|Software for Operational
Modal Analysis of the Infante D. Henrique Bridge
using SSI-UPC Merged Test Setups
This case study presents a new Operational Modal
Analysis made using the SSI-UPC Merged Test Setups algorithm available in
ARTeMIS Modal Pro.
Figure 1: 15 Test Setups of data from the Infante D. Henrique Bridge
analyzed with SSI-UPC Merged Test Setups estimator in ARTeMIS Modal Pro.
The Operational Modal Analysis of the Infante D. Henrique Bridge in Porto, Portugal
The results of an Ambient Vibration Test and
Analysis of the Infante D. Henrique Bridge are presented below. The
measurements have been made by Professors Alvaro Cunha and Filipe Magalhães,
Faculdade de Engenharia da Universidade do Porto,
Laboratory of Vibrations and Monitoring (http://paginas.fe.up.pt/vibest/),
Figure 2: The bridge seen upstream.
Figure 3: Downstream arial view of the
The Infante D. Henrique Bridge in Porto, Portugal
The Infante D. Henrique Bridge, over the Douro
River, was open to traffic in 2004 to link the cities of Porto and Gaia,
located at the north of Portugal. The bridge is composed of a rigid
prestressed concrete box girder, 4.50m deep, supported by a shallow and thin
reinforced concrete arch, 1.50 m thick. The arch spans 280 m between
abutments and rises 25 m until the crown. In the 70 m central segment, arch
and deck join to define a box girder 6m deep. The arch has constant
thickness and its width increases linearly from 10m in the central span up
to 20 m at the springs.
The Ambient Vibration Test
The ambient vibration test was made without
disturbing the normal use of the bridge, with accelerations induced by
traffic and wind.
To measure the very low amplitude accelerations, 4
tri-axial 18-bit strong motion recorders were used. During the ambient
vibration test, two recorders served as references located permanently at
the reference cross-section (see the blue arrows in figure 3) of the deck, in both sides of the
deck (upstream and downstream), while the other two recorders scanned the
bridge deck measuring the acceleration along the 3 orthogonal directions in
both sides of the 15 cross-sections. All sensor positions in all 15 test
setups can be seen in Figure 4.
For each test
setup, time series of 16 minutes were collected. The sampling frequency was
100 Hz, a value that is imposed by the filters of the acquisition equipment
and that is much higher than the required for this bridge. Most
of the relevant natural frequencies of the bridge are below 10 Hz. Therefore, a
decimation of order 5 was applied before the operational modal analysis,
reducing the sampling frequency from 100 Hz to 20 Hz.
Figure 4: The
displaying all sensors
of the 15 Test Setups.
The blue arrows are the
Modal Analysis using
SSI-UPC Merged Test
The algorithm is developed in cooperation with our
strategic partner - the French Institute National de Recherche en
Informatique et en Automatique (Inria). This algorithm can be applied in the
vast number of cases where several test setups have been measured using a
set of fixed positioned reference sensors and a set of rowing sensors being
moved across a structure from measurement to measurement.
The Algorithm in Short
The algorithm can be described by the following
The input to the algorithm is multiple time
series measurements (Test Setups) that typically are uploaded through
e.g. the SVS Configuration File.
Prepare Data Task in
ARTeMIS Modal Pro these measurements are then compressed into a set
of so-called Common SSI matrices. These matrices are then merged
together using a sophisticated scaling technique that utilizes the
information of the references sensors of the Test Setups. This scaling
technique is introduced to account for a potential change of vibration
level from measurement to measurement.
The estimation of modes are then performed
using a single Stabilization Diagram that displays the modal parameters
of the range of state space models being estimated. The estimation of
the state space models are made using the new fast implementation of the Crystal Clear SSI
estimator. The global modes are automatically estimated based on the
stable modes of the diagram by a single click on the Auto button.
After uploading the 15
Test Setups the Common
SSI matrices were
estimated using a Max.
Dimension of 300. This
high dimension has been
chosen because of the
very low frequency modes
of the data and the
large number of modes in
the data - The larger
number and lower
the modes are in
frequency the higher
dimension should be
Below the one and only
Stabilization Diagram is
shown. It displays the
Decomposition (SVD) of
the Spectral Densities
of all the Test Setups
with an indication of
all the global modes based
on all Test Setups. The
Crystal Clear SSI
estimator was applied
using a Max. No. of
setting of 66 that was
automatically chosen by
the algorithms, see the
first picture on this
page. The result is 25
global modes shown in
the table below:
Table 1: Estimated natural frequencies and damping
ratios, and corresponding estimated standard deviations.
Figure 5: Mode shapes of six of the estimated modes.
6: Modal Assusrance Criterion of all estimated modes.
Try SSI-UPC Merged Test
Setups On Your Own!
If you like to try the SSI-UPC Merged Test Setups
algorithm you can
download your own free
demo version of ARTeMIS Modal Pro. If you have any
questions to the usage please do not hesitate to get on contact with us at
M. Döhler, P. Andersen, L. Mevel
Operational Modal Analysis using a Fast Stochastic Subspace Identification
Proceedings of the 30th International Modal Analysis Conference (IMAC)
Jacksonville, Florida USA, 2012.
M. Döhler, P. Andersen, L. Mevel
Data Merging for Multi-Setup Operational Modal Analysis with Data-Driven SSI
Proceedings of the 28th International Modal Analysis Conference (IMAC)
Jacksonville, Florida USA, 2010.
A. & Caetano,
Dynamic monitoring of a long span arch bridge
Engineering Structures, Vol. 30, pp. 3034-3044