoelectronic measurement devices such as laser scanners (Huang et al. 1988; Darboux and
Huang 2003), and image processing techniques (Abd-Elbasit et al. 2008). Point gauges have
been widely replaced by laser scanners, because the former make contact with the soil and

can thus disturb it or sink into it (Römkens et al. 1988). While laser scanners have proven
their usefulness in many experiments, a photogrammetric system is more advanced,
comparatively cheaper, and provides images and morphological properties simultaneously
(Hodge et al. 2009; Chandler et al. 2005).
Automated digital photogrammetry allows DEMs to be generated with sufficient resolution
for microtopographical analysis. Jeschke (1990) applied correlation matching to soft-copy
images taken by a Zeiss SMK 40 camera to analyze soil microtopography. Recent advances
in digital image processing and camera calibration techniques make it possible to use the
digitized images taken by consumer-grade analog cameras to automate the generation of
DEMs (Brasington and Smart 2003; Abd-Elbasit et al. 2009) Some researchers, e.g., Chandler
et al. (2002) and Lascelles et al. (2002), have calibrated consumer-grade cameras and
employed the images taken with them to generate DEMs automatically on digital
photogrammetric workstations, which are becoming increasingly accessible to non-
photogrammetrists.
Analytical photogrammetry has often been used in geomorphological studies of gully and
rill formation (Elliot et al. 1997; Pyle and Richards 1997; Helming et al. 1998; DeRose et al.
1998; Pellikka et al. 2004; Rieke-Zapp and Nearing 2005). In these previous studies, the DEM
resolutions were generally produced from photographs taken under a no-rainfall condition,
i.e., the photographs were taken just before and after the rainfall and wind events (Rieke-
Zapp and Nearing 2005). Moreover, study reporting this method to monitor sheet and wind
erosions, which predominate in drylands, is relatively few. It is necessary to evaluate the
reliability of the DEM produced using either a camera and rainfall simulator or camera and
wind tunnel at the laboratory scale before field scale application. The purpose of this study
was to generate DEMs with high spatial and temporal resolutions from soil surfaces that
developed sheet and wind erosions. Digital photogrammetry was used to measure the
erosion rates and to monitor the evolution of the soil surface network under laboratory
simulated conditions.
2. Overview of the photogrammetry system
In order to study in three dimensions the soil surface evolution that results from water
erosion, a new automated photogrammetry system was developed by Tottori University’s

Arid Land Research Center (ALRC), in collaboration with Asia Air Survey Co., Ltd. Fig. 1
shows a flow chart of this photogrammetry system (Moritani et al. 2006).
Two Nikon D2H digital cameras were focused on the center of the target object, as shown in
Fig. 2. A focus length of 50 mm was used. The CCD sensor had a matrix of 2464 × 1632 picture
elements (pixels). The distance between two pixel centers, δ
CCD
, was 0.0094 mm. The memory
card used was capable of storing approximately 60 7.9-MB images, allowing the analysis to be
performed on uncompressed Tagged Image File Format (TIFF) images. A PC software program
was used to analyze the pictures taken by the D2H cameras. The inner orientation factor was
obtained from a calibration factor called the calibration field (CF), as shown in Fig. 3.
It is well known that even two cameras of the same type do not have exactly equal
characteristics such as the shape of the lens and the spatial arrangement of the CCD and lens
(Weng et al. 1992). This made inner orientation calibration necessary for each camera to
Using Digital Photogrammetry to Monitor
Soil Erosion Under Conditions of Simulated Rainfall and Wind

449
obtain more accurate DEM data. As shown in Fig. 5, the camera calibration was performed
using a three-dimensional calibration field (CF) with 32 well-distributed control points,
known with an accuracy of 0.2 mm. This CF was equipped with 20 square poles with three
different lengths, and 12 points on the planar table (which was placed between the square
poles by 3 horizontal lines). Pictures of the CF were taken by each camera from a fixed
distance, H (camera pair to object), of approximately 3.0 m. During this photography
process, the camera position was shifted parallel with the CF board to capture six multiple
images of the entire area of the image plane, including every corner of the image plane,
where there were large amounts of radial distortion. The least-square of the bundle
adjustment among these images was then used to determine the inner orientation
parameters, lens focus length, principal point offsets, and radial distortion (Hung and
Mitchell 1995; Rieke-Zapp et al. 2001; Abd-Elbasit et al. 2008).

Fig. 1. Flowchart of photogrammetry measurement.
Installing the digital image into PC

Determination of factors of inner
orientation

Creation of a pair of rectification
pictures
Point measurement
Surface measurement
3 dimensional measurements
Absolute orientation
Inner orientation
Determination of the DEM
Relative orientation

Wind Tunnels and Experimental Fluid Dynamics Research

450

Fig. 2. The layout of two cameras and object. Each dashed line is oriented direction by pair
of cameras

O
C
C’
P (x
1

y
1
)
P’ (x
2
y
2
)
l
l’
O
C
C’
P (x
3a
y
3
)
P’ (x
3b
y
3
)
Base line
X
1
Y
1
X
2

Y
2
X
3
Y
3
Image plane
Rectified plane

Fig. 3. Illustration of the coplanar condition and rectification. The object point O is projected
onto the image planes corresponding to P and P’ from different viewpoints of C and C’. The
coplanar is defined by the point O and the base line. l and l’are the epipolar lines, which are
the intersections of the coplanar and the two image planes (upper). The rectification
involves both image planes to be at the same coordinate system (X
3
Y
3
) and makes the y-axis
of P and P’ to be at the same position (
P and P
′
).
B
H
Left camera
Ri
g
ht camera
Object (soil box)
X

Y
Z
Using Digital Photogrammetry to Monitor
Soil Erosion Under Conditions of Simulated Rainfall and Wind

451
The gradient of the pair of pictures was adjusted to minimize the parallax, and then the
relative orientation was determined with the resulting points fixed on the x-axis. The result
of this process is called a rectified photograph. The relative orientation yielding the rectified
images was determined by a complicated equation based on a geometric consideration of
the coplanar condition (Fig. 3), in which the image points
P and P’ always lay on the
epipolar lines l and l’, respectively (Huang and Mitchell 1995; Heipke 1997). The rectification
required that both image planes used the same coordinate system (X
3
, Y
3
) and that the y-
axes of
P and P’ were at the same position ( P and P
′
). This reduced the search space for P
and
P’ from two dimensions to one, and thus increased the speed and reliability of the
matching (Jeong et al. 2004).
The three-dimensional calculation consisted of two methods: (1) point measurement and (2)
surface measurement. Point measurement was used for visual matching to acquire a limited
number of DEMs, while surface measurement was used to automatically calculate an
enormous number of dense DEMs such as for the contour line of a surface. In the point
measurement, as illustrated in Fig. 4, the cursor (shown as a ☆) was first moved onto a

reference pixel point selected in the left rectified picture. The corresponding cursor in the
right picture automatically followed along the y-axis to a position that matched that on the
left. Then, the cursor in the right picture was moved along the x-axis (epipolar line) to the
same corresponding point. Three-dimensional data were calculated based on the absolute
orientation from the
x
1
y
1
and x
2
y
2
coordinates of the image points (Fig. 3). In the case of
surface measurement, a quadrangular analytical frame was placed in each of the rectified
images. These frames were aligned as closely as possible to cover and represent the same
image area to reduce the matching error. Finally, approximately 16,000 pixels (shown as ○
marks) were calculated and automatically matched in a few seconds to acquire DEMs, based
on a coarse-to-fine matching strategy using multi-resolution representations, with a
Laplacian of Gaussian filter (Kim et al. 1997; Cruz et al. 1995).


Fig. 4. Three-dimensional measurement in rectified photograph. The marks of ☆ and ○ in the
figure indicate the measurement point used for point and surface measurement, respectively.
Left rectified picture
Right rectified
Y
3
X
3

Y
3
X
3

Analytical frame
☆
☆