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Design and Implementation of Scalable Wireless Sensor Network for Structural Monitoring


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An integrated hardware and software system for a scalable wireless sensor network WSN is designed and developed for structural health monitoring. An accelerometer sensor node is designed, developed, and calibrated to meet the requirements for structural vibration monitoring and modal identification. The nodes have four channels of accelerometers in two directions and a microcontroller for processing and wireless communication in a multihop network. Software components have been implemented within the TinyOS oper-ating system to provide a flexible software platform and scalable performance for structural health monitoring applications. These components include a protocol for reliable command dissemination through the network and data collection, and improvements to software components for data pipelining, jitter control, and high-frequency sampling. The prototype WSN was deployed on a long-span bridge with 64 nodes. The data acquired from the testbed were used to examine the scalability of the network and the data quality. Robust and scalable performance was demonstrated even with a large number of hops required for communication. The results showed that the WSN provides spatially dense and accurate ambient vibration data for identifying vibration modes of a bridge.
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Design and Implementation of Scalable Wireless Sensor
Network for Structural Monitoring
Shamim N. Pakzad1; Gregory L. Fenves2; Sukun Kim3; and David E. Culler4
Abstract: An integrated hardware and software system for a scalable wireless sensor network WSNis designed and developed for
structural health monitoring. An accelerometer sensor node is designed, developed, and calibrated to meet the requirements for structural
vibration monitoring and modal identification. The nodes have four channels of accelerometers in two directions and a microcontroller for
processing and wireless communication in a multihop network. Software components have been implemented within the TinyOS oper-
ating system to provide a flexible software platform and scalable performance for structural health monitoring applications. These
components include a protocol for reliable command dissemination through the network and data collection, and improvements to
software components for data pipelining, jitter control, and high-frequency sampling. The prototype WSN was deployed on a long-span
bridge with 64 nodes. The data acquired from the testbed were used to examine the scalability of the network and the data quality. Robust
and scalable performance was demonstrated even with a large number of hops required for communication. The results showed that the
WSN provides spatially dense and accurate ambient vibration data for identifying vibration modes of a bridge.
DOI: 10.1061/ASCE1076-0342200814:189
CE Database subject headings: Sensors; Design; Implementation; Networks; Monitoring.
Structural health monitoring SHMis a rapidly developing field
encompassing the technology and algorithms for sensing the state
of a structural system, diagnosing the structure’s current condi-
tion, performing a prognosis of expected future performance, and
providing information for decisions about maintenance, safety,
and emergency actions Farrar 2001; Doebling et al. 1996; Lynch
and Loh 2006. Advances in micro-electro-mechanical-systems
MEMStechnology in the past decade provide opportunities for
sensing, wireless communication, and distributed data processing
for a variety of new SHM applications. There have been several
prototypes of sensor networks, emphasizing the sensing devices,
such as Wang and Pran 2000, Westermo and Thompson 1997,
and Zimmermann 1999; wireless communication, such as Ihler
et al. 2000, Paek et al. 2005and Pei et al. 2005; and data
processing for SHM, such as Williams and Messina 1999,
Strubbs et al. 1999, and Sohn and Farrar 2000. The rapid
reduction in physical size and cost of MEMS-based wireless sen-
sors has driven increased interest in the scalability of wireless
sensor networks WSNto hundreds or even thousands of nodes.
While the current research in SHM has made substantial
progress, the scalability of the WSN for structural monitoring
applications has not been thoroughly investigated or demon-
strated. Wireless communication is essential for scalability be-
cause installation and maintenance of a monitoring system with a
wired or tethered communication network would be too expen-
sive and complex for hundreds to thousands of nodes. Scalability
of a wireless sensor network involves the sensors, data acquisition
and processing, and wireless communication. A scalable network
is one that can be expanded in terms of the number of sensors,
complexity of the network topology, data quality e.g., sampling
rate, sensor sensitivity, and amount of data while the cost of the
expansion installation and operational cost, communication time,
processing time, power, and reliabilityis no worse than a linear,
or nearly linear, function of the number of sensors. WSN scalabil-
ity needs to consider an integrated view of the hardware and
software. For hardware, scalability involves sensitivity and range
of MEMS sensors, communication bandwidth of the radio, and
power usage. The software issues include reliability of command
dissemination and data transfer, management of large volume of
data, and scalable algorithms for analyzing the data. The com-
bined hardware-software issues include high-frequency sampling,
which is necessary for structural health monitoring, and the
tradeoffs between on-board computations compared with wireless
communication between nodes. Addressing these problems is es-
sential for the application of WSN beyond laboratory prototypes
to the scale needed for structural monitoring applications.
Wireless sensor networks have been developed for a variety of
purposes that range from low duty-cycle, low-power environmen-
tal monitoring applications, such as described by Mainwaring et
al. 2002and Tolle et al. 2005, to high-fidelity applications
accurate measurements, high sampling rate, lossless communica-
tionfor monitoring of mechanical and structural systems.
Mastroleon et al. 2004examined the architecture of a wireless
1Doctoral Student, Dept. of Civil and Environmental Engineering,
Univ. of California, Berkeley, CA 94720 corresponding author. E-mail:
2Professor, Dept. of Civil and Environmental Engineering, Univ. of
California, Berkeley, CA 94720.
3Doctoral Student, Dept. of Electrical Engineering and Computer
Sciences, Univ. of California, Berkeley, CA 94720.
4Professor, Dept. of Electrical Engineering and Computer Sciences,
Univ. of California, Berkeley, CA 94720.
Note. Discussion open until August 1, 2008. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and pos-
sible publication on April 9, 2007; approved on June 8, 2007. This paper
is part of the Journal of Infrastructure Systems, Vol. 14, No. 1, March 1,
2008. ©ASCE, ISSN 1076-0342/2008/1-89–101/$25.00.
system for SHM with an emphasis on low-power multisensor
modular units. Ruiz-Sandoval et al. 2006developed a MEMS-
based accelerometer and strain sensor board for a WSN for struc-
tural health monitoring using Mica motes for communication and
control. Maser et al. 1996described the field deployment of a
wireless sensor network on a highway bridge. The wireless trans-
ceiver used one-hop communication with a base station, and the
base stations were interconnected using cellular telephony. Lynch
et al. 2003examined the quality of data from a seven-node
wireless network with MEMS accelerometers by comparison with
conventional wired accelerometers. Lynch et al. 2005presented
the deployment of 14 wireless sensors to monitor forced accelera-
tion response of Geumdang Bridge in Korea. These studies have
been advances in wireless sensor networks for structural health
monitoring, but since the systems rely on one-hop wireless com-
munication between a sensor and a base station, the studies do not
address the question of scalability.
The objective of this paper is to present the design, develop-
ment, and large-scale deployment and testing of a scalable wire-
less sensor network for structural health monitoring. The key
technology innovations are: 1a new approach for maximizing
the effective network bandwidth with a large number of commu-
nication hops; and 2reliable command dissemination and data
transfer for high-frequency sampling, all using a low-power mi-
crocontroller and radio. Both aspects use multihop communica-
tion between nodes, which is essential for scalable networking
because the radio power required for single-hop communication
in a large network is impractical. The first section of the paper
presents the requirements and design for the WSN architecture,
describes the hardware and software components, and summa-
rizes the calibration of the system. The second section describes
the network topology and deployment of the scalable WSN for a
long-span bridge, analyzes the network performance, and presents
ambient vibration data of the bridge. The third section describes
the algorithms used to analyze the data and presents information
about the spatial sampling of the vibration properties of the
bridge. The paper concludes with recommendations for achieving
scalability in wireless sensor networks.
Wireless Sensor Network Architecture
The first step in designing a sensor network is deciding on the
physical quantities to measure. In the case of a structure as a
dynamic system, the measurement of acceleration is the most
straightforward, but is recognized that acceleration is an indirect
function of damage and structural condition. Although sensing
displacement is possible using global positioning system GPS
technology, for example, the reliability, accuracy, and sampling
rate are not yet sufficient for many applications, particularly those
needing high-frequency sampling of small displacements. Strain
measurements could provide a direct measure of damage, but the
installation, operation, and interpretation of reliable strain sensors
on a large structure is difficult. Consequently, accelerations pro-
vide useful information about structural vibration characteristics,
so they are adequate for the primary goal of this investigation,
which is to examine the scalability of wireless sensor networks.
For bridge applications, the accelerometer range should be large
enough to capture 12 gduring an earthquake, yet they should be
sensitive enough to measure ambient vibrations due to wind and
traffic on the order of tens to hundreds of g.
The network must be designed for fast sampling rates for tem-
poral scalability, and reliable command dissemination and data
collection over many nodes to provide spatial scalability. Consid-
ering the sampling rate for accelerations or other structural re-
sponse quantities, the lower vibration frequencies of a structure
are generally on the order of 10−1–10+1 Hz, but higher sampling
rates are desirable for two reasons. Local features of response are
characteristic of much higher vibration frequencies and, second,
high-frequency sampling can be used to reduce noise and increase
the signal-to-noise ratio Oppenheim and Schafer 1999. High-
frequency sampling, however, complicates time synchronization
of nodes over the network and may generate large volumes
of data that need to be managed, processed, and possibly
Another design requirement is that the network must have high
communication reliability to transmit data and disseminate com-
mands without loss of information packet loss. Particularly for
rare events, such as an earthquake, data loss is not acceptable. For
ambient vibration applications, data loss would have the affect of
increasing the noise, which would make modal identification
more difficult. In this work the requirement of no data loss is
High-frequency sampling, multihop communication, and reli-
able data transmission are stringent requirements. The following
subsections provide details about how the hardware and software
components of the scalable WSN are designed to address these
Sensor Node Hardware Design
The network consists of a set of sensor nodes, and each node has
three main hardware components, sensors, filters and microcon-
troller, and radio for wireless communication. Fig. 1 is a sche-
matic of the major components of a node. For the measurement of
low-level and high-level accelerations, two commercially avail-
able MEMS accelerometer sensors are used each in two directions
one horizontal and one vertical. The use of two sensor types is a
cost-effective solution and allows examination of performance-
price tradeoffs. The high-level sensor is Analog Device’s
ADXL202, a widely used device that provides a ±2 grange with
a sensitivity of 1 mg at 25 Hz Analog Devices 1999. For low-
level ambient vibrations, a Silicon Design 1221L provides accept-
able sensitivity for ambient structural vibrations at a relatively
low cost Silicon Designs 2007. Tests show that the Silicon De-
sign accelerometers have a hardware noise ceiling of 10 g
Fig. 1. Schematic diagram of sensor node
Pakzad and Fenves 2004.Pakzad et al. 2005, which is small
enough to resolve signals with amplitude of a few hundreds of
Each channel from the MEMS accelerometers provides an
analog voltage that is fed to a single-pole anti-aliasing low-pass
filter with a cutoff frequency of 25 Hz. The filter was set for a
long-span bridge application because even very high vibration
modes have frequencies well below the anti-aliasing filter. The
filtered analog signal is fed to a 16-bit analog-to-digital converter
ADCfor each of the four channels. Sampling is done at a high
frequency 1 kHz, but the digitized signal is downsampled by
averaging, which acts as a digital filter and reduces the Gaussian
noise level by a factor of n, when every nsample is averaged.
This analog anti-aliasing filter at 25 Hz, high-frequency sampling
at 1,000 Hz, and downsampling to 50 Hz provide a simple
and power-efficient approach for high-resolution acceleration
For each node, a mote with a microcontroller provides local
processing and storage capability and a low-power radio commu-
nication. The MicaZ mote was selected because it has a good
tradeoff between processing and communication capability, and
power requirements Crossbow 2007a. The MicaZ has 512 kB
flash memory, which can store up to 250,000 2-byte data samples,
and a 2.4 GHz radio-frequency RFChipcon CC2420 transceiver
with a hardware interface that can support commercially available
bi-directional antennas. The ability of the mote to connect with a
bi-directional antenna was an important factor because the long-
span bridge application required a linear topology and a standard
omni-directional antenna would have wasted a significant amount
of radio power.
Power consumption is a critical factor in scalability of wireless
sensor networks. To analyze power for the sensor node with the
MicaZ mote, Fig. 2 shows the power draw for the major compo-
nents of the node in various operational modes based on a 9 V
power source. The power consumption of the sensor board
MEMS sensors, anti-aliasing filters, and ADCis more than
twice that of the MicaZ mote. This is a result of a design decision
made to use a single power regulator for the node. An improved,
but more complex, hardware design would have separate power
regulators for the sensors and mote, thus allowing the mote to
operate while the sensors are in a sleep mode. Fig. 2 shows that
the mote draws a significant portion of power while idle because
the radio is in a listening mode. The broadcast mode only in-
creases the power consumption by about 10%. The test data were
consistent with the specification sheet that estimates that the radio
uses 62 mW in the listening mode versus 57 mW in broadcast
mode Chipcon Products 2007. Based on the power usage testing
of the node, it was decided to use four 6 V lantern batteries to
provide 12 V and 15 A-h in the deployment.
An alternative to the MicaZ mote would have been iMote2,
which has similar functionality as MicaZ but consumes more
power. Crossbow 2007a,bestimates power consumption of
24 mW for MicaZ in active mode with an 8-bit bus size and
8 MHz clock speed versus 139.5 mW for iMote2 with 32-bit bus
size and 12 MHz clock speed. The greater computational power
of iMote2, however, does not make a critical difference in the
performance of the node for the bridge testbed application. The
power consumption was the principal factor in the selection of the
System Software
The system software for a scalable wireless sensor network
is based on the TinyOS operating system TinyOS 2007an open-
source, framework for programming Mica motes Hill et al.
2000. TinyOS is multilevel component-oriented software that
supports a wide variety of applications for wireless sensor net-
works. Low-level components perform basic tasks, and higher-
level components use sequences of low-level components to
achieve more complex functionality while maintaining efficiency
and simplicity of coding. The components range from providing
simple diagnostic operations such as turning an indicator light
emitting diode LEDon/off, to sophisticated components for
routing of data packets in a self-configuring wireless communica-
tion network. With this background, Fig. 3 shows the system
software architecture and the main components of the TinyOS
operating system and application layer that were developed or
adapted for scalable structural health monitoring. The important
components are discussed in the following subsections.
Multihop Communication
A focus of the recent work on WSN has been on multihop com-
munication. Multihop communication is the transfer of data and
commands between two nodes that are not in the direct radio
range, using intermediary nodes. Multihop communication is es-
sential for scalability of low-power wireless sensor networks be-
Fig. 2. Power consumption of sensor node in operational modes
Fig. 3. Software architecture of TinyOS components for reliable and
high-frequency sampling wireless network
cause single-hop networks are spatially limited by the radio range
and cannot span long distances without a large power supply.
However, multihop presents major challenges to several aspects
of a WSN. The routing of data packets in a single-hop network
only needs a queue for all of the nodes to transmit their packets
directly to a base station. In a multihop network, routing is more
complex because each node has to determine how to find the most
efficient way to forward packets to the base station and coordinate
transmission of packets received from other nodes. The routing
needs to reconfigure dynamically for robustness if a node fails
and is no longer able to serve as an intermediary such as because
of radio interferencefor multihop communication.
One of the most important aspects of a multihop network is
establishing and updating the routing information typically re-
ferred to as routing tables or chartsfor each node to communi-
cate with the base station. The TinyOS component MintRoute
Woo et al. 2003provides multihop connectivity in the wireless
network. MintRoute establishes the routing of packets by mini-
mizing the power cost of the multihop travel of a packet from a
generating node to the base station, subject to a constraint on
minimally acceptable transmission quality for each one-hop link.
If a link falls below a threshold quality level, MintRoute seeks an
alternative route that bypasses the weak link with the minimum
power requirement. The TinyOS component GenericComm pro-
vides low-level communication between a node and one nearby
node that requires the least amount of power Hill et al. 2003.
The component Broadcast Buonadonna 2003builds upon Ge-
nericComm to provide radio connectivity between the two nodes.
Data Pipelining
Each node in a multihop network has two functions. Its first func-
tion is to generate data by sampling and sending data packets to
the base station through the network. A node also acts as an
intermediary relay by receiving data packets generated by other
nodes and passing them towards the base station. Spatial reuse of
network bandwidth is essential for a scalable multihop network.
Bandwidth reuse by pipelining means that several nodes in addi-
tion to the one that generated the data, transmit packets at the
same time within a network. Although this increases the amount
of data communicated within the network, pipelining must be
designed so that the nodes transmitting simultaneously do not
interfere with each other. Single-hop networks cannot reuse band-
width because only one node broadcasts at any time to the base
station. Pipelining significantly increases the effective bandwidth
of large networks by maintaining a higher throughput for the net-
work regardless of the number of hops.
Fig. 4 illustrates how pipelining allows packets from a node to
travel through different parts of the network at the same time, thus
increasing the effective bandwidth of the network. The parameter
Knumber of hops between transmitting nodes. If K=n, where
nnumber of hops in the route, there is no pipelining and the
sender waits until the first packet is received by the base station
before sending another packet. As Kdecreases, pipelining reuses
more of the bandwidth, but with an increased potential for radio
interference. The interference causes a higher rate of packet loss
and data retransmission, thus reducing bandwidth. In the limit, K
has a lower bound of 3 because radio interference would jam the
network if K=2, and K=1 is not possible.
For a multihop network without pipelining K=nthe total
transfer time for mpackets from a sender that is nhops away
from the base station is mnT, where Ttransfer time of one
packet for one hop. Pipelining with a length Kreduces this time
to n+mKKT. The effective bandwidth of a network with a
pipeline length of Knto a network without pipelining K=nis
Fig. 4. Transfer time for n-hop network using pipelining
bandwith with pipelining
bandwith without pipelining =
n+mK KT
mK +nK
The increase in bandwidth is significant for a network with large
number of hops, n, and using a small pipeline length K.
To provide spatial reuse of bandwidth in a multihop wireless
sensor network, Kim et al. 2006developed a new TinyOS com-
ponent for data pipelining. The length Kis selected based on the
link quality and radio interference. In this application, Kis set
when the routing table is established and held constant. Addi-
tional work by Kim et al. 2006extends pipelining to set the
optimal value of Kin different parts of a network dynamically.
Reliable Data Communication
Even with multihop routing and data pipelining in a wireless sen-
sor network, data packets will be lost because of electromagnetic
interference and collision of packets that arrive at a node at the
same time. In many applications it is not critically important if a
small percentage of packets are lost, but for SHM it is vital to
have a protocol that guarantees reliable transmission of data be-
cause features of the response characteristics may be affected by
data loss. Furthermore, for monitoring critical events such as an
earthquake, data loss is also unacceptable because of the value of
the information. The challenge is to provide reliability with mini-
mal network resources, in terms of computation and memory, and
hence power. To satisfy the requirement of reliable data commu-
nication, a new protocol, scalable thin and rapid amassment with-
out loss Strawwas developed, tested, and deployed. It is a
selective negative-acknowledgement NACKcollection protocol,
in which the data transfer is always initiated by the receiver. The
sender transmits the data when it is requested by the receiver, and
the receiver then identifies and returns a list of missing packets
back to the sender. The sender retransmits those packets again
until all packets are received. Straw provides reliable data transfer
when the sender and receiver are separated by an arbitrary num-
ber of communication hops Kim et al. 2007.
Time Synchronization and Jitter Control
Multihop networks have to perform time synchronization. In a
single-hop network this is a trivial task since the base station
sends a start command and all of the nodes receive it virtually at
the same time. The roundtrip communication time from a node to
the base station over multiple hops needs to be accurately esti-
mated for efficient transmission, recognizing that the time is non-
deterministic in a multihop network. This problem is addressed by
a global synchronized clock mechanism with time stamping and
regression algorithms Maróti et al. 2004.
Jitter is the distortion of a signal caused by variance in the
time-sampling interval as a result of poor synchronization. Ying
et al. 2005explains how accurate jitter control is essential for
high-frequency sampling, since asynchronous data can produce
errors in identifying the mode shapes of a structural system. As
illustrated in the schematic shown in Fig. 5, there are two sources
of jitter: temporal and spatial. Temporal jitter occurs at a node
when the sampling intervals are not uniform due to uneven clock
ticks, event handling, or other hardware bias. Spatial jitter is the
time-synchronization error between different nodes, which occurs
because of uncertainty in estimating latency in propagating a glo-
bal time across the network and the drift of the clock at a node.
To provide time synchronization in a network by controlling
jitter, a TinyOS component named flooding time-synchronization
protocol FTSPis used. FTSP propagates the global time gener-
ated by the base station through the network by a series of hand-
shakes between adjacent nodes, until the entire network is in the
same time zone. Experiments by Maróti et al. 2004show that
the protocol limits the spatial jitter to 67 s over a network of 59
nodes and 11 hops. High-frequency sampling and logging can
increase this jitter, so Kim et al. 2007performed a jitter analysis
and the tests showed that the temporal jitter using the Timer com-
ponent of TinyOS is limited to 10 s for a sampling rate of up to
6.67 kHz. For a harmonic signal of 25 Hz, the highest frequency
of interest in the current application, this time synchronization
error causes a maximum 0.16% error in the measured value of the
signal. For an ambient acceleration signal of 10 mgamplitude,
the jitter is equivalent to 16 gnoise level, which falls below the
sensitivity of the MEMS accelerometers.
The jitter analysis of the nodes with FTSP provided insight
into the limitations of the motes for a WSN in structural health
monitoring. While the MicaZ microcontrollers are faster than the
flash memory, other microcontroller tasks are delayed because of
sampling, which is a time-consuming operation and thus blocking
computation and communication. Using multiplexed ADC with
its own clock would marginally limit temporal jitter, but at the
cost of consuming additional power for the separate clock. A
faster microcontroller would have smaller jitter but still have the
same fundamental problem that would need to be addressed.
Network Control
For structural health monitoring, Kim et al. 2007developed an
application named Sentri, based on TinyOS, for high-level control
of a wireless network from a base station. The control program
consists of two components: one for the individual nodes and the
second one for the base station. The node software allows the
mote to listen to the network, join the network, control the sensor
board sampling, filtering, logging, and be a sender/receiver for
multihop communication. It is designed for a very small memory
footprint because of the limited resources for the motes. The base
station control software has more functionality for sending inquir-
ies to all nodes in the network, evaluating connectivity and com-
munications, and executing commands on parts or the entire
Testing and Calibration
The sensor nodes, network, and the system software were tested
by several laboratory and field experiments to determine sensitiv-
ity of the sensors, communication reliability and bandwidth, and
the robustness of the system components. Pakzad et al. 2005
describe these tests, which included quiet-environment tests to
determine the noise floor of the MEMS accelerometers, shaking
table tests to asses the accuracy of the sensors over a wide fre-
quency range, and a variety of field tests to study the multihop
networking and reliable data collection components. Each sensor
node was individually calibrated by a rotary tilt table and shift
and scale factors for converting the ADC output to acceleration
were determined for all channels.
Full-Scale Deployment on Long-Span Bridge
Long-span, suspension bridges have been the subject of study for
structural health monitoring because they are important physical
infrastructure and can have unique vibration properties and re-
sponse to earthquake ground motion. As two examples of studies
using data from wired sensors, Smyth et al. 2003examined the
Vincent Thomas Bridge in the 1987 Whittier and 1994 Northridge
earthquakes with linear and nonlinear system identification tech-
niques to develop a multiinput, multioutput dynamic model of the
bridge using data from 26 accelerometer sensors on the super-
structure and the footings. Abdel-Ghaffar and Scanlan 1985a,b
used spectral densities and ambient vibration data caused by wind
and traffic and collected at 28 locations on the span and a tower of
the Golden Gate Bridge to estimate vibration frequencies and
mode shapes of the bridge.
Building upon the Abdel-Ghaffar and Scanlan study, the
Golden Gate Bridge was selected for the full-scale deployment of
the scalable wireless sensor network described in the previous
sections. The bridge has a main-span 1,280 m, two side-spans
342.9 m, and two towers 210.3 m above the water level. The
objective of the WSN deployment was to identify the vibration
characteristics of the main span and the south tower. The deploy-
ment on the Golden Gate Bridge provided the opportunity to test
the WSN in a difficult environment and with a linear topology
that required a large number of hops for communication.
Fig. 6 shows the instrumentation plan for the bridge with a
total of 64 nodes, 56 on the main span measuring transverse and
vertical accelerationand eight on the South Tower measuring
transverse and longitudinal acceleration. On the main span 53
nodes were deployed on the west side, and three nodes on the east
side. Each main span node was attached to the top flange of the
floor girder directly inside of the cable. Fig. 7 shows a node with
the bidirectional antenna, along with the clamps and guy wires for
temporary installation of the testbed. The node spacing on the
west side was selected based on the range of the radio with a
majority of nodes placed 30.5 m apart, but at places where an
obstacle obstructs a clear line of sight this distance was reduced to
15.25 m. The three nodes on the east side, added in the second
phase after changing the batteries, were located at the two quarter
spans and the midspan of the bridge. The east side nodes have
radio communication with the west side nodes under the roadway
deck. For the South Tower, there is a node on each side of each
strut. The tower nodes have a clear line of sight between them and
hence have greater radio range than the main-span nodes. The
node on the west side of the strut above the superstructure collects
data from all the nodes on the tower and transmits them to the
network on the main-span.
Installation of the network began on July 14, 2006 and the last
set of data was collected on September 22, 2006. The 512 kB
flash memory of each node can buffer about 250,000 samples of
data, which can be allocated to any combination of the five sensor
channels on the node four accelerometers and a temperature sen-
sor. Each run starts with a pause to synchronize the network and
disseminate a command to start sampling at a future time. After
the scheduled sampling takes place there is a pause to establish
the network routing. The recorded data are then transferred from
Fig. 5. Spatial and temporal sources of jitter
Fig. 6. Instrumentation plan for 56 nodes on main span of the Golden Gate Bridge
each node to the base station using the reliable data communica-
tion and pipelining. A complete cycle of sampling and data col-
lection for the full network produces 20 MB of data and takes
about 9 hours. There were a total of 174 such runs during the
deployment. This total includes runs where the network was being
installed and tested so all of the collected data sets do not contain
data from all of the nodes.
The network was fully installed on the west side of the main
span and the south tower on August 1, 2006 and 13 sets of data
were collected with the first set of batteries. At the time of chang-
ing batteries on September 22, 2006, the nodes on the east side of
the main span were installed and three more sets of data collected.
The runs include a variety of combinations of sensor channels,
which always included the two low-level Silicon Design 1221
accelerometers, but the other two high-level ADXL202 acceler-
ometers and the temperature sensor were turned off in some of the
runs to reduce the volume of the data or increase the sampling
Ambient Vibration Data
As an example of the ambient vibration data, the vertical accel-
erations from the low-level accelerometers in a typical run 174
are shown in Figs. 8–10 for the three quarter points on the main-
span. The sampling frequency was 50 Hz over 1,600 s, resulting
in 80,000 samples per channel. Each figure includes plots of the
signal and the power spectral density PSDusing the Welch
method Welch 1967.
The amplitudes of the ambient accelerations are about
±10 mg, but spikes of up to 50 mgare apparent, presumably
caused by heavy vehicles traveling on the roadway. The PSD
plots show clear and consistent peaks at frequencies at several
nodes. These spectral peaks are distinct in lower frequencies.
Twenty peaks are visible in the frequency plots, which correspond
to vertical and torsional vibration mode shapes of the bridge, as
will be shown later. The PSD plots indicate that the low-
frequency noise level is very small compared with the peaks of
the spectra the power of the noise is about two orders of magni-
tude smaller than the power at peak frequencies.
Wireless Network Performance
Three aspects of the wireless communication performance for the
network were examined empirically using data from the bridge:
effective bandwidth, loss rate, and average network bandwidth.
These three metrics are important indications of network quality
and are critical to scalability of the network. The effective band-
width is defined as the amount of data per unit time that is sent to
the base station from a node n-hops away. Fig. 11 shows the
effective bandwidth based on empirical measurements of network
performance for four different runs. The one-hop bandwidth of
about 1,200 bytes/s is reduced by each additional hop because
each node has to receive, buffer, and transmit the packets in the
communication stream. A pipeline length of K= 5 was established
for the network, so the effective bandwidth remains relatively
constant for nodes that are beyond the fifth node up to the 45th
hop, which was the deepest hop of the network. These results
show that the data pipelining is very effective for producing a
constant effective bandwidth in a large multihop network.
Considering communication packet loss and retransmission,
Fig. 12 plots the loss rate versus hop count for four runs. Al-
though the loss rate increases as hop count goes up, it is less than
2.5% for 45 hops, which means that the effective volume of trans-
mitted data from the deepest node in the network is only in-
creased slightly due to packet loss. The figure also shows the loss
rate for the four runs compared with the estimated loss rates for
different values of pipeline length. Using a smaller pipeline length
increases the effective bandwidth but the volume of transmitted
data increases because interference causes higher losses and more
retransmission. In the current deployment K=5 provides a good
balance between effective bandwidth and loss rate.
Another measure of performance is the average network band-
width, defined as the average amount of data collected during a
run per unit time. Fig. 13 shows this metric during the 2-month
deployment. In the installation phase only a few nodes were op-
Fig. 7. Node with its battery pack and bi-directional antenna on main
span of the Golden Gate Bridge
Fig. 8. Time-history and power spectral density for vertical sensor at
west-side south 1/4-span run 174, node 64
erational, and the average network bandwidth was dominated by
the effective bandwidth of nodes that are close to the base station.
When additional nodes were being installed and the network de-
bugged, the average bandwidth fluctuated based on which part of
the network was operational and how far the nodes were from the
base station. When the entire network was operational, the aver-
age bandwidth stabilized at 550 bytes/s, taking full advantage of
pipelining. In summary, the empirical data on bandwidth and
packet loss in a large-scale deployment show that the pipelining
of data is very effective in providing a constant and reliable ef-
fective bandwidth for a large number of hops.
Analysis of Vibration Modes
Although the vibration modes of a structure, particularly the
lower modes, are not very sensitive indicators of the health of a
structure Doebling et al. 1998, they are useful measures to study
the quality of data acquired in the WSN. The ambient vibration
data from the Golden Gate Bridge is used to estimate modal prop-
erties using off-line modal realization methods. The analysis ex-
amines the repeatability of the data and the effect of a spatially
dense sensor network on estimated modal properties.
Modal Identification Methods
The continuous-time dynamic system can be modeled by a
multiinput-multioutput MIMOsystem. The system reacts to the
input signals x1,...,xp, and produces response signals y1, ...,yq.
A multi-degree-of-freedom mass-damper-spring system is an ex-
ample of such a system and can be mathematically modeled by
where M=mass matrix; C=damping matrix; K=stiffness matrix;
Ut=displacement vector; and Ft=external forces.
The objective of the system identification process is to esti-
mate properties of the system transfer function Hs, using the
observed input and output response.
A system identification method using multivariate autoregres-
sive models ARXis used in this study to estimate modal prop-
erties of the bridge Ljung 1999. The multivariate ARXM,N
consists of Mautoregressive matrices and Nexogenous matrices
Fig. 9. Time-history and power spectral density for vertical sensor at
west-side midspan run 174, node 78
Fig. 10. Time-history and power spectral density for vertical sensor
at west-side north 1/4–span run 174, node 45
Fig. 11. Effective bandwidth of wireless sensor network with
pipelining for four runs
where Aqand Bq=autoregressive- and exogenous operators in
discrete time domain, respectively; and Hq=Bq/Aq
=discrete system transfer function. The discrete functions y
n, and e
n=output, input, and noise vectors, respectively,
where y
nT0, and T0=sampling period. This
equation can be rewritten in time domain as
The discrete-time input and output vectors are p- and
q-dimensional vectors x
n=x1nx2n¯xpn兲兴Tand y
=y1ny2n¯yqn兲兴T.Aiare qqmatrices of AR coefficients
while Biare qpcoefficient matrices of exogenous terms. The
noise vector e
nis assumed to be independent and identically
distributed IID. For a MIMO system with measured input and
output signals, i.e., known as x
nand y
nfor n=1,2,...,k,a
number of computational algorithms to estimate Aiand Biparam-
eters are described in Ljung 1999. Stochastic output-onlysys-
tems are special cases of this general model, and when the input
can be reasonably assumed to have characteristics of white noise,
an equivalent autoregressive ARor autoregressive with moving
average ARMAmodel can be used Peeters and Roeck 2001.
The computational steps for determining the parameters in both
cases are similar to that of ARX methods Juang and Phan 2001.
After the modal vibration properties are identified, modal
phase collinearity MPCis used to distinguish actual modes from
spurious ones that are an artifact of the computation. Vibrations of
different parts of a structure in a classical normal mode are mono-
phase, i.e., the difference between their phases is either 0 or .
MPC is a measure to quantify this monophase behavior Pappa
et al. 1993. The MPC value for a mode is close to unity for a
noise-free set of data. In this study, a cutoff MPC of 0.90 is
chosen; however, most of the selected modes have MPC values of
above 0.95.
Modal Results for Main-Span
With a 50 Hz sampling rate, the signals have a Nyquist frequency
of 25 Hz, but analyzing a large system in this frequency range
requires a very high-order model. To reduce model order and
concentrate on important vibration modes of the main-span below
5 Hz, the signals were low-pass filtered off-line with a Chebychev
Type-II filter with a 5 Hz cutoff frequency and then downsampled
accordingly. Figs. 14–17 show several estimated vertical and tor-
Fig. 12. Network loss rate versus hop count using pipelining for four
runs compared with theoretical rates with K-nodes pipelining
Fig. 13. Average network bandwidth for individual runs of wireless
sensor network
Fig. 14. Estimated vertical mode shapes of main span for four data
sional modes with frequencies in the 05 Hz frequency band.
The various vibration mode estimates shown in the figures are
used to evaluate the repeatability of the information in the ambi-
ent vibration data.
With a high spatial resolution network on the main-span of the
bridge, it is possible to examine how the spatial sampling affects
the repeatability of identified vibration properties. Two aspects of
node configuration are examined studying relation to the repeat-
ability of modal information: spatial density of the network and
shift in node locations. To study spatial repeatability, the modal
properties using different data sets with different spatial densities
are compared. For shift repeatability, the modal properties from
two different data sets with the same number of nodes but at
different locations are compared with reference modal properties
estimated using the full network data.
Three modes in vertical and torsional directions are used to
examine the effect of spatial resolution in estimated vibration
properties: Modes 1, 11, and 23 in the vertical direction, and
torsional modes 1, 8, and 18. These modes represent the lower,
middle, and higher range of identified frequencies in each direc-
tion. Figs. 14 and 15 show the mode shapes, frequencies, and
damping ratios of four sets of data. Each set of data consists of a
series of nodes: six nodes in the smallest set, ten nodes in the
second set, 20 nodes in the third set, and 49 nodes in the largest
set. Each set includes three nodes on the east side of the main-
span, and the remaining nodes are on the west side. The east-side
nodes are included to distinguish between vertical and torsional
modes. The data sets used in spatial repeatability analysis are
increasing in size with the doubling of nodes for each subsequent
set. The solid lines in the figures are fitted splines to the 49-node
data set, which are considered the reference mode shapes. Figs.
14 and 15 show that the mode shapes from all data sets are con-
sistent with the reference shapes. Furthermore, the estimated
frequencies are comparable. On the other hand, the estimated
damping ratios decrease as the number of nodes used in the sys-
tem identification increase. This is because the damping estimate
is sensitive to measurement noise. As the number of data points
increases, the model certainty improves, the effect of noise de-
creases, and hence the damping ratio estimate decreases.
Repeatability with respect to the location of the nodes gives a
different measure of consistency of the collected data, because
mutually exclusive data sets with similar sizes can be selected to
compare their vibration contents. Using data sets with similar
sizes makes the effect of measurement noise in estimated param-
Fig. 15. Estimated torsional mode shapes of main span for four data
sets Fig. 16. Estimated vertical mode shapes of main span for shifted
data sets
eters equal. Additionally, using mutually exclusive data sets guar-
antees that the compatibility of the estimated modal properties by
each set is because they independently reflect the vibration prop-
erties of the bridge. Two sets of 20 nodes are selected, where the
two sets only share one node at the midspan and all other nodes
are between 15.25 and 30.5 m apart from each other such that one
set is a shifted version of the other set. The same three modes in
vertical and torsional directions are considered in Figs. 16 and 17.
The plots show shift repeatability in the data, and the estimated
frequencies and damping ratios of the two sets match each other
and the mode shapes are consistent with the reference mode shape
estimated using the full record.
The design, implementation, and deployment of a wireless sensor
network for structural health monitoring applications has pro-
vided new information about the scalability and performance of
the network. Hardware components were developed to provide
the range and sensitivity for sensing acceleration from strong mo-
tion as well as ambient structural vibration. Software components
were developed for the TinyOS operating system for reliable
command dissemination and data collection and spatial reuse of
network bandwidth is implemented through pipelining. Time syn-
chronization for high-frequency sampling is provided by modify-
ing TinyOS components to limit total network jitter.
The performance of the network is analyzed during the testbed
deployment on a long-span bridge. The data on network perfor-
mance confirm the effectiveness of spatial reuse of radio band-
width through pipelining in maintaining a scalable network. The
quality of ambient structural vibration data is investigated by
studying the repeatability of the estimated modal properties of the
structure with variable numbers and locations of the nodes. The
estimated structural modal properties are consistent as the number
of nodes increases. The scalable WSN enables a high spatial den-
sity network, which makes it possible to identify higher modes of
vibration with greater accuracy. The identified modes are also
consistent for data sets with different configuration of nodes that
independently reflect the vibration properties of the bridge.
Tests and analysis of the hardware and software provided valu-
able insight in designing real-time WSN for SHM and a roadmap
to future work. In order to guarantee a real-time system that can
instantly react to commands and triggers, two main principles
should be observed in the architecture of software and hardware.
First, the operating system needs to be capable of supporting mul-
tiple threads to avoid delays of computation and communication
tasks while sampling data from the sensors. Second, the hardware
needs to be equipped with a separate microcontroller that is dedi-
cated to sampling job, to let a sampling-only process be enforced.
This is clearly an extra component in the hardware architecture,
which results in more power usage by the node, but is a necessary
feature for a real-time WSN. The addition of a second microcon-
troller also provides more computational power to the node,
which can be used for in-network processing to reduce the vol-
ume of transmitted data and transform the WSN from a sensing/
routing entity to a parallel computing unit as well.
This paper reflects the advice and guidance of Professor James
Demmel and Professor Steven Glaser, who participated and sup-
ported the research. The writers provide special thanks to the staff
and management of Golden Gate Bridge District, in particular
Dennis Mulligan and Jerry Kao, for their close cooperation in
every step of the project. Jorge Lee provided extraordinary help in
the deployment, which made this project possible. Thanks to Tom
Oberheim who helped design and develop the sensor board. This
research is supported by the National Science Foundation under
Grant No. EIA-0122599 and by the Center for Information Tech-
nology Research in the Interest of Society CITRISat the Uni-
versity of California, Berkeley.
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... However, the laboratory studies utilized a wired data acquisition system and were based on simplifying the traffic loading as a harmonic function, whereas real traffic-induced bridge responses consist of impulsive signals. To fill these gaps in the knowledge and transfer this technology from the laboratory to the field for long-term bridge fatigue crack monitoring, this paper presents two critical novelties: (1) by integrating the SEC with the Xnode sensing platform, a wireless large-area strain sensor (WLASS) is created to wirelessly collect the large-area strain data to support fatigue crack monitoring; (2) an effective automated algorithm is developed based on wavelet transform to process the traffic-induced bridge response data consisting of numerous impulsive peak events for monitoring fatigue crack growth. The remainder of this paper is organized as follows. ...
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There has been a major push over the past 2 decades toward the adoption of wireless communications within structural monitoring systems as a means of reducing cost and enhancing deployment modularity. Specifically, wireless sensor networks (WSNs) are an empowering sensing platform that can be used to simplify and reduce the cost of structural monitoring systems. At the same time, they provide additional functionality including on-board data processing. This chapter provides a detailed overview of WSN for structural health monitoring (SHM) applications. This chapter provides a complete description of the operational principles of WSN. Included in this chapter are discussions on network architectures, wireless node hardware, and distributed embedded software. Although rapidly maturing and reaching commercialization, research opportunities still exist in the fields of data and power management which are discussed as this chapter culminates.
Wireless sensors are a rapidly maturing technology well suited for installation in large-scale civil engineering structures. When compared with wired counterparts, wireless sensors enjoy lower costs and less complex installations making them attractive to many structure owners. Given the important role bridges play in transportation systems, the cost advantages of wireless sensing are especially attractive to the bridge engineering community. This chapter reports on five deployments of wireless structural monitoring systems on operational bridge structures. The aim of the chapter is to highlight noteworthy case studies that have advanced the state of the art in wireless monitoring. First, two early short-term deployments are presented including a dense wireless monitoring system on the Golden Gate Bridge in California and a smaller deployment on the Stork Bridge in Switzerland. Next, two long-span bridges (Jindo Bridge, Korea, and the New Carquinez Bridge, California) are presented where long-term deployments have been made possible based on hardening the wireless sensing hardware and resolving power constraints. The last case study on the Telegraph Road Bridge in Michigan presents a permanent wireless monitoring system deployed on a short-span slab-on-girder highway bridge for assessment of structural performance and health. In all of the studies presented, the hardware and software design of the wireless system is highlighted along with lessons learned from short- and long-term deployments.
With more than 600,000 highway bridges, 46.4% of which rated as fair and 7.6% rated in poor condition, United States is one of those countries in which the installation of reliable bridge health monitoring systems is strategically necessary to minimize and optimize repair and rehabilitation costs and to prevent failures. In this review paper, a synthesis of the scientific literature relative to the SHM systems installed in some U.S. bridges over the last 20 years is presented. This review aims to offer interested readers a holistic perspective of recent and current state-of-the-art in bridge health monitoring systems and to extract a “general paradigm” that is common to many real structures. The review, conducted through a comprehensive search of peer-reviewed documents available in the scientific literature, discusses several bridges in terms of the instrumentation used, scope of the monitoring, and main outcomes.
Integrated structural health monitoring (SHM) uses the mechanism analysis, monitoring technology and data analytics to diagnose the classification, location and significance of structural situations (e.g., sudden or cumulative damages) to ensure the functionality and operation of bridges. Integrated SHM systems have improved the maintenance, management and decision-making of bridges by continuously monitoring and evaluating working conditions. This review article discusses the current process and future trends of bridge monitoring focusing on the cutting-edge SHM technologies, transmission and analytics methods of the sensing data, and prediction and early-warning models. In particular, four extensively applied sensing technologies (i.e., fiber optic sensors, piezoelectric sensors, global navigation satellite system and magnetostrictive sensors) are reviewed and compared, the wireless data transmission approaches (i.e., ZigBee, Bluetooth, NB-IoT, Wi-Fi, LoRa) are discussed, the artificial intelligence-based data processing methods are presented, and the performance prediction and early warning systems are summarized. In the end, the challenges and future research avenues of the current integrated SHM systems are discussed with respect to the characteristics of bridges.
The online strain acquisition is highly desired for structural monitoring of key equipment such as aircrafts or high-speed trains. However, there are still enormous challenges to monitor full-field strain in large area with arbitrary shape, especially when the non-contact approaches are not applicable. In this study, we firstly develop an optimization design principle for arbitrary-shape-adaptable sensor array with scalable circuit layout, and then a hierarchical printing strategy by direct-ink-writing is proposed to enable simultaneous monitoring in large-scale area or multiple domains. According to the design principle and printing strategy, the proof-of-concept sensor arrays (e.g. with 8 × 8 and 4 × 16 grids) are designed and printed by bottom-up hierarchies from the layered components (e.g. wires, filaments and isolation intervals) to the main arrays through distributed printing sub-arrays (4 × 4 grids). In particular, the strain field surrounding a hole is monitored in high-precision based on the present strain sensor. This work also provides insights of sensor array from adaptive design to high-efficient DIW-fabrication for other applications including wearable electronics, small-batch equipment and individual medical devices.
Effective measurement and monitoring of certain parameters (temperature, pressure, flow etc.) is crucial for the safety and optimization of processes in the Oil and Gas Industry. Wired sensors have been extensively utilized for this purpose but are costly, not best suited for harsh environments and are difficult to deploy and maintain. Wireless Sensor Network Solutions is revolutionizing the Offshore Oil and Gas industry providing evolving solutions that introduces significant benefits in cost, ease of deployment, flexibility and convenience. The adoption of Wireless Sensor Networks is expected to be tremendous in industrial automation owing to a report that projected the deployment of 24 million wireless-enabled sensors and actuators worldwide by 2016. With limited literature on this specific subject matter, this paper presents a critical survey into oil industry monitoring specifications, requirements and Wireless Sensor Network applications as it directly impacts the Oil and Gas Industry. An overview of Wireless Sensor Networks is presented, applications from literature are highlighted and finally challenges and existing solutions are discussed.
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In recent years, there has been an increasing interest in the adoption of emerging sensing technologies for instrumentation within a variety of structural systems. Wire- less sensors and sensor networks are emerging as sensing paradigms that the structural engineering field has begun to consider as substitutes for traditional tethered monitoring systems. A benefit of wireless structural monitoring systems is that they are inexpensive to install because extensive wir- ing is no longer required between sensors and the data acquisition system. Researchers are discovering that wire- less sensors are an exciting technology that should not be viewed as simply a substitute for traditional tethered monitor- ing systems. Rather, wireless sensors can play greater roles in the processing of structural response data; this feature can be utilized to screen data for signs of structural damage. Also, wireless sensors have limitations that require novel system architectures and modes of operation. This paper is intended to serve as a summary review of the collective experience the structural engineering community has gained from the use of wireless sensors and sensor networks for monitoring structural performance and health.
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Industrialised nations have dedicated significant investments toward the development of civil infrastructure. To preserve this investment, attention must be given to proper maintenance. Structural Health Monitoring (SHM) has emerged as a tool to support this task. Networks of smart sensors, built upon wireless communication, have the potential to significantly improve SHM. Numerous platforms for smart sensors have been developed, most of which utilise proprietary hardware/software. The Berkeley Mote, utilised in this study, was the first open hardware/software platform to be developed. However, the Berkeley Mote was designed for generic applications and therefore the available sensors are not optimised for use in civil infrastructure applications. Acceleration and strain are among the most important physical quantities to judge the health of a structure. Although commercially available sensor boards have accelerometers, their applicability towards civil infrastructure is limited. This paper presents the development of new acceleration and strain sensor boards based on the Berkely-Mote platform and provides experimental verification of their performance within civil infrastructure applications.
Conference Paper
A combination of linear and nonlinear system identification techniques is employed to obtain a reduced-order, multi-input-multi-output (MIMO) dynamic model of the Vincent Thomas Bridge based on the available acceleration measurements of the structure to the 1987 Whittier and 1994 Northridge earthquakes. Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non-proportional damping) as well as quantitative measures of the extent and nature of nonlinear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identification procedure, the apparent nonlinearities in the system restoring forces are quite significant, and they contribute substantially to the improved fidelity of the model. Also shown is the potential of the identification technique under discussion to detect slight changes in the structure’s influence coefficients, which may be indicators of damage and degradation in the structure being monitored. Difficulties associated with accurately estimating damping for lightly damped long-span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identified mathematical models of structural systems with the broadest range of validity.
Dynamic characteristics such as natural frequencies, mode shapes, and damping ratios of the Golden Gate Bridge tower were determined using ambient vibration data. The ambient vibration tests involved the simultaneous measurement of longitudinal and lateral vibrations of the main tower (San Francisco side). Measurements were made at different elevations of the tower and on the pier, at a total of 10 stations. Good modal identification was achieved by special deployment and orientation of the motion-sensing accelerometers and by summing and subtracting records to identify and enhance definition of longitudinal, torsional, and lateral vibration modes of the tower. A total of 46 modal frequencies and modal displacement shapes of the tower were identified: 20 longitudinal, 15 torsional, and 11 lateral, all in the frequency range of 0.0- 5.0 Hz. Finally, comparison with previously computed two- and three-dimensional mode shapes and frequencies shows good agreement with the experimental results, thus confirming both the accuracy of the experimental determination and the reliability of the methods of computation.
Extensive experimental investigations were conducted on the Golden Gate Bridge in San Francisco, California, to determine, using ambient vibration data, parameters of major interest in both wind and earthquake problems, such as effective damping, the three-dimensional mode shapes, and the associated frequencies of the bridge vibration. The paper deals with the tests that involved the simultaneous measurement of vertical, lateral, and longitudinal vibration of the suspended structure; a subsequent paper addresses the measurement of the tower vibration. Measurements were made at selected points on different cross sections of the stiffening structure: 12 were on the main span and 6 on the side span. Good modal identification was achieved by special deployment and orientation of the motion-sensing accelerometers and by summing and subtracting records to identify and enhance vertical, torsional, lateral, and longitudinal vibrational modes. In all, 91 modal frequencies and modal displacement shapes of the suspended span were recovered: 20 vertical, 18 torsional, 33 lateral, and 20 longitudinal, all in the frequency range 0.0-1.5 Hz. These numbers include symmetric and antisymmetric modes of vibration. Finally, comparison with previously computed two- and three-dimensional mode shapes and frequencies shows good agreement with the experimental results, thus confirming both the accuracy of the experimental determination and the reliability of the methods of computation.
Preface 1. Ordinary differential equations 2. Elementary matrix algebra 3. Modeling techniques 4. Finite-element method 5. Response of dynamic systems 6. Virtual passive controllers 7. State-space models 8. State-feedback control 9. Dynamic feedback controller 10. System identification 11. Predictive control Bibliography Suggested reading Index.