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MODELING THE NATURAL HEARBEAT OF REINFORCED
CONCRETE BUILDINGS IN METRO MANILA
Andres Winston C. Oreta
ABSTRACT: The natural heartbeat or period of vibration is an important
dynamic property of a building since it characterises the behavior and
performance of the structure to external forces. An estimate of the fundamental
period of a building is useful to a structural engineer, civil engineer or urban
disaster manager. The present study illustrates the use of neural networks in
estimating the period of reinforced concrete (RC) buildings. Data from ambient
vibration measurements conducted in medium-rise and high-rise buildings in
Metro Manila were used to train a neural network. A model for estimating the
period of RC moment-resisting space frame buildings and RC dual buildings,
using global building parameters - type of structural system and height of the
building - was developed and its performance was evaluated and compared with
existing empirical formulas.
KEYWORDS: period, building, reinforced concrete, ambient vibration, neural network
1. INTRODUCTION
The health of a human heart can be monitored by an electrocardiogram (ECG or
EKG).
Through the tracings of an ECG (Figure 1), the physician can identify important
parameters of the heart such as the heartbeat rate and other heart rhythms. Like
the
human being, a building also has its own rhythms. A building vibrates under
ambient
conditions or under severe
loading conditions such as
earthquakes. The building
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vibration can also be monitored
similar to an ECG and important
parameter may be extracted from
the these measurements. One
important parameter which can
be obtained from vibration
measurements of a building is
the period or the natural
Figure 1. An ECG Tracing heartbeat The fundamental period is a dynamic property
of a building which characterises the
behavior and performance of the structure to external forces. The natural period,
sometimes referred to as the natural heartbeat (Pacheco 1999) of the building,
can be
determined experimentally from vibration data recorded in instrumented buildings.
Depending on the type of vibration on the building, the natural period of a building
may
be classified as either (a) period at ambient condition; or (b) period at large-
amplitude
motions or seismic condition.
At ambient condition, the vibrations of the building are usually very small in
amplitude
and quite random in waveform. The vibrations are typically induced at the base or
foundation and some may be caused by wind which acts at the surrounding walls.
Pacheco (2001) describes that the underlying principle used to evaluate the
natural
period of a building using ambient vibration testing is that the prevailing ground-
borne
and wind-induced excitations in the building are composed of an almost infinite
number
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of harmonics with different periods of vibration, and every harmonic component
whose
period corresponds to a natural period of the building is amplified in the building
response, due to resonance. Ambient vibration tests generally have to be repeated
several times, preferably at different times of the day, to check the consistency of
the
results and to avoid recording unintentionally any occasional dominant forced
excitations. The natural period at ambient condition can not include the effect of
partial
cracking in reinforced concrete which usually occurs under large-amplitude
vibrations
during an earthquake.
The period at large-amplitude vibrations, on the other hand, are obtained in
buildings that
are shaken strongly but not deformed into the inelastic range (Goel and Chopra
1997)
during past earthquakes. Such data are scarce because relatively few buildings
have
accelerometers permanently installed and earthquakes are not that frequent. For a
building with the same height, the effective natural period of a building during an
earthquake is usually longer than at ambient condition due to the reduction of the
stiffness of the building caused by partial cracking of some structural elements such
as
beams and columns and cracking of non-structural members such as in-filled walls.
The natural period can be estimated from vibration time history by converting the
data
into the frequency domain as a spectrum. In most cases whether under ambient or
seismic
condition, a predominant peak which corresponds to a natural period of the building
can
be identified from the spectrum of the vibration history of a point in a building.
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The fundamental period of a building is useful to a structural engineer, civil
engineer or
urban disaster manager. The natural period is an important parameter in the
computation
of the design base shear and lateral forces due to earthquakes. Building codes
recommend
methods for estimating the period through an empirical equation or by a refined
dynamic
modeling and analysis (NSCP 2001). Improved formulas for possible code
applications
to estimate the fundamental periods of RC and steel moment-resisting frame
buildings
using data from more recent earthquakes in the Unites States have been developed
(Goel
and Chopra 1997). Alternative period formulas for estimating seismic displacements
have
also been recommended (Chopra and Goel 2003). The building period may be used
in
classifying a building population in an urban metropolis for the purpose of
earthquake disaster preparedness and mitigation. For example, the natural period
of buildings are
compared with a similar survey of ground natural periods to identify buildings with
periods very close to the ground which may result to resonance. The natural period
of a
building may be used also as a parameter in developing seismic capacity curves
that can
be used in building damage assessments based on a scenario earthquake in
densely
populated cities (Pacheco, Tanzo and Peckley 2003).
The present study introduces the application of neural networks in estimating the
period
of reinforced concrete (RC) buildings. Data from ambient vibration measurements
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conducted in medium-rise and high-rise buildings in Metro Manila were used to train
a
neural network. A model for estimating the period of reinforced concrete moment
resisting space frame (RC-MRSF) and reinforced concrete dual (RC-Dual) buildings,
using global building parameters : (a) type of structural system; and (b) height of
the
building, was developed and its performance was evaluated.
2. EMPIRICAL AND CODE FORMULAS
Empirical models for predicting the natural period of buildings are usually developed
by
deriving empirical equations using regression analysis. In this method, the form of
the
regression equation is assumed, e.g., T = H
, where and are determined by curve
fitting using the least squares method.
2.1 Code Period Formula
The National Structural Code of the Philippines (NSCP 2001), which has its reference
the
Uniform Building Code 1997, uses an empirical equation derived from the actual
behavior of buildings in California in past earthquakes. The equation, here referred
to as
Method A, has the following form:
T = Ct
H 0.75 (1)
where:
Ct
= 0.0853 for steel moment-resisting frames
Ct
= 0.0731 for reinforced concrete moment-resisting frames and eccentrically
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braced frames
Ct
= 0.0488 for all other buildings
H = height above the base to level n
2.2 Regression Equation from Ambient Vibration Survey
In a report on a survey of vibration characteristics of multistory buildings in Metro
Manila (NDCC-PHIVOLCS-ASEP Project Team 2001), regression equations, similar to
the NSCP equation, were derived using ambient vibration data of RC-MRSF buildings
and RC-Dual buildings. The coefficients, Ct , derived are as follows:
Ct
= 0.045 for RC-MRSF buildings, six stories and above
Ct
= 0.051 for RC-Dual Buildings
A comparison of the code and survey coefficients shows that the code equation will
result
to longer periods than the survey equation, particularly for RC-MRSF buildings.
Since the code equation coefficients were derived based on data of buildings whichwere
shaken by past earthquakes resulting to cracks in RC members reducing the
stiffness,
the code periods are usually longer. Surprisingly, the coefficient of the survey
equation
for RC-Dual buildings is larger than the code coefficient for other buildings. The
applicability of the code coefficient for other buildings may have limitations; that
is
why the code provides an alternative value for Ct
for structures with concrete or masonry
shear walls where the area of the shear wall in the first story is a parameter.
Lumping
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buildings not belonging to steel moment-resisting frames, reinforced concrete
momentresisting frames and eccentrically braced frames to one group as other
buildings may
not be practical.
3. AMBIENT VIBRATION SURVEY OF BUILDINGS IN METRO MANILA
Seventy two buildings, majority of which have reinforced concrete moment resisting
space frame (RC-MRSF) and reinforced concrete dual (RC-Dual) structural systems,
were surveyed by the Philippine Institute of Volcanology and Seismology
(PHIVOLCS),
in collaboration with Japanese research groups from Kanto Gakuin University led by
Prof. Norio Abeki and Tokyo Institute of Technology lead by Prof. Saburoh
Midorikawa
from 1998 to 1999 (NDCC-PHIVOLCS-ASEP Project Team 2001). Small-amplitude
vibrations of medium-rise to high-rise buildings in Metro Manila under random,
ambient
conditions were measured using portable instruments installed at various buildings.
The
natural periods of vibration of each building along either or both the longitudinal
and
lateral direction of the floor plan of the building were extracted from spectral
analysis of
the recorded vibration histories. Although different survey equipment and
methodologies
were employed Abeki measured displacement and neglected torsional effects,
while
Midorikawa measured velocity and considered torsional vibrations both methods
yielded consistent fundamental natural periods, with similar trends, taller buildings
having longer periods. However, the longitudinal and lateral periods of the same
building
can be very different. The results of the survey of buildings for this project were
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envisioned to be used in assessing the general trend of seismic vulnerability of
buildings
around Metro Manila.
4. NEURAL NETWORK MODELING
4.1 Neural Network Architecture and Implementation
An ANN is a collection of simple processing units or neurons connected through
links
called connections. The topology or architecture of a three-layer feed-forward
neural
network may be presented schematically, as in Figure 2. The neural network is
represented in the form of a directed graph, where the nodes represent the neuron
or
processing unit, the arcs represent the connections with the normal direction of
signal
flow is from left to right. The processing units may be grouped into layers of input,
hidden and output neurons. The neural network in the figure consists of two input
neurons, two hidden neurons and one output neuron. The main tasks of neurons are
to
receive input from its neighboring units which provide incoming activations,
compute an
output, and send that output to its neighbors receiving its output. The strength of
the
connections among the processing units is provided by a set of weights that affect
the magnitude of the input that will be received by the neighboring units. These set
of
weights are determined by presenting the network a set of training data and using a
training algorithm such as the back-propagation neural network (BPNN) algorithm
(see
Freeman and Skapura 1991), the weights are updated until a stable set of weights
are
obtained.
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4.2 Experimental Data
The present study uses the results of the survey for RC-MRSF buildings and RC-Dual
buildings. The information available for each building in the report by
NDCCPHIVOLCS-ASEP Project Team (2001) are general location, structural system,
number
of floors, height of building and the fundamental natural periods in the lateral and
longitudinal directions. The building height was estimated from the number of floor
levels multiplied by an average floor height which is assumed here as equal to 3.5
m. The
estimated periods for the lateral and longitudinal vibrations are not always the
same since
the stiffness of the building in any direction is affected by various factors such as
dimension of building, existence of shear walls or CHB walls. The difference
between
the longitudinal and lateral periods ranges from 0.01 s to 0.85 s. Since no
information
about the lateral and longitudinal dimensions of the buildings is available, then the
input
parameters used in the ANN modeling to estimate the period are limited to thefollowing
available data; (a) type of structural system; and (b) height of the building. It is
assumed
that the building dimension is not a
significant factor in the period of
the building. This may be true for
buildings which are fairly regular
in plan and for those with rigid
floor diaphragms. To eliminate the
possible effect of building
dimension in the estimation of the
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period, the data for buildings with
the difference between
longitudinal and lateral periods
greater than 0.2 s were not
included. Hence the number of
data of buildings used was reduced
from 72 to 47.
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0
2
4
6
8
10
12
5 15 25 35 45 55 65 75 85 95 105
RC-Dual RC-MRSF
COUNT
HEIGHT (m)
Figure. 3. Histogram of Building Data
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Bldg. Height
Bldg. Type
Bldg. Period
Hidden
Layer
Input
Layer
Output
Layer
Figure 2. A three-layer feed-forward neural network Using the lateral andlongitudinal periods separately of the 47 buildings results to 94 sets
of data with 68 for RC-MRSF buildings and 26 for RC-Dual buildings. A histogram of
the building data used with respect to height is shown in Figure 3. The RC-MRSF
buildings were generally 70 m or about 20 stories or lower, while the RC-Dual
systems
ranges from 60 m to 110 m in height or about 20 to 30 stories. The data were
divided
randomly into two subsets a training set of 70 data and a testing set of 24 data.
4.3 Neural Network Architecture
A three-layered feed-forward neural network model (Figure 2) is used. The neural
network considered in the study consists of two inputs: (a) height of the building;
and (b)
type of structural system. The building height is in meters, while the type of
structural
system has a value of either 1 for RC-MRSF or 2 for RC-Dual. The output is the
natural
period at ambient conditions in seconds. The number of hidden nodes is varied and
the
simplest model which is found to be acceptable is selected.
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4.4 Network Data Preparation
The raw experimental data need to be pre-processed or normalized by scaling to
improve the training of the neural network. To avoid the slow rate of learning near
the
end points specifically of the output range due to the property of the sigmoid
function
which is asymptotic to values 0 and 1, the input and output data were scaled
between the
interval 0.1 and 0.9. The linear scaling equation : y =( 0.8 / ) x + ( 0.9 0.8 xmax /
)
was used in this study for a variable limited to minimum (x
min) and maximum (x
max )
values. The minimum and maximum values of the building height are 7 m and 119
m,
respectively while the period varies from minimum of 0.1 s to a maximum of 2.5 s.
The
numerical values, 1 and 2, corresponding to the type of structural system were also
normalized to 0.1 (RC-MRSF) and 0.9 (RC-Dual).
4.5 A Neural Network Model for Predicting Natural Periods of RC Buildings
4.5.1 Selecting the Model
ANN simulations were
conducted by varying the
number of hidden layer
nodes (2 to 4 nodes) and the
BPNN learning algorithm
parameters such as the
learning parameter (0.5 1.0), momentum parameter (0.005 0.05) and number of
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epochs or cycles (1,000 4,000 cycles). A noise of 0.01% was also added to the
data.
The different networks were compared with respect to the error metrics such as
mean
average error (MAE), root mean square error (RMSE), average percent error and the
Pearson product moment correlation coefficient, R. Based on the comparison of
networks with different number of hidden layer nodes, the neural network with two
hidden layer nodes, which will be referred to as the T221 model, is the simplest
model
and has the best MAE, RMSE and R for the test data of the combined RC-MRSF and
RC-Dual buildings. Table 1 presents the connection weights for this model.
Table 1. Connection Weights of T221 Model
H idden Ou tpu t
No des Bldg . He ig ht B ldg . T yp e N ode
1 -4.451696 1.074989 -5.239752
2 -3.587910 4.178850 1.130453
Input NodesUsing eqn. (2), the neural network output, y, can be computed using
normalized inputs,
xi
, the computed weights, wji (connection weights between input nodes and hidden
layer
nodes) and wkj(connection weights between hidden layer nodes and output node).
(2)
The activation function, f [ ], in this case, is the sigmoid function f(z) = 1/ (1 + e-z ).
The
output of the network is a value between 0.1 and 0.9 and can be converted to
period in
seconds using the linear scaling equation in Sect. 4.4.
4.5.2 Performance of the T221 Model
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The performance of the T221 model in predicting the natural period at ambient
conditions is evaluated with respect to the error metrics as shown in Table 2. The
error
metrics, MAE, RMSE and percent error are shown for various cases such as
predictions
for RC-MRSF buildings or RC-Dual Buildings for the training data only, test data only
or
combined data. The mean percentage error for RC-MRSF buildings and RC-Dual
buildings for the combined training and test data are about 39% and 23%,
respectively.
The error metrics for the combined data for RC-MRSF and RC-Dual buildings for the
training data only, test data only or combined data are also shown in the last
column of
Table 2.
Table 2. Summary of Prediction Errors of T221 Model
RC-MRSF Bldg Data RC-DUAL Bldg. Data Combined Data
Training Data Only
MAE (s) 0.19 0.30 0.22
RMSE (s) 0.22 0.33 0.26
Average Percent Error 37.43 23.83 33.74
Percent < 30% Error 60.78 68.42 62.86
Test Data Only
MAE (s) 0.15 0.35 0.21
RMSE (s) 0.17 0.39 0.26
Average Percent Error 43.38 20.52 36.71
Percent < 30% Error 58.82 85.71 66.67
Combined Training and Test Data
MAE (s) 0.18 0.31 0.22
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RMSE (s) 0.21 0.35 0.27
Average Percent Error 38.91 22.94 34.50
Percent < 30% Error 60.30 73.08 63.83
Figure 4 shows the histogram of the percentage error of the predictions of the T221
model for RC-MRSF buildings and RC-Dual buildings. More than 60% of the
predictions
for RC-MRSF buildings have a percentage error less than 30%; while more than 70%
of
the predictions for RC-Dual buildings have a percentage error less than 30%.
( ( )) i
x
ji f w kj y = f
w
Figure 5 and Figure 6 show the comparison of the predictions of the T221 model
and
the survey regression equation with respect to the experimental values for RC-MRSF
and
RC-Dual buildings, respectively. The Pearson product moment correlationcoefficients,
R, is a measure of the linear relationship between the predicted and experimental
data
sets an R value equal to 1.0 means the predicted and experimental values are
equal. The
R values of the T221 model are slightly better than the R values for the survey
equations
(NDCC-PHIVOLCS-ASEP Project Team 2001). The R value of the T221 model for
RCMRSF buildings is about 0.7849 for the combined training and test data, as
compared to
R = 0.7793 for the survey regression equation. On the other hand, the R value of
the
T221 model for RC-Dual buildings is about 0.5023 for the combined training and test
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data, as compared to R = 0.4871 for the survey regression equation. The R value
for the
combined training and test data for both RC-MRSF and RC-Dual buildings is about
0.85
for the T221 model.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
RC-MRSF
T221 (Training Data)
T221 (Test Data)
Predicted Period (s)
Experimental Period (s)
T221 (R=0.7849)
0
0.2
0.4
0.6
0.8
1
1.2
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1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
RC-MRSF
Survey Regression Eqn. (R=0.7793)
Predicted Period (s)
Experimental Period (s)
(a) (b)
Figure 5. Predictions for RC-MRSF Buildings. (a) T221 model; (b) Survey Regression
Eqn
0
5
10
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15
20
0 20 40 60 80 100 120 140 160 180
RC-MRSF
Training Data
Test Data
Count
Percent Error (%)
T221 Model
0 2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100
RC-DUAL
Training Data
Test Data
Count
Percent Error (%)
T221 Model
Figure 4. Percentage Error of T221 Neural Network Predictions The performance of
the T221 model with respect to the parameter, building height, is
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compared with respect to the empirical models derived using regression analysis.
By
setting the input for building type as constant, either 1 or 2, and varying the input
for
building height, the neural network predictions of the natural period at ambient
conditions as a function of height can be derived as shown in Figure 7. Shown in the
figure also are the curves corresponding to the survey regression equation and the
code
equation. Plotted also in the figure are experimental periods obtained from the
survey.
The trend of the T221 predictions when compared to the regression equations is the
same
taller buildings have longer periods however there is a gradual decrease in the
slope
of the T221 curve as the height increases. The predictions of the T221 model are
also
slightly larger than the survey regression equation for most RC-MRSF buildings and
for
heights less than about 95 m for RC-Dual buildings..
0
0.5
1
1.5
2
0 10 20 30 40 50 60 70 80
RC-MRSF
NSCP (2001)
Survey Regression Eqn.
T221
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Survey Expt. D ata Natural Period (s)
Building Height (m)
0
0.5
1
1.5
2
50 60 70 80 90 100 110 120 130
RC-DUAL
NSCP (2001)
Survey Regression Eqn.
T221
Survey Expt. Data
Natural Period (s)
Building Height (m)
(a) (b)
Figure 7. Natural Period with Respect to Building Height
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5
RC-DUAL
Survey Regression Eqn. (R=0.4871) Predicted Period (s)
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Experimental Period (s)
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5
RC-DUAL
T221 (Training Data)
T221 (Test Data)
Predicted Period (s)
Experim ental Period (s)
T221 (R=0.5023)
(a) (b)
Figure 6 Predictions for RC-Dual Buildings. (a) T221 model; (b) Survey Regression
Eqn. As expected, the code predictions for RC-MRSF buildings are greater than the
neural
network model and the survey regression equation since the code equation was
derived
from large-amplitude vibrations of buildings in the US during past earthquakes. The
effective natural periods of buildings during earthquakes become longer due to the
reduction of the stiffness of the building caused by partial cracking of some
structural
elements such as beams and columns and cracking of non-structural members such
as infilled walls. On the other hand, a comparison of the predictions for RC-Dual
buildings
using the neural network model, survey regression equation and the code equation
shows
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that the curves are nearly coincident, although the T221 predictions are slight
larger at
heights less than about 95 m. How come the periods at ambient condition and the
code
periods which are based on large-amplitude vibrations are almost similar needs
further
investigation. However, it must be noted here that the code equation used in the
Figure
7(b) is the one specified for all other buildings. Obviously the code equation for
all
other buildings has limitations and its applicability to RC-Dual buildings needs to be
clarified. Incidentally, the code provides an alternative value for Ct
for structures with
concrete or masonry shear walls where the area of the shear wall in the first story is
a
parameter.
Figure 8 shows the curves of the seismic coefficient, C, using base shear equations
of the
NSCP (2001) and the corresponding periods predicted using the T221 model and the
code equation for an RC-MRSF building with specified base shear parameters. As
expected, the seismic coefficients using ambient vibration periods (T221) are larger
than
the NSCP since the predicted periods are smaller when compared to the code
periods.
Pacheco (2001) suggested, for tentative comparison between code periods and
ambient
vibration periods, multiplying the ambient vibration period of about 1.3 to account
for the
increase in period due to the reduction of stiffness when partial cracking occurs in
RCMRSF under seismic conditions. The seismic coefficient for the adjusted period is
shown
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as the middle curve in Figure 8. The base shear computation using the adjusted
ambient
vibration periods of the T221 model resulted to values less than the ambient
vibration
periods but slightly larger than the base shear using code periods; hence larger
lateral
forces and a conservative design is obtained. Base shear computation using the
adjusted
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 10 20 30 40 50 60 70 80
RC-MRSF
NSCP (2001)
T221
1.3 * T221
Base Shear Parameters
Z=0.4, I=1.0, R=3.5,
Na=1.0, Nv=1.0, Ca=0.44, Cv=0.64 Seismic Coefficient (C=V/W)
Building Height (m)
Figure 8. Seismic Coefficient with Respect to Building Height ambient vibration
periods may be considered as an upper bound for RC-MRSF
buildings in this example.
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5. CONCLUSIONS
An alternative approach in estimating the natural period of RC buildings at ambient
conditions was presented using ANNs. One advantage of neural network modeling is
that
there is no need to know a priori the functional relationship among the various
variables
involved, unlike in regression analysis. The ANNs automatically construct the
relationships for a given network architecture as experimental data are processed
through
a learning algorithm. The present study illustrates the capability of neural networks
in
estimating the period of reinforced concrete (RC) buildings using data from ambient
vibration measurements conducted in medium-rise and high-rise buildings in Metro
Manila. Because of the limited information of the vibration data, only two input
parameters were considered - type of structural system and height of the building -
in
developing an ANN model for estimating the period of RC moment-resisting space
frame
(MRSF) buildings and RC dual buildings. If more information become available from
vibration survey of buildings such as building dimension, length of walls, type of
soil,
etc., increasing the number of input parameters in an ANN model for predicting the
natural period of a building can be done easily by simply modifying the neural
network
architecture.
REFERENCES
Chopra, A.K. and Goel, R. K. (2003). Building period formulas for estimating
seismic
displacements, http://ceenve.calpdy.edu.goel/research/period
%20formula/eeri_period.pdf
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26/27
Freeman, J. A. and Skapura, D.M. (1991). Neural Networks: Algorithms,
Applications, and
Programming Techniques, AddisonWesley, Reading, Mass. , USA, pp. 89-125
Goel, R. K. and Chopra A. K. (1997). Period formulas for moment-resisting frame
buildings. J.
Structural Engineering, American Society of Civil Engineers, 123 (11), 1454-1481,
New York.
National Structural Code of the Philippines (NSCP 2001) , Volume 1. 5th ed.,
Association of
Structural Engineers of the Philippines (ASEP), Manila
NDCC-PHIVOLCS-ASEP Project Team (2001). Survey of vibration characteristics of
about 100
multistory buildings, February 26, 2001, Report submitted to PHIVOLCS, Quezon
City
Pacheco, B. M. (1999). Why every building needs an electrocardiogram, Phil.
Civil Engineering,
Phil. Institute of Civil Engineers, Vol. 2, July-Dec. 1999, pp. 66-74, Quezon City
Pacheco, B. M. (2001). The natural heartbeat of 100 buildings in Metro Manila,
Proc. JapanPhilippine Workshop on Safety and Stability of Infrastructures against
Environmental Impacts,
University of the Philippines, Quezon City , Sept. 10-13, pp. 33-46
Pacheco, B. M., Tanzo, W. T. and Peckley, Jr. D.C.(2003). Survey of experts
judgement on seismic
capacity of selected building types in Metro Manila using the Delphi Technique,
Proc. 10th ASEP
International Convention -Art & Science of Structural Engineering, Vol. 2, pp. 593-
620, Quezon
City
ACKNOWLEDGEMENT
The author expresses his sincere thanks to the University Research Coordination
Office (URCO) of De La
7/30/2019 Modeling the Natural Hearbeat of Reinforced
27/27
Salle University for supporting this research. Thanks also to PHIVOLCS for sharing
the ambient vibration
data of the project: Survey of Vibration Characteristics of about 100 Multistory
Buildings.