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A wireless sensor network For structural monitoring

TLDR
Wisden incorporates two novel mechanisms, reliable data transport using a hybrid of end-to-end and hop-by-hop recovery, and low-overhead data time-stamping that does not require global clock synchronization.
Abstract
Structural monitoring---the collection and analysis of structural response to ambient or forced excitation--is an important application of networked embedded sensing with significant commercial potential. The first generation of sensor networks for structural monitoring are likely to be data acquisition systems that collect data at a single node for centralized processing. In this paper, we discuss the design and evaluation of a wireless sensor network system (called Wisden for structural data acquisition. Wisden incorporates two novel mechanisms, reliable data transport using a hybrid of end-to-end and hop-by-hop recovery, and low-overhead data time-stamping that does not require global clock synchronization. We also study the applicability of wavelet-based compression techniques to overcome the bandwidth limitations imposed by low-power wireless radios. We describe our implementation of these mechanisms on the Mica-2 motes and evaluate the performance of our implementation. We also report experiences from deploying Wisden on a large structure.

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Title
A Wireless Sensor Network for Structural Monitoring
Permalink
https://escholarship.org/uc/item/7694j52g
Authors
N. Xu
S. Rangwala
K. Chintalapudi
et al.
Publication Date
2004
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

A Wireless Sensor Network For Structural Monitoring
Ning Xu
Sumit Rangwala
Krishna Kant Chintalapudi
Deepak Ganesan
§
Alan Broad
Ramesh Govindan
Deborah Estrin
§
ABSTRACT
Structural monitoring—the collection and analysis of structural re-
sponse to ambient or forced excitation–is an important application
of networked embedded sensing with significant commercial po-
tential. The first generation of sensor networks for structural mon-
itoring are likely to be data acquisition systems that collect data
at a single node for centralized processing. In this paper, we dis-
cuss the design and evaluation of a wireless sensor network sys-
tem (called Wisden) for structural data acquisition. Wisden in-
corporates two novel mechanisms, reliable data transport using a
hybrid of end-to-end and hop-by-hop recovery, and low-overhead
data time-stamping that does not require global clock synchroniza-
tion. We also study the applicability of wavelet-based compression
techniques to overcome the bandwidth limitations imposed by low-
power wireless radios. We describe our implementation of these
mechanisms on the Mica-2 motes and evaluate the performance of
our implementation. We also report experiences from deploying
Wisden on a large structure.
Categories and Subject Descriptors
C.2.1 [Computer Communication Networks]: Wireless commu-
nication; C.3 [Special-Purpose and Application-Based Systems]:
Embedded Systems
This material is based upon work supported by the National Sci-
ence Foundation under Grants No. 0121778 (Center for Embedded
Networked Systems) and 0325875 (ITR: Structural Health Moni-
toring Using Local Excitations and Dense Sensing). Any opinions,
findings and conclusions or recomendations expressed in this ma-
terial are those of the author(s) and do not necessarily reflect the
views of the National Science Foundation (NSF).
Computer Science Department, University of Southern California,
{nxu, srangwal, chintala, ramesh}@usc.edu
Current Affiliation - Center for Embedded Networked Sensing,
Los Angeles
§
Computer Science Department, University of California, Los An-
geles {deepak, destrin}@cs.ucla.edu
Crossbow Technology Inc. abroad@xbow.com
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission and/or a fee.
SenSys’04, November 3–5, 2004, Baltimore, Maryland, USA.
Copyright 2004 ACM 1-58113-879-2/04/0011 ...$5.00.
General Terms
Reliability, Design
Keywords
Sensor Network, Structural Health Monitoring, Wisden
1. INTRODUCTION
Structural health monitoring systems seek to detect and local-
ize damage in buildings, bridges, ships, and aircraft. The design
of such systems is an active and well-established area of research.
When built, such systems would infer the existence and location
of damage by measuring structural response to ambient or forced
excitation. Wireless sensor networks are a natural candidate for
structural health monitoring systems, since they enable dense in-
situ sensing and simplify deployment of instrumentation. However,
techniques for damage assessment are quite complex, and practical
wireless networked structural health monitoring systems are sev-
eral years away.
Wireless sensor networks do have a more immediate role to play
in structural monitoring. Advances in structural engineering de-
pend upon the availability of many detailed data sets that record
the response of different structures to ambient vibration (caused,
for example, by earthquakes, wind, or passing vehicles) or forced
excitation (delivered by large special-purpose shakers). Currently,
structural engineers use wired or single-hop wireless data acqui-
sition systems to acquire such data sets. These systems consist of
a device that collects and stores vibration measurements from a
small number of sensors. However, power and wiring constraints
imposed by these systems can increase the cost of acquiring these
data sets, impose significant setup delays, and limit the number
and location of sensors. Wireless sensor networks can help address
these issues.
In this paper, we describe the design of Wisden, a wireless sen-
sor network system for structural-response data acquisition. Wis-
den continuously collects structural response data from a multi-hop
network of sensor nodes, and displays and stores the data at a base
station. Wisden can be thought of as a first-generation wireless
structural monitoring system; it incorporates some in-network pro-
cessing, but later systems will move more processing into the net-
work once the precise structural monitoring applications are better
understood. In being essentially a data collection system, Wisden
resembles other early sensor networks such as those being deployed
for habitat monitoring [10].
While the architecture of Wisden is simple—a base station cen-
trally collecting data—its design is a bit more challenging than that
of other sensor networks built till date. Structural response data
is generated at higher data rates than most sensing applications

(typically, structures are sampled upwards of 100 Hz). Further-
more, this application requires loss intolerant
1
data transmission,
and time synchronization of readings from different sensors. The
relatively low radio bandwidths, the high packet loss rates observed
in many environments [21], and the resource constraints of existing
sensor platforms add significant challenges to the design of Wis-
den.
In this paper, we discuss the design and implementation of Wis-
den. Wisden currently uses a vibration card, especially designed
for structural applications. In addition to describing this card, our
description of Wisden focuses on its three novel software compo-
nents:
Reliable Data Transport Wisden uses existing topology manage-
ment techniques to construct a routing tree [20], but imple-
ments a hybrid error recovery scheme that recovers packet
losses both hop-by-hop and end-to-end.
Compression Wisden uses a simple run-length encoding scheme
to suppress periods of inactivity in structural response, but
we also evaluate the feasibility of wavelet compression tech-
niques to reduce Wisden’s data rate requirements and to im-
prove latency.
Data Synchronization Wisden also implements a data synchro-
nization scheme that requires little overhead and avoids the
need to synchronize clocks network-wide.
For each of these components, we evaluate its performance through
experiments on the motes. We also report experiences from a small
deployment of Wisden on a real structure.
Our choice of platform (Mica2 motes, Chipcon radios) is largely
dictated by availability of interface hardware (e.g., the vibration
card). However, as these platforms evolve to using perhaps ARM-
based processors and Zigbee radios, we do not see the need for our
proposed mechanisms going away. Rather, such an evolution (par-
ticularly to higher-bandwidth radios) will help increase the scale
of Wisden deployments. One kind of platform we have explicitly
not considered are more powerful processors equipped with 802.11
radios. While there has been some work on using high-powered
radios as cable replacements in wired instrumentation systems [9],
these platforms are significantly more energy-intensive, and have
less software support for multi-hopping (which can increase de-
ployment flexibility).
2. BACKGROUND AND MOTIVATION
In this section, we first discuss the requirements of structural
monitoring and describe devicesused to measure structural response.
We then discuss structural data acquisition systems, their capabil-
ities and their shortcomings. This sets the stage for the design of
Wisden, which we discuss in the next section.
2.1 Sensing Structural Response
Structural engineers use different kinds of sensors to monitor
structures: displacement sensors, strain gauges, and accelerome-
ters, to name a few. While Wisden can be used with displacement
sensors and strain gauges, we focus in this paper on an accelerometer-
based system. Accelerometers measure, as the name suggests, ac-
celerations of the surface they are mounted on. Accelerations are
translated into changes in capacitance or in other electrical proper-
ties. These analog signals are then sampled at a specified frequency.
1
We should note that Wisden’s silence suppression technique is
lossy, but the system attempts to deliver useful structural vibration
data reliably.
From a structural engineering standpoint, accelerometers are char-
acterized by several performance parameters: sensitivity, which
denotes the smallest measurable acceleration and is expressed in
gs (gravitational acceleration); dynamic range, which denotes the
range of accelerations that the device is capable of measuring and
is also expressed in gs; and noise, which is measured either as an
RMS value, or is expressed as a function of the frequency of vibra-
tion.
From a software designer’s perspective, the output of an accelerom-
eter is a time series of sensor readings with a specified resolution
and a specified sampling rate. Strictly speaking, these are param-
eters associated with the analog-to-digital circuitry attached to an
accelerometer, but they nevertheless constrain the performance of
the accelerometer. The resolution constrains the sensitivity of an
accelerometer; a 10-bit accelerometer whose dynamic range is 1g
cannot have a sensitivity less than 1mg. The sampling rate, on the
other hand, governs the frequencies that can by measured by the
accelerometers.
Accelerometers are used for a wide variety of applications. For
monitoring large structures, though, it is generally considered suf-
ficient to have a dynamic range of 1-2 gs, a sensitivity in the µg
range and low noise characteristics. This translates to a sampling
resolution of at least 16 bits per sample. Finally, since many struc-
tural engineering methods monitor the frequency response of struc-
tures (which are usually focused in the tens of Hz), a sampling rate
of 100 Hz is considered to be a minimum requirement.
Thus, from our perspective, an accelerometer might be modeled
as a device that generates about 100 2-byte samples a second. More
generally, a single sensor node might be attached to an accelerom-
eter capable of measuring accelerations along three axes. Such tri-
axial accelerometers are capable of generating about 600 bytes a
second, which is a significant fraction of the bandwidth of current
and future low-power wireless radios such as the Chipcon CC1000,
and the Zigbee (IEEE 802.15.4) radios.
2.2 Structural Data Acquisition Systems
Accelerometers (or displacement sensors and strain gauges, for
that matter) collect structural response from a single location on
a large structure. Structural engineers would like to collect data
from tens or hundreds of locations. A long-term goal of such an
instrumentation infrastructure is an on-line system for damage de-
tection and localization. In such a system, structural response from
different locations can be used to parametrize a model of the struc-
ture; when damage occurs, the parameters of this model change,
allowing the system to infer the existence (and possibly location)
of damage. Practical damage detection and localization systems are
several years away. As an aside, there is no inherent reason for such
systems to be centralized; wireless sensor networks employing de-
centralized detection and localization algorithms are plausible, but
are beyond the scope of this paper.
In order to develop methods for detecting and locating dam-
age, structural engineers rely on extensive data-sets of structural
response. These data-sets can help validate, benchmark, and pro-
vide intuition for such methods. Currently, these data sets are col-
lected by expensive wired (or one hop wireless) and powered data
acquisition systems. These systems typically consist of a single
device that supports a fixed number of channels. Each channel
is connected to one sensor. Data acquisition systems include so-
phisticated signal conditioning, processing and analysis functions.
A simpler, and cheaper, variant of a data acquisition system is a
data logger—it lacks some of the analysis capabilities of a data ac-
quisition system, and merely provides storage and high-bandwidth
transmission capabilities for the collected data.

Data acquisition systems collect structural response either to am-
bient vibrations, or forced vibrations. Ambient vibrations can be
caused by earthquakes, or passing vehicles. In large structures such
as bridges and buildings, wind can also evoke structural response.
Obviously, systems that collect structural response to ambient vi-
brations are generally long-running, since the occurrence of signif-
icant ambients may be unpredictable. For this reason, especially
from structures under test, engineers collect structural response to
forced vibrations. Occasionally, these are delivered by large shak-
ers: mechanical devices with large moving parts attached to the
structure, whose motion vibrates the structure at different frequen-
cies.
In either scenario, setting up a data acquisition system is an ex-
pensive proposition and a cumbersome endeavor. Data acquisition
systems are expensive, which limits the number of points on the
structure that can be instrumented. Furthermore, installing the ca-
bling for the sensors and the power for the data acquisition sys-
tem itself is a logistical challenge. Anecdotally, engineers reckon
preparing a structure for data collection can take 2-3 weeks.
In this paper, we consider whether wireless sensor networks can
potentially replace structural data acquisition systems. Sensor de-
vices offer the freedom from cabling and associated placement con-
straints. This, together with multi-hop routing, allows a very flexi-
ble instrumentation infrastructure. On the other hand, several con-
straints of sensor networks make it difficult to design a wireless
structural data acquisition system. Most important of these is en-
ergy: not only is wireless communication energy-intensive, but
accelerometers themselves are not low-power as we discuss later.
Other challenges include limited radio bandwidths, high packet loss
in wireless environments, and lack of time synchronization. We re-
turn to these challenges later.
Given our discussions above, a wireless long-lived (for several
weeks) structural data acquisition system for measuring response to
ambient vibrations will require careful systems engineering. We do
not undertake this endeavor in this paper. Rather, we focus on the
design of a structural data acquisition system that can be deployed
for a short-term (a few hours to a day), such that it is possible to
provision adequate battery power. Usually, such a system will be
deployed in situations where forced vibrations are used to excite a
structure. In these situations, a wireless system has two advantages:
rapid deployment and flexibility. Both these advantages are evident
in the following actual episode. A transportation agency is ready to
declare a newly built bridge open, but allows a team of structural
engineers one or two days to measure structural properties by, for
example, driving a large truck through the bridge. While wiring
such a structure might take hours to days, a wireless network can be
deployed in tens of minutes. Often, the challenge in such scenarios
is not knowing where to instrument the structure. This is usually
because the structural characteristics may not be precisely known.
A wireless data acquisition system allows the engineers to iterate
on sensor placement to determine appropriate locations.
3. Wisden: BACKGROUND AND DESIGN
OVERVIEW
In this section, we discuss the design of Wisden, our structural
data acquisition system. We first describe the hardware that we use,
then present the abstraction that the system provides to the user,
and finally give a brief overview of how the system works. In the
subsequent sections, we describe the system internals in detail.
3.1 Hardware
Wisden uses mostly off-the-shelf hardware. Specifically, our
sensor nodes are the Mica-2s. The Mica-2 represented a conve-
nient low-power platform which already had a few software com-
ponents that we could re-use for our purpose. Although careful
power management and recording ambients was not a goal of our
project, moving in that direction is now easier since we have started
with the Mica-2. However, the memory constraints of the Mica-2
made it a slightly more difficult platform choice, since our applica-
tion is memory intensive.
Existing sensor platforms do not, however, have hardware sup-
port for high quality vibration sensing. So, Wisden uses a 16-
bit vibration card designed specifically for high-quality vibration
sensing. The card was originally designed for high-frequency (up
to 20ksps), sampling at 16 bits per sample. It consists of 4 sepa-
rate analog input channels. Each channel has sensor excitation (5V
or 18 V constant current), gain, attenuation and a programmable
anti-aliasing filter. The analog channels are interfaced to a 16-bit
analog-to-digital converter. The ADC is controlled by an on-board
microprocessor, and exhibit a sensitivity of 100mV/g.
2
In turn,
the microprocessor can be commanded by an attached Mica2 mote
(which runs the Wisden software) to set the sampling rate, read
the output data, and stores the samples into an external 64K byte
SRAM.
The vibration card is designed for low power operation. Two
separate, controllable, power supplies allow the card to power up
different circuits. One of the circuits supplies power to the on-board
microprocessor and is enabled by a control line from the Mica2.
Once the microprocessor is powered, commands from the mica2
then enable analog power to the sensors and signal conditioning
circuits. Full power is only used during data acquisition; during
this time, the current draw is about 100 mA. After data is stored in
the on-board SRAM the analog power can be disabled while data
is being retrieved. Data can be retained in the SRAM at a very low
sleep current (< 50 µA) until needed.
The vibration card was not specifically designed for our appli-
cation: lower frequency (100 Hz) continuous sampling. As such,
it draws rather more power than one would expect from a board
specifically designed for our application. We believe we can reduce
the current draw by customizing the board to our application us-
ing various tricks: removing the on-board microprocessor and the
SRAM, and multiplexing the signal conditioning circuitry across
the different channels. We estimate that the current draw in such a
board will be in the 40 mA range.
Finally, we modified the on-board microprocessor’s software to
permit continuous sampling. Our modified software allows peri-
odic, sample-by-sample, data acquisition and does not use the on-
board SRAM on the vibration card. Getting our new firmware
working proved to be a significant software engineering challenge
because there was a pin conflict between the vibration card and
the EEPROM which Wisden uses to store vibration samples. We
finally solved this using some tricky low-level handshaking to arbi-
trate the use of the conflicting pin.
3.2 Wisden Abstraction
The goal of Wisden is to provide the abstraction of a data acqui-
sition system (in its current form, Wisden provides the functionality
of a data logger as it lacks the on-line data processing capabilities
present in data acquisition systems). Traditional data loggers sup-
port a fixed number of channels. By contrast, Wisden can support
a flexible number of channels by trading off acquisition latency or
if the measured vibration activity is intermittent (see below). In all
other respects, Wisden seeks to emulate data loggers as closely as
2
The accelerometer used with the vibration card provided a low
noise of 300µgrms.

possible. Of course, the implementation of Wisden is quite differ-
ent from that of traditional data loggers, as we discuss below.
A data logger or acquisition system abstraction implies that sam-
ples are centrally collected in near real-time. An alternative ap-
proach would have been to design a system where the data at each
sensor is stored at the sensor node and retrieved later manually. The
storage limitations on current platforms limit the amount of vibra-
tion data one could collect. More fundamentally, however, such a
system would be cumbersome to use. It would also not allow struc-
tural engineers to iteratively decide where to place the accelerome-
ters, a crucial requirement for data collection.
3.3 Wisden Overview
Although the abstraction presented by Wisden is simple, its de-
sign and implementation is rather challenging. A typical Wisden
deployment will consist of several tens of nodes placed at differ-
ent locations on a large structure. Each node has an attached ac-
celerometer that is capable of sensing up to three channels of vi-
bration data, with a configurable sampling rate. A base station
provides the functionality equivalent to a data logger or acquisi-
tion unit—the ability to store samples and to provide near real-time
display of samples. Nodes self-configure to form a tree topology,
then send their vibration data to the base station, potentially over
multiple-hops.
Implicit in the data acquisition system abstraction that Wisden
provides are two essential design requirements: that the vibration
samples be delivered reliably to the base station, and that samples
be time-synchronized. Further complicating the design of the sys-
tem is the fact that the data rates from a single sensor node can be
a significant fraction of the radio bandwidth available on current
sensor platforms. For example, a tri-axial accelerometer generat-
ing 16-bit samples at 100 Hz requires 4.8 Kbps. The Chipcon radio
nominally provides 19.9 Kbps after accounting for coding over-
head, but achievable radio data rates are closer to 10 Kbps.
Clearly, the bandwidth limitation implies that reliably delivering
every sample from tens of nodes is infeasible. Fortunately, struc-
tural engineers are content to acquire vibration data correspond-
ing to interesting events relatively large motions caused by earth-
quakes, high wind, or large vehicles.
3
Accordingly, nodes in Wis-
den locally compress the data before transmitting it to the base sta-
tion. Of course, this approach serves to reduce energy usage as
well, and represent the kind of in-network processing that sensor
networks are predicated on. Our current implementation of Wis-
den incorporates a simple run-length encoding scheme, but we also
implement and evaluate more sophisticated wavelet compression
schemes. We have not yet integrated the latter into Wisden given
memory limitations.
Once the nodes generate compressed data, they transmit data to
the base station. Data transmitted by a node is rate-limited, and the
rate limits are currently manually configured (we discuss this later
in detail). Wisden nodes implement a hybrid hop-by-hop and end-
to-end error recovery scheme to enable reliable transmission of data
to the base station. In this scheme, vibration samples are recovered,
to the extent possible, in a hop-by-hop fashion. Wisden’s error re-
covery protocol aggressively uses overhearing and piggybacking
techniques in order to detect and repair packet loss. (We can do this
because, at least in its current design, Wisden does not put nodes
or radios into low-power states.) Given high packet losses on links,
3
By contrast, seismologists, who sometimes monitor structural re-
sponses to micro-tremors, usually require even low-levels of vibra-
tion to be recorded. Another interesting difference is that seismol-
ogists are interested in 24-bit data, so the current instantiation of
Wisden is insufficient for their needs.
this approach can reduce the overhead of error recovery. However,
topology changes and high packet loss rates necessitate a fallback
end-to-end recovery scheme that ensures reliable end-to-end deliv-
ery.
Finally, Wisden also implements a data time-stamping scheme
that is qualitatively different from the time synchronization schemes
discussed in the literature [3, 4]. In this scheme, as a packet is
transmitted to the base station hop-by-hop, it acquires enough tim-
ing information for the base station to determine when (by its local
clock), the corresponding samples were generated by the sending
node. In this fashion, samples corresponding to the same event, but
generated by two different nodes, can be synchronized at the base
station
4
.
The rest of the paper discussed these three main components
of Wisden: reliable data transport, compression and data time-
stamping. In each section, we discuss the design of each com-
ponent, then evaluate it using our implementation. We follow this
with a section that presents preliminary measurement data from an
actual structure.
4. RELIABLE DATA TRANSPORT
The first challenge in Wisden is to reliably transmit data from
each sensor to the base station. Techniques for reliable transport in
networking are well-studied in the networking literature and Wis-
den leverages many of these techniques. In particular, Wisden uses
both hop-by-hop and end-to-end recovery; the former is a necessary
performance optimization in wireless networks where link losses of
up to 30% are not uncommon [21].
In our current implementation of Wisden, nodes first self-organize
into a tree topology. Each node stores the generated vibration data
into its EEPROM (after run-length encoding compression, described
in the next section), and then transmits it to the base station. An
aspect closely related to reliable transport is sending rate adapta-
tion. In our current implementation of Wisden, node transmission
is rate-limited to a configured value. In this section, we describe
the topology self-configuration and data transport components of
Wisden, and evaluate its performance.
4.1 Related Work
Reliable, congestion-adaptive data transport for wireless sensor
networks is an ongoing area of research. Recently several relia-
bility protocols have been proposed. RMST [13] (Reliable Multi-
Segment Transport) is a transport layer protocol that is designed
to add reliable service on top of Directed Diffusion. RMST is a
NACK-based protocol, receiver detects loss and loss is repaired
hop-by-hop. In this respect, it most closely resembles Wisden’s
mechanisms, but because it is integrated with Diffusion, designed
for larger platforms, and optimized for recovering losses of image
fragments, it was unsuitable for our application. PSFQ [17] (Pump
Slowly, Fetch Quickly) is a hop-by-hop reliable transport protocol
designed for sensor network reprogramming. In this application,
the direction of data transfer is from a base station to all the nodes
in the network. In Wisden, data transfer is in the opposite direction.
There has also been some recent work on congestion control
for wireless sensor networks. Two examples of such work are
CODA [18] and ESRT [12]. Both these pieces of work are less
concerned with reliable data transfer from sources to sinks. Rather,
they are designed for applications in which an event may be de-
tected by correlated sources, and the system needs to avoid a degra-
4
Of course, this technique generalizes easily to synchronizing sam-
ples at intermediate network nodes (e.g., at a common ancestor in
the sink tree), but we have not implemented this in Wisden.

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Q1. What contributions have the authors mentioned in the paper "A wireless sensor network for structural monitoring" ?

In this paper, the authors discuss the design and evaluation of a wireless sensor network system ( called Wisden ) for structural data acquisition. The authors also study the applicability of wavelet-based compression techniques to overcome the bandwidth limitations imposed by lowpower wireless radios. The authors describe their implementation of these mechanisms on the Mica-2 motes and evaluate the performance of their implementation. The authors also report experiences from deploying Wisden on a large structure. 

The choice of signal threshold and number of quantization bins is assumed to be determined by a priori analyis of training data to obtain maximum compression benefit within the specified error bounds. 

The authors were able to perform sensor data sampling, 128 sample CDF(2,2) wavelet lifting transform as well as writing the decomposed buffer to the EEPROM for sampling rates upto 250Hz. 

The authors believe the authors can reduce the current draw by customizing the board to their application using various tricks: removing the on-board microprocessor and the SRAM, and multiplexing the signal conditioning circuitry across the different channels. 

Advances in structural engineering depend upon the availability of many detailed data sets that record the response of different structures to ambient vibration (caused, for example, by earthquakes, wind, or passing vehicles) or forced excitation (delivered by large special-purpose shakers). 

A transportation agency is ready to declare a newly built bridge open, but allows a team of structural engineers one or two days to measure structural properties by, for example, driving a large truck through the bridge. 

The slope of the line corresponds to a drift of 10ppm, which matches the relative drift the authors measured usingbelieve that because their timestamping requirements are relatively coarse (order of ms), they will not affect Wisden significantly. 

The predict and update operations for the CDF(2,2) lifting transform are:di ← di − 12 (si + si+1)si ← si − 14 (−di−1 − di)The choice of the above lifting transform over other kernels was based on two factors: computation overhead and compression performance. 

Even if the data sets are used only for frequency analysis, it is necessary to timestamp the samples in order to distinguish responses due to different events. 

if the authors set the sending rate to 2 packet/sec per node, their network essentially collapses and very few of the packets are received. 

systems that collect structural response to ambient vibrations are generally long-running, since the occurrence of significant ambients may be unpredictable. 

The authors used an oscilloscope to extract the clock signal from 7 different Mica-2s, then analyzed the dominant frequency in the signal. 

As the authors show below, such an approach can compress vibration data by a factor of 20; when coupled with event detection, it can reduce the acquisition latency to less than a minute in many cases. 

the overall data rate required to transmit the samples is a function of the duty-cycle of the vibrations, and directly affects7 

The authors perform the normalization operations during the wavelet thresholding step rather than during wavelet decomposition to be more computationally efficient. 

This packet loss performance can be measured both passively (using actual data transmissions) and actively (using probes sent by nodes).