Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
1
Real-Time Wireless Vibration Monitoring for
Operational Modal Analysis of an Integral
Abutment Highway Bridge
Matthew J. Whelan, Michael V. Gangone, Kerop D. Janoyan, Ratneshwar Jha
Abstract— Remote structural health monitoring systems
employing a sensor-based quantitative assessment of in-service
demands and structural condition are perceived as the future in
long-term bridge management programs. However, the data
analysis techniques and, in particular, the technology conceived
years ago that are necessary for accurately and efficiently
extracting condition assessment measures from highway
infrastructure have just recently begun maturation. In this
study, a large-scale wireless sensor network is deployed for
ambient vibration testing of a single span integral abutment
bridge to derive in-service modal parameters. Dynamic behavior
of the structure from ambient and traffic loads was measured
with accelerometers for experimental determination of the
natural frequencies, damping ratios, and mode shapes of the
bridge. Real-time data collection from a 40-channel single
network operating with a sampling rate of 128Hz per sensor was
achieved with essentially lossless data transmission. Successful
acquisition of high-rate, lossless data on the highway bridge
validates the proprietary wireless network protocol within an
actual service environment. Operational modal analysis is
performed to demonstrate the capabilities of the acquisition
hardware with additional correlation of the derived modal
parameters to a Finite Element Analysis of a model developed
using as-built drawings to check plausibility of the mode shapes.
Results from this testing demonstrate that wireless sensor
technology has matured to the degree that modal analysis of
large civil structures with a distributed network is a currently
feasible and a comparable alternative to cable-based
measurement approaches.
Index Terms— Bridge dynamics, Modal analysis, Bridge
inspection, Wireless sensor network, Structural health
monitoring, Stochastic Subspace Identification (SSI)
H
I. INTRODUCTION
IGHWAY administrators have been faced with the burden
of managing a rapidly aging network of highway bridges
M. J. Whelan is a graduate student at Clarkson University, Potsdam, NY
13699 USA (e-mail: [email protected]).
M. V. Gangone is a graduate student at Clarkson University, Potsdam, NY
13699 USA (e-mail: [email protected]).
K. D. Janoyan is with the Civil and Environmental Engineering
Department, Clarkson University, Potsdam, NY 13699 USA (phone: 315-2686506 fax: 315-268-7985 e-mail: [email protected]).
R. Jha is with the Mechanical and Aeronautical Engineering Department,
Clarkson University, Potsdam, NY 13699 USA (email: [email protected])
in which a significant portion have met or exceeded their
design lifetime and service limits. As demonstrated in the
aftermath of recent bridge collapses over the past several
decades, current schedule-based visual inspections fall short
of ensuring a safe operational model for highway bridge
management with bridge closures preceding imminent failure.
Following development of advanced diagnostic and
prognostic approaches, in-service monitoring of highway
bridges with sensor networks may serve to evaluate the
operational health of a particular structure and estimate the
remaining service life. Wireless sensor networks furthermore
enable the rapid instrumentation of bridges for assessing the
impact of construction-related activities and evaluating the
effect of structural retrofitting.
Additionally, inherent
monitoring of environmental loads and influences, operational
loads, and traffic patterns and densities can be used to collect
a database of field measurements for providing feedback on
bridge design practice.
A study of over 500 bridge failures conducted by Wardhana
and Hadipriono [1] assessing events from 1989 to 2000
concluded that the majority of collapse instances occur due to
a triggering event. In particular, short-term hydraulic events,
long-term scour, collision, and overload were sighted for 73%
of the documented collapse, while deterioration of structural
members, design flaws, and construction-related issues
resulted in nearly 12% of the failures. Collisions, scour, and
structural deterioration significant enough to produce bridge
collapse should produce detectable changes in the dynamic
response of the structure. Feedback from a sensor-based
monitoring system would preemptively signal such
deterioration to permit a schedule of repair or closure prior to
unsafe operation. The aforementioned study also noted that
bridge failures due to overloading were the most devastating
in terms of human casualties. Since the load carrying
capability is not a static quantity over its service life, routinely
assessing and posting the structural capacity of bridge
structures is further essential for maintaining public safety.
Due to the reasonable limitation on the density of deployed
sensors across large civil structures, nondestructive testing has
generally focused on characterization of changes in global
dynamic properties as a consequence of local damage. A
limited library of vibration-based instrumentation studies exist
that have measured modal parameters of a full-scale bridge
prior to and after progressive induced damage scenarios [2-5].
However, a definitive method of deriving damage
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
identification and localization has yet to be formulated.
Consequent to the prohibitively high cost and oversight
associated with permanent, continuous monitoring of a county
or statewide distributed system of bridges, short-term
monitoring, concurrent to existing visual inspections, has also
been another, more utilized, approach. As an overwhelming
number of bridges nationwide have approached or surpassed
their service lifespan, it has become critical to allocate
resources to the structures most in need of repair or
replacement. Diagnostic testing through short-term strain
measurements from known truck load patterns has been
utilized to assess the condition of these bridges [6]. This
approach generally merges the results of the experimental
strain analysis with codified analytical load rating measures to
determine revised operating loads and ratings for the inservice bridge. The hardware deployed in this study is unique
in that it provides a wireless platform for both vibration
response measurement as well as static load ratings through
strain readings.
While traditional cable-based sensors can be utilized to
assist the field engineer with schedule-based inspections, the
excessive instrumentation costs and time of installation often
limits their use to special cases. Recently, there has been
much interest in the use of wireless transceivers for
communication of sensor data to alleviate the burdens
associated with widely-distributed cable-based sensors [7].
However, while the number of unique wireless sensor
platforms has continued to rapidly expand, there has been
limited success in replicating previous cable-based test
programs in regard to the number of deployed sensors and
data acquisition rates. A review of recent wireless sensor
deployments for structural health monitoring of bridges [8-10]
reveals that the networks have generally relied on either local
data logging and post-sampling transmission of sensor data or
on low sampling rates and/or limited numbers of sensors in
order to address transceiver bandwidth limitations. Such
concessions severely limit the versatility and capability of a
structural health monitoring system in terms of sampling
duration, data acquisition rates, and spatial resolution as well
as quality of the derived mode shapes.
The wireless sensor network deployed in this study has
achieved more than adequate sampling rates necessary for
modal analysis of highway bridges, including short-span and
stiff structures, while maintaining reliable communication
within a large, dense array of sensors. Consequent to years of
development and limited field success with high throughput
networks, wireless sensor technology has often become
viewed as a conceptually ideal solution to the problem of inservice structural condition assessment, although incapable of
providing the instrumentation framework needed. The results
of this paper aim to demonstrate that low-cost wireless
technology has emerged to the point that it is now a feasible
and comparable alternative to cable-based structural
instrumentation systems.
(9.5 in) thick reinforced concrete slab supported by four
integral abutment girders with a single span of 17.07 m (56
ft). Carrying Wright Road over Trout Brook in Potsdam,
N.Y., the bridge was constructed in 2004 and is under the
jurisdiction of the St. Lawrence County Department of
Highways (NBI# 000000003231620). Four W36x135 steel
beams are spaced at 2.74 m (9 ft) with MC8x20 end
diaphragms and two equally spaced C15x33.9 intermediate
diaphragms between all girders (Fig. 1). The abutments are a
U-type integral design supported by nine HP10x42 piles with
strong-axis orientation at the south abutment and weak-axis
orientation at the north abutment. The bridge has an inventory
load rating of 40.8 metric tons for the HS25.4 truck and an
operational load rating of 68.9 metric tons for the HS42.4, as
determined through the load factor (LF) method. The bridge
was inspected by a Professional Engineer through the
NYSDOT under the National Bridge Inspection Standards
(NBIS) in the same month as the in-service monitoring.
Given that the bridge was only two years old at the time of
inspection, the deck, superstructure, and substructure were all
assigned condition ratings of 8 on the NBIS 0-9 rating scale.
III. TEST SETUP, METHODOLOGY, AND INSTRUMENTATION
A total of 20 data points were monitored with dual-axis
accelerometers, as shown in Fig. 2. The instrumentation
layout was chosen to balance the requirements of the modal
testing outlined and a concurrent quasi-static investigation
using strain transducers connected to the same wireless
hardware. The general test setup consists of twenty dual-axis
accelerometers deployed alongside eleven reusable strain
transducers that were interfaced with twenty wireless sensor
II. TEST STRUCTURE
The in-service bridge investigated consists of a 24.1 cm
2
Fig. 1. Concrete slab on steel girder integral abutment bridge
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
Fig. 2. Vibration measurement locations - Dual-axis
nodes. All wireless sensor nodes communicated in a singlenetwork star topology with a central coordinator node
connected to a local microcomputer notebook. Acceleration
responses of the bridge from ambient excitation were
measured using low-cost Micro-Electro-Mechanical Systems
(MEMS) accelerometers mounted directly to the web of each
girder using a fast curing epoxy. All measurement data was
wirelessly streamed to the microcomputer in real-time in an
acceleration time history format. The acquisition of complete
time histories, rather than preprocessed spectrums or extracted
parameters, permits the application of multiple postprocessing analysis methods including those necessitating
multi-node time-series data or high computational overhead,
such as stochastic subspace identification.
A. Test Methodology
Individual tests consisted of time history responses
concurrently streamed in real-time from all forty sensor
channels distributed across twenty wireless sensor units.
Durations of three minutes and six seconds (186 seconds)
were specified with an effective sampling rate of 128Hz in an
effort to replicate similar recent experimental programs
utilizing wired instrumentation as documented in Wenzel and
Pichler [11]. Excitation of the structure was provided only by
ambient environmental loads and vehicular traffic. The bridge
selected exhibits very low-level vibration from ambient
loading due to its relatively short span length and the integral
abutment design, thereby providing a challenging platform for
structural response measurement and modal analysis.
The accelerometers were distributed along all of the girders
in a pattern (Fig. 2) established to derive the operational mode
shapes. Finite element analysis was performed in advance to
ensure that data points did not correspond with nodes of zero
displacement for the modes of interest. One central girder was
instrumented with a denser array as a result of concurrent
strain monitoring; this configuration resulted in increased
spatial resolution along this girder.
The vertical and
longitudinal vibration responses were measured as a result of
sensor orientation. Longitudinal responses were inadvertently
measured due to the orientation of the sensor placement.
Transmission of the longitudinal acceleration served solely to
demonstrate
the
network
throughput
capability.
Consequently, only the vertical vibration response was
incorporated in the operational modal analysis.
3
Capacitance-based dual-axis MEMS accelerometers
(STMicroelectronics LIS2L02AL) were selected for lowpower consumption and ultra-low noise floor characteristics.
These integrated circuit sensors were mounted on printed
circuit boards and encased in a small external housing with
potting epoxy to enable direct placement of the sensor on the
structure for superior vibration transfer. The accelerometers
feature +/-2g full-scale range, 600mVg-1 sensitivity at 3V
supply, and an ultra-low 30µg/√Hz noise density. Signal
amplification of 64V/V or 128V/V was applied to the
accelerometer channels depending on sensor location to
maximize the range and resolution of the conversion. This
signal conditioning resulted in approximate sensitivities of
38Vg-1 and 76Vg-1, respectively, with analog-to-digital
conversion resolution of 16µg and 8µg, accordingly.
Conversion of the raw signals is provided at each node by a
12-bit ADC (Analog-to-Digital Converter) that was
programmed to over-sample each measurement channel at
512Hz. The data was then processed using a 56th-order digital
low-pass filter to remove potential alias frequencies and then
down-sampled to an effective rate of 128Hz.
The
oversampling approach implemented increases the effective
resolution of the ADC, rejects alias frequencies from the
transition band of the analog low-pass filter, and produces a
near brick-wall filter response with less than 0.01dB of
attenuation in the 0-50Hz bandwidth.
B. Wireless Sensor Network
A wireless sensor is comprised of a traditional sensor and
appropriate signal conditioning integrated with a transceiver
unit for the digital conversion and transmission of the raw
signal from a remote measurement location to a central
acquisition station without cabling. The wireless sensor
network deployed utilized a commercial transceiver platform
Fig. 3.
Wireless Sensor Solution (WSS) Hardware with MEMS
Accelerometer and BDI Strain Transducer
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
(MoteIV Tmote Sky) incorporated with a custom software,
signal conditioning hardware, and sensor design developed inhouse to specifically address the requirements of bridge
condition assessment through modal analysis and load rating.
The commercial transceiver platform features a 4MHz
microcontroller interfaced with a 2.4GHz chip transceiver
with a maximum data rate of 250kbps. The device is
compliant with U.S. and Canadian radio frequency regulations
and is certified by the FCC and Industry Canada for
unlicensed use in either country. A complete description of
the wireless sensor network hardware and software as well as
results of laboratory validation can be found in Whelan and
Janoyan [12].
The Wireless Sensor Solution (WSS) is a multi-functional
system developed in-house by the authors to address both
dynamic response and strain monitoring for load rating of inservice highway bridges. Independent circuits accommodate
signal conditioning hardware specific to vibration
measurement of typical bridge spectrums and strain
measurement from commercial transducers.
The
accelerometer conditioning section provides a two-channel
interface featuring a low-noise 3V power supply, 14-stage
digitally programmable signal amplification, auto-offset
A
nulling, and a 5th order analog low pass filter.
complementary signal conditioning circuit for differential
sensors, such as strain transducers, offers an applicationspecific integrated circuit (ASIC) tailored to high-resolution
measurements of resistive-bridge sensors. The chip features
programmable gain and offset of the differential signal, a 15bit charge-balancing ADC, a temperature interface with a
digital correction algorithm for compensating strain
measurements, and nonvolatile memory for storing
configuration settings during power cycling. Hardware
shutdown of the individual signal conditioning circuits as well
as the transceiver provides for power conservation during
periods of inactivity.
Custom embedded software applications were written for
the sensor nodes to accommodate in-network task triggering
and large-scale concurrent node operation. Unique features of
the software include digital filtering of sensor data using the
hardware multiplier, in-network remote sensor configuration,
control of component power supplies, and robust
communication. An optimized radio transmission protocol
that coordinates the sampling and transmission software
operations with node-based scheduling is implemented in
favor of the TinyOS radio stack typically used for this
transceiver platform, which relies on concurrent processing of
these tasks. Embedded software was also written for the
microcontroller at the host transceiver; a high-speed
transparent bridge between the chip transceiver and the virtual
COM port operating at 262144 baud across the USB bus
enables significantly higher data throughput. A user-friendly
LabVIEW software application controls bidirectional
communication through the base transceiver, configures the
sensor nodes remotely, displays real-time sensor data, and
logs time histories to the hard disk for subsequent analysis.
The radio transmission protocol developed enabled nearly
100% data delivery across the entire twenty node network.
4
Data packets from each node are scheduled for transmission
based on the local address of the node to prevent packet
collision. The built-in clear channel assessment (CCA)
feature of the transceiver is also utilized to further prevent
packet transmission when the channel is already active. Data
packets request an acknowledgement message from the base
transceiver upon reception of packets that pass the error
checking algorithm.
Data packets that fail to receive
acknowledgements are placed in a transmission queue for
retransmission during a second scheduled window. Packets
are removed from the queue only upon successful receipt of
their respective acknowledgement. The optimized network
transmission protocol coupled with high-speed base node
communication transfers between the chip transceiver and the
host microcomputer are directly responsible for alleviating
issues with data delivery, reduced sampling rates, and limited
remote acquisition channels that have typically plagued
wireless sensor networks.
IV. TEST RESULTS
A. Wireless Sensor Network Performance
The average data success rate across all of the sensor nodes
over ten 3 minute test cycles was 99.91%, with 184 of the 200
time histories reported with 100% data delivery success. The
minimum data success rate over these tests was 98.0%, which
corresponds to a loss of only 17 data packets of the 850
requested for the sampling duration specified. The small loss
of data has been attributed to a software bug discovered in the
portion of the embedded software code responsible for
transmitting any residual packets in the transmission queue
after completion of sampling. While correction of the
software will likely improve the data success rates, the current
level of data recovery is generally more than sufficient for
structural health monitoring as the system identification
analysis suffered from no noticeable adverse distortion. For
the network size and sampling rate of the deployment in this
study, the radio protocol during active sampling resulted in a
transmission overhead in the range of 97kpbs to 126kbps
depending on the packet success and retransmission rates.
The degree of transmission reliability attained at the high data
throughput rate prescribed in this testing demonstrates that
wireless sensor networks are currently capable of performing
large-scale, real-time structural health monitoring.
B. Dynamic Bridge Response
A single-span integral abutment bridge provides an ideal
platform for testing the performance of a structural health
monitoring system as the high stiffness of the bridge results in
a demanding measurement scenario in that structural
vibrations are of very low amplitude. Throughout the
duration of testing, peak accelerations across the structure
ranged from less than 2mg to only nearly 10mg. Despite this
low excitation, the amplified sensor signals produced clear
time-history representations of the traffic loading (Fig. 4) as
well as distinct peaks in the frequency spectra. The WSS
signal conditioning hardware provides an extensive range of
programmable gain amplification and therefore can adapt to
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
5
the assumption that an accurate crystal oscillator can provide
time synchronization of the network for at least the sampling
duration utilized.
Fig. 4. Typical Acceleration Time Histories
the measurement range of bridges of various span lengths and
support conditions. Likewise, it can be reasonably assumed
that the system will even provide improved measurement
performance on longer-span structures with larger amplitude
vibrations, as the signal-to-noise ratio will be increased.
A particular concern with wireless sensor networks is that
in using localized self-contained data acquisition nodes
distributed across a structure, there is no longer a shared
sample clock by which time synchronization of measurements
can be strictly enforced. Conversely, all nodes operate with
their own clocks that will have unique offset and drift
characteristics affecting the relative timing of tasks among
nodes in the network. Unlike many wireless sensor networks
that use the main microcontroller oscillator to provide sample
timing, the WSS system relies on an accurate 32.768 kHz
crystal oscillator to provide a precise, stable clock to each of
the nodes. Synchronized initiation of sampling is invoked by
a single command broadcast to all nodes in the network.
Since the radio packet is an electromagnetic wave, therefore
travelling at the speed of light, the difference in reception time
amongst the nodes in the network will be on the order of
nanoseconds. Consequently, the accuracy and stability of the
crystal oscillators dictates the time synchronization of the
samples relative to each node throughout time. Investigation
of the accelerations measured across the network during
traffic events reveals that the wireless sensors maintain phase
amongst themselves, which is imperative for accurate
operational modal analysis (Fig. 5). This thereby substantiates
Fig. 5. Time window overlay of accelerations during a traffic event 100
seconds into real-time collection cycle
C. Operational Modal Analysis
Analysis of in-service dynamic measurements of highway
bridges challenges conventional modal analysis techniques as
it is often impractical to measure the input excitation. The use
of impulse excitation (drop-weight) or a shaker to provide
forced vibration to the bridge would require at least a partial
closure of traffic and does not lead itself to long-term
continuous or autonomous structural health monitoring.
Furthermore, the presence of any nearby vibration sources,
such as machinery or traffic, and the effect of dynamic
environmental loads, such as wind, geological, and
hydrodynamic forces, are additional system inputs that are not
accounted for in the measurement of the controlled excitation
input. Consequently, extraction of system modal parameters
of civil structures from ambient excitation has recently
emerged as a widely sought-after approach for in-service
condition assessment.
Traditional system identification
methods requiring both input and output measurements, such
as using the frequency response function (FRF), can not be
applied to data yielded from ambient excitation, as there is no
measure of the system input. Recent work in the development
of ambient vibration methods has produced several
approaches for output-only system identification to enable
modal parameter extraction from ambient time histories
[13,14]. In this study, output-only system identification from
the accelerometer time histories was performed using the
Modal Analysis on Civil Engineering Constructions
(MACEC) software package [15]. This software analysis
package permits the use of both the classical Fourier-based
Frequency Domain Decomposition (FDD) with peak peaking
as well as the stochastic subspace identification (SSI) method
for deriving mode shapes, natural frequencies, and damping
ratios.
During implementation of FDD modal analysis, a 4096point average normalized power spectral density (ANPSD)
was computed using the time histories from all test sequences
and sensor locations (Fig. 6). Natural frequencies were
selected from the modal peaks present in the power spectrum
and the corresponding mode shapes were derived for each test
sequence. In this approach, discrete mode shape data are
determined using the relative magnitude and phase angle of
the spectral peaks at each sensor location, corresponding to
the eigenfrequency, with respect to a specified reference
sensor. Since multiple time histories were available for
analysis, the derived mode shapes were then normalized and
averaged to provide the final mode shape estimates (Fig. 7).
Averaging reduces the effects of noise and improves the
resolution of the mode shapes. Due to the mass of passing
vehicles, the mode shapes and natural frequencies of the
unloaded bridge will be slightly affected by traffic loads and
patterns. When using traffic excitation, averaging mode
shapes from a large number of tests also alleviates the effect
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
Fig. 6. Average Normalized Power Spectral Density – Vertical Direction
Fig. 7. Operational defleciton shapes extracted by Frequency Domain
Decomposition (FDD) (Numbering corresponds to mode as identified in
subsequent FEA analysis)
of traffic load bias on one lane of the bridge, which is more
probable from the results of only a single test.
Application of the FDD method on the experimental data
was found to produce smooth mode shapes that correlate well
with the FEA analysis. However, this method relies on
sufficient excitation of the eigenfrequencies to permit
identification of each modal peak in the average normalized
power spectrum. Additionally, the mode must be sufficiently
under-damped such that resonance at the natural frequency is
represented by a distinct peak. In fact, the frequency domain
peak-picking method actually produces operational deflection
shapes rather than mode shapes in that the shape constructed
from the spectral data is the naturally weighted combination of
all mode shapes that would arise if the structure was excited
by a pure harmonic at the selected natural frequency [16].
Since only spectral content near the natural frequency
contribute noticeably to the constructed mode shape estimate,
the operational deflection shapes are generally similar to the
mode shapes. However, for structures with closely spaced
modes, the estimated mode shapes will be a combination of
multiple modes and therefore may not produce accurate
response estimation. Fortunately, the structure tested has
adequately spaced natural frequencies with sufficient damping
to permit clear extraction of many of the dominant modes
within the measured bandwidth. However, the traffic patterns
captured in the field testing either did not adequately excite
several additional modes identified in the subsequent SSI
analysis to permit identification in the frequency spectra
6
and/or these mode were damped sufficiently to prohibit visual
identification. Furthermore, while the second longitudinal
bending mode (4th mode) was identified and estimated, the
peak was relatively small in the spectrum and, as evident in
the mode shape estimate, the low signal-to-noise ratio resulted
in a relatively coarse approximation.
While the Fourier-based peak picking method analyzes the
frequency-spectrum to extract natural frequencies and mode
shapes, stochastic subspace identification techniques use a
time-domain driven approach to solving for modal parameters
from a discrete-time stochastic state-space model. The
derivation of this method is outside the scope of this paper;
full presentation of the state-space equations and model
development can be found elsewhere [14], [16]. In short, the
method uses a state-space model developed from the linear,
second-order differential equation for a multi-degree of
freedom spring, mass, and damper system with input forces.
To account for inherent sensor noise and fixed-width
computational effects, the state-space model includes
stochastic terms to represent measurement and process noise
that are assumed to have zero-mean, white noise
characteristics. The MEMS accelerometers utilized in this
study do in fact exhibit a white noise spectrum according to
electrical specifications, so spurious poles should not arise in
the model as a result of violations of this assumption. Since
the system inputs are unknown and immeasurable in the case
of ambient excitation, the input terms are then implicitly
modeled within the noise terms resulting in a purely stochastic
system. It should be noted that by modeling the unknown
excitation forces with the noise terms, the inputs are assumed
to also exhibit zero-mean, white noise characteristics.
Violation of this assumption may produce spurious poles in
the state-space model that are not inherent to the dynamics of
the structure but arise from spectral bias within the excitation
force. Once the system inputs to the state-space model are
reduced solely to the stochastic terms, numerical methods can
be used to solve for the state-space matrices from the
measurement data in order to produce a mathematical
description of the system from which all the modal
parameters, except the mode scaling factor, can be
determined.
Although the mathematical formulation of the SSI method
and subsequent numerical solution is rather rigorous,
especially to civil engineers unfamiliar with systems and
control modeling, the application of the method is facilitated
through the MACEC software environment, which requires
only a basic understanding of state-space models and general
system identification methodology. Following calculation of
Fig. 8. Principal angles between subspaces and stabilization plot for typical
SSI analysis (– - stable pole, x - pole with partial pass of stability criteria)
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
the system model from the measurement data, the principal
angles between subspaces can be plotted to provide a means
of estimating the model order (Fig. 8a). A gap in subsequent
principal angles indicates the model order [15], which
correlates to twice the number of system poles, or
eigenfrequencies, captured in the measurement bandwidth.
Unfortunately, real-world data rarely produces a single,
distinct gap, as evidenced in the results for the Wright Road
Bridge analysis in which gaps indicate several possible model
orders ranging from as low as six and as high as 44. Given
this all too common scenario, over-specifying the model order
is recommended [15] and the suggested model order can be
determined from the number of stable poles identified in the
stabilization diagram (Fig. 8b). At this point, subjectivity is
required to select the poles likely to be a result of structural
dynamics rather than spurious poles resulting from the
numerical process.
The previously outlined approach to extracting modal
parameters from a SSI model, as suggested by the MACEC
manual, can be treated as a relatively simple means of quickly
extracting mode shapes, natural frequencies, and damping
ratio estimates from experimental data. However, through
experience with application of output-only system
identification to in-service dynamic response measurements
from highway bridges, the authors of this paper highly
recommend developing a single state-space model from which
all modal parameters are estimated.
In this manner,
subjectivity in identification of actual structural poles versus
spurious poles can be greatly reduced and the derived modal
parameters will reflect a more consistent estimate of the
system response less affected by spurious poles. The
appropriate model order can be coarsely predicted by doubling
the number of spectral peaks evident in the average power
spectrum and then more accurately estimated by finding a gap
in the principal angle plot (Fig. 8a) greater than the coarse
model order prediction. This process can be aided by
comparing the spectral density estimate of state-space model
to the power spectrum of the measured data. For the case
study presented, a model order 44 was determined to be most
appropriate; the discontinuity in the principal angle plot was
found to be the last significant gap in the profile. The average
spectral density of the 44th order state-space model (Fig. 9)
correlates well with spectral content of the ANPSD computed
from the measurement data (Fig. 6) and the majority of poles
have been found to arise from the structural response.
Fig. 9. Average Spectral Density of Computed SSI State-Space Model
(Order 44, Poles Indicated with Star)
7
Fig. 10. Operational Mode Shapes Present in SSI Model of 44th Order
(3D surface plot and plan view with magnitude shading; Numbering
corresponds to mode as identified in subsequent FEA analysis)
Plotting the poles over the average spectral density of the
state-space model provides an efficient means of identifying
which poles are spurious and which relate to the structural
dynamics of the structure. Structural poles, i.e. the natural
frequencies of the bridge, coincide with distinct peaks in the
average spectral density, whereas the spurious poles generally
fall between peaks for a model of appropriate order.
Modal parameters were then extracted from the state-space
model to estimate the natural frequencies and damping ratios
of the in-service bridge. Twelve non-spurious poles were
identified in the model permitting successful extraction of
twelve mode shapes from the measurement data, thereby
demonstrating significant improvement over the application of
FDD system identification (Fig. 10).
In addition to
identifying mode shapes that are less pronounced in the
frequency spectrum, the SSI analysis resulted in smoother
mode shapes, alleviating signal-to-noise issues for poorly
excited modes. Consequently, although the SSI technique
requires substantially more understanding of system
identification and state-space modeling, is computationally
more complex, and necessitates a higher degree of
subjectivity, the process effectively yields a greater number of
modes with higher quality shape estimation than the FDD
technique for output-only modal analysis.
Given the
insignificant number of spurious poles in the state-space
model, particularly in the portion of the spectrum above 8Hz
where the dynamic structural response occurs, the signal-tonoise ratio is low enough to permit reliable extraction of these
twelve modes. It will be shown in the subsequent section that
by over-specifying the model order, as suggested in the
MACEC manual, the remaining two structural modes can be
extracted from the in-service measurements.
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
8
Fig. 12. Finite element analysis mode shape development
Fig. 11. Finite element model: a) mesh, b) loads and boundary constraints
V. NUMERICAL MODEL OF TEST STRUCTURE
A solid model of the bridge tested consisting of the steel
superstructure, concrete slab, abutments, and railings was
drafted in AutoCAD 2004 from the as-built Department of
Highways drawings (Fig. 11). Finite element analysis of the
model was performed using the FEMPRO software package
by ALGOR Incorporated. Natural frequency (Modal) with
Load Stiffening analysis was performed using threedimensional solids consisting of brick elements. A mesh size
of 20.32 cm (8 in.) was specified in the auto-mesh generation,
which resulted in 33768 total solid elements across the model.
Abutment and slab properties were specified by assigning the
material type to medium-strength concrete as defined by the
built-in library, while the steel superstructure and railings
were assigned the material properties of A588 and A500 steel,
respectively.
Modeling the behavior of an integral abutment bridge is
substantially more complex than developing a similar model
for a deck supported by bearings, as the soil-structure
interaction on the abutments and piles has a significant
influence on the dynamics of the superstructure [17]. Given
that the analysis was performed simply to provide a
plausibility check with the measured response, some
assumptions and modeling simplifications were made in
providing boundary constraints and loads on the surfaces of
the abutments. Lateral soil pressure on the abutments and
wingwalls was provided using an assumed linear pressure
distribution, a 1.922 Mg/m3 (120 lb/ft3) unit weight of the
backfill soil, and a coefficient of lateral earth pressure of 0.5.
This soil pressure results in a slight decrease in natural
frequencies, due to the longitudinal compressive force applied
on the deck. While nonlinear spring elements are often used
to model soil-structure interaction, the FEA software allowed
only for linear elastic spring elements in the natural frequency
with load stiffening analysis. Consequently, the National
Cooperative Highway Research Program (NCHRP) curves for
earth pressure coefficient versus relative wall displacement, as
presented by Civjan [18] were approximated with a linear fit
to the initial slope of passive pressure development. Since the
backfill soil properties are unknown, the linear slope
approximations for loose and dense sand were averaged.
Translational spring elements were placed on vertices across
the abutment in both the longitudinal and transverse directions
of the bridge deck. The elastic modulus of each spring
element was assigned with a linear profile increasing with
depth, as determined by the approximation to the NCHRP
curve. Translational stiffness was applied to the base of the
abutment to represent bearing pressure and frictional forces
along this surface. A moderate 350.4 kN/m (31.25 lb/in/in2)
spring stiffness was assigned to the lateral springs on these
vertices; vertical springs were applied with 14.01 MN/m
(1250 lb/in/in2) stiffness. The contribution from support piles
was modeled with additional translational springs at the
vertices corresponding to pile locations. Although the pile
axis orientations differed at each abutment, the translational
springs applied to represent the piles assumed equal stiffness
in both lateral directions.
The superstructure-dominant mode shapes, i.e. those
Fig. 13. Remaining experimental mode shapes extracted through overspecification of model order in stochastic subspace identification (respective
poles identified over average spectral density of 76th order model)
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
Table 1. Comparison of Experimental and FEA Natural
Frequency Estimates
measurable through the accelerometer placement on the
girders, estimated within the measurement bandwidth through
the FEA are presented in Fig. 12. While additional mode
shapes were identified in FEA, these mode shapes were
generally either dominated by slab or wingwall movement
rather than motion at the girders or the result of rigid body
translation and rotation on the boundary springs. Comparison
of the analytical modal parameters with those identified in the
experimental system identification techniques yielded
excellent correlation in terms of both visual comparisons of
mode shapes and relative estimation of natural frequencies
(Table 1). There are some differences in the order of the
natural frequencies between the FEA analysis and the
experimentally measured modes, particularly at the higher end
of the spectrum. Given the bending orders of the modes, it is
natural to assume that, for instance, the third order
longitudinal bending mode with first order bending in the
lateral direction will occur at a lower frequency than the third
order longitudinal bending mode with second order bending in
the lateral direction despite the discrepancy in the results of
the FEA analysis. These differences can be attributed to the
assumptions, approximations, and simplifications made in the
finite element model. Consequently, the mode shapes have
been sequentially numbered according to the proper order as
measured experimentally.
9
It should be noted that the four highest order modes have
natural frequencies that reside in the portion of the bandwidth
with potential aliasing. As a result, these natural frequency
estimates may be incorrectly aliased from the 64-78Hz
frequency range. However, due to the model order associated
with the bending patterns, it is likely that all of the modes,
aside from the last, can be assumed to be correctly associated
with the 50-64Hz band, as the last mode is of the highest
bending order. Furthermore, signal attenuation in the aliased
region for these modes is also significant enough that
identification of an aliased peak in the spectrum would be
highly unlikely. Consequently, only the last mode has been
identified with two possible natural frequency estimates for
the experimental analysis. While some discrepancies exists
among the analytical and experimentally derived modal
parameters, the complexity of modeling an integral abutment
bridge coupled with modeling assumptions could accounts for
these slight differences as well as any inconsistencies between
the bridge design and actual construction tolerances and
material properties.
Given that the FEA identified two additional superstructuredominant modes within the measured bandwidth, stochastic
subspace identification was revisited to employ a higher
model order to extract these missing modes. At a model order
of 76, the remaining two modes became apparent in the statespace model, though the shapes are only approximate due to
the low excitation and large damping ratios associated with
these poles. Examining the spectral density of the state space
model, it becomes apparent that these modes suffer from a
lack of excitation as well as significant damping.
Furthermore, after introducing the additional degrees of
freedom necessary for the corresponding poles to arise in the
model, there are significantly more spurious poles introduced.
These spurious poles are not intrinsic to the structural
response, but arise from noise and excitation violations of the
zero-mean, white noise assumptions. Consequently, the overspecified model is not recommended for implementation in
any further analysis, such as forward prediction with a
Kalman filter. It is recommended to use the lower order
model even though it does not include two of the fourteen
modes known to be present in the bandwidth of interest.
VI. CONCLUSION AND DISCUSSION
To field-test the performance of a wireless sensor network
for dynamic response assessment of in-service highway
bridges, a single-span integral abutment bridge has been
investigated through operational modal analysis using ambient
vibration testing. As a consequence of the experimental
program, the Wireless Sensor Solution (WSS) platform for
structural health monitoring developed at Clarkson University
has demonstrated the capability to replace cable-based
instrumentation for the majority of in-service condition
assessment routines. In addition, the alleviation of obstacles
associated with cabling, such as the associated installation
time and cost, introduces the potential to monitor the
performance of an increased number of bridges in a more
condensed time frame.
Whelan, M.J., Gangone, M.V, Janoyan, K.D., and Jha, R. (2009) “Real-Time wireless vibration monitoring for operational
modal analysis of an integral abutment highway bridge,” Engineering Structures 31(10), 2224-2235.
expressed in this paper are those of the authors and do not
reflect the views of the agencies.
The primary objective of the study was to evaluate the
performance of the wireless sensor network and local data
acquisition hardware in a typical field setup outside of the
laboratory environment. Real-time streaming of 40 channels
of measurement data sampled at an effective rate of 128Hz per
sensor for ten test durations each exceeding three minutes was
successfully achieved while maintaining nearly 100% data
delivery across the network.
Additionally, the signal
conditioning and data acquisition interface provided an innetwork reconfigurable platform that enabled sufficient
resolution of the low amplitude vibration experienced to
extract fourteen mode shapes of the relatively stiff single-span
bridge using low-cost MEMS accelerometers. These results
present a significant breakthrough in the use of wireless
sensor networks for structural health monitoring.
By
essentially replicating a typical cable-based dynamic test
routine in terms of not only sampling rates, number of
deployed sensors, and test duration but also in the quality and
breadth of extracted modal parameters, the developed wireless
sensing platform has emerged as both a feasible and
comparable alternative to wired instrumentation in structural
health monitoring and in-service condition assessment.
In analyzing the ambient vibrations measured by the
wireless sensor nodes, a complementary study was performed
in which the effectiveness of applying two output-only system
identification methods to real-world measurements was
evaluated. The frequency domain decomposition technique
was compared to stochastic subspace identification to contrast
the ability of the two methods to extract modal parameters.
Overall, FDD was capable of constructing mode shapes and
estimating natural frequencies for well excited modes in good
agreement with finite element analysis. However, the use of
the SSI technique permitted the extraction of an additional
four modes from the time histories in addition to damping
ratio estimates for all vibration modes. Furthermore, the
relative quality of the mode shapes derived through SSI was
deemed to be higher than obtained from FDD and is likely a
result of the inclusion of stochastic noise components in the
mathematical formulation of the SSI state-space model. In
general, the use of SSI techniques to estimate modal
parameters from output-only experimental data has been
found to be preferable to the FDD method despite the
increased computational effort and subjectivity required to
identify system poles. Lastly, the authors present an approach
for estimating modal parameters using a single order statespace model developed through the SSI system identification,
rather than selecting poles from a stabilization diagram.
[16]
ACKNOWLEDGEMENTS
[17]
This research has been funded by the New York State
Energy Research and Development Authority (NYSERDA),
in collaboration with the St. Lawrence Highway Department,
and the New York State Department of Transportation
(NYSDOT). The authors would also like to acknowledge the
assistance of Kevin Cross and Dan Nyanjom during the field
deployment and Michael Fuchs with system development.
Any opinions, findings, and conclusions or recommendations
10
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