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In-Pavement Wireless Weigh-In-Motion
Ravneet Bajwa, Ram Rajagopal, Erdem Coleri, Pravin Varaiya and
Christopher FloresSensys Networks, Inc1608 4th St, Suite 200
Berkeley CA 94710{rbajwa, rrajagopal, pvaraiya, cflores }
@sensysnetworks.com, [email protected]
ABSTRACTTruck weight data is used in many areas of
transportationsuch as weight enforcement and pavement condition
assess-ment. This paper describes a wireless sensor network
(WSN)that estimates the weight of moving vehicles from
pavementvibrations caused by vehicular motion. The WSN consistsof:
acceleration sensors that report pavement vibration; ve-hicle
detection sensors that report a vehicle’s arrival anddeparture
times; and an access point (AP) that synchro-nizes all the sensors
and records the sensor data. The paperalso describes a novel
algorithm that estimates a vehicle’sweight from pavement vibration
and vehicle detection data,and calculates pavement deflection in
the process. A pro-totype of the system has been deployed near a
conventionalWeigh-In-Motion (WIM) system on I-80 W in Pinole,
CA.Weights of 52 trucks at different speeds and loads were
es-timated by the system under different pavement tempera-tures and
varying environmental conditions, adding to thechallenges the
system must overcome. The error in loadestimates was less than 10%
for gross weight and 15% forindividual axle weights. Different
states have different re-quirements for WIM but the system
described here outper-formed the nearby conventional WIM, and meets
commonlyused standards in United States. The system also opens
upexciting new opportunities for WSNs in pavement engineer-ing and
intelligent transportation.
Categories and Subject DescriptorsC.3 [Special-Purpose and
Application-Based Systems]:Realtime and Embedded Systems, Signal
Processing Sys-tems; I.5.4 [Applications]: Signal Processing,
WaveformAnalysis
General TermsDesign, Measurement, Experimentation,
Algorithms
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KeywordsWeigh-In-Motion (WIM), traffic monitoring, pavement
vi-brations, pavement deflection, real-time pavement monitor-ing,
structural health monitoring, pavement-vehicle interac-tion model,
accelerometers
1. INTRODUCTIONTransportation agencies such as Caltrans use
weigh sta-
tions to enforce weight limits, collect fees, and record
truckweight data. For assessment of pavement life and
pavementquality, it is critical to know the loads being applied to
thepavement. The weight data is, therefore, used to make im-portant
decisions concerning road maintenance, pavementdesign, and
transportation policy at both the state and na-tional levels [10].
Federal Highway Administration (FHWA)recognizes the importance of
weight data and recommendsan increase in the number of stations
collecting such data.However, traditional static weight stations
are very expen-sive to install and operate, and also require that
the trucksare stopped and weighed individually. An alternative
totraditional weigh station is a weigh-in-motion (WIM) sys-tem that
is installed on an existing highway lane and canestimate the weight
of vehicles at highway speeds withoutdisrupting the traffic flow.
However, since the typical costof a WIM system is around $0.5M,
they are very expen-sive for widespread deployment. The main
reasons for suchhigh cost are: use of expensive force sensors;
constructionwork required to embed the wired sensors in the road;
andthe prolonged road closures during installation and
main-tenance. In this paper we describe an alternative
systemcomprising an embedded wireless sensor network that mea-sures
pavement vibration, temperature and vehicle speed toinfer the
individual axle loads of moving vehicles. Unlikecurrent WIM
systems, the wireless WIM uses relatively in-expensive sensors and
a much easier installation procedureto reduce the overall cost. We
believe this is the first wire-less sensor network capable of
weigh-in-motion in individuallanes at highway speeds.
Current WIM technologies. The most widely used WIMtechnologies
consist of a pair of wired magnetic loops and aforce sensor, as
shown in Figure 1. The magnetic loops de-tect vehicles and estimate
their speed. The force sensors(piezoelectric plates, load cells or
bending plate sensors)measure the instantaneous force (or load)
applied by thetires of a vehicle. A major drawback of these
technologiesis that they require smooth concrete pavement to be
builtaround the force sensors to achieve the desired accuracy.
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Figure 1: WIM station consisting of two wired mag-netic loops
and piezoelectric plates in the middle formeasuring force (left).
Installation procedure for aWIM station (right). The load cells are
installedfirst and smooth concrete pavement is built aroundthem to
reduce the effect of vehicle’s suspension sys-tem on measured load
[2].
Pavement roughness excites the vehicle’s suspension
systemcausing the instantaneous axle load to be different from
thestatic load. The difference between the instantaneous andstatic
load, known as the dynamic component of appliedload, is reduced by
having a smooth pavement. However,this construction increases the
system cost and the installa-tion time, typically requiring several
days or even weeks oflane closure. As an alternative to this
approach, the use ofmultiple force sensors on existing pavement has
been sug-gested to improve the estimate of static load [5], but
currenttechnologies are too costly to make this approach
feasible.The WSN described here uses a different sensing
principle,and makes this multi-sensor approach much more cost
effec-tive.
Contributions. Enabling wireless WIM requires overcom-ing
significant challenges in sensing, pavement modeling, sig-nal
processing and estimation. The main contributions ofthis paper to
enable this concept are:
• An easy to install embedded wireless vibration sensorcapable
of measuring pavement acceleration in a verynoisy environment
(Section 3).
• Design and verification of the wireless WIM systemcomprising
vibration, speed and temperature sensors,and an access point that
can be used to compute loadsin real-time (Section 3, 7).
• A simplified and novel model relating individual axleload to
pavement acceleration (or displacement), tem-perature and speed of
the vehicle (Section 5).
• A new algorithm to estimate pavement displacementfrom ground
acceleration and to isolate individual axleresponses from the
combined response (Section 5).
• A novel load estimation procedure that calibrates
fortemperature, vehicle speed, and local pavement condi-tions
(Section 5).
• Experimental testing of the system on a real highway,under
different weather conditions, and a variety ofaxle load
distributions (Section 6).
The paper is organized as follows. Section 2 describes
theproblem of weigh-in-motion, related work, proposed solutionand
its challenges. Section 3 describes the wireless WIMand associated
components. Section 4 describes the experi-mental setup used to
collect data for calibration and systemevaluation. Section 5
proposes a simplified pavement-vehicleinteraction model and
describes the load estimation algo-rithm. Section 6 reports
experimental results and Section 7concludes the paper.
2. WEIGH-IN-MOTIONIn this section, we state the problem of
weigh-in-motion
and propose a wireless solution. We list the challenges
thesystem must overcome and conclude with a discussion ofrelated
work done in the field.
2.1 Problem statementA vehicle with K axles moves in a traffic
lane at v miles
per hour. Axle i weighs fi and the total vehicle weight is
fpounds. The goal of a WIM system is to detect the presenceof a
vehicle, measure its speed v, count the number of axlesK and
measure inter-axle spacing, and provide estimates offi and f with a
required statistical accuracy. The systemcan be calibrated once a
year, utilizing a few pre-weighedvehicles.
There are some important additional requirements thatany
solution to this problem must meet. The system shouldweigh vehicles
in individual lanes and should be accurateindependent of time and
weather conditions. It should alsobe able to account for vehicle
wander, i.e., vehicles movingslightly off-center in a given lane.
Finally, installation andmaintenance costs should be kept at a
minimum to enablewidespread deployment. A significant portion of
the costis due to traffic disruption from lane closures during
instal-lation and maintenance. These costs are easily five to
tentimes more than the cost of measurement system.
2.2 Proposed solution: Wireless WIMReducing cost of the WIM
system requires rethinking the
most critical component of the system: the force sensor.
Theforce sensor works by replacing part of the pavement witha
platform that bears the full load of each axle, and provid-ing
signals to estimate it. In order to avoid replacing thepavement, we
propose utilizing the existing pavement itselfas the transducer and
estimating individual axle loads fromthe measured vibration
response of the roadway. Small vi-bration and vehicle detection
sensors are embedded in thepavement utilizing a convenient and low
cost procedure. Thevehicle detection sensors [13] report the
arrival and depar-ture times of a vehicle which are used to
calculate its speedand length. The vibration sensors report the
pavement’svertical acceleration and its temperature. Multiple
arraysof vibration sensors are used to average out the
dynamiccomponent of load. The acceleration data is processed
toextract the pavement’s response due to each individual axle.This,
along with speed and temperature data are then usedto estimate axle
loads. The axle loads are simply added toget gross vehicle weight.
Vehicle length, number of axles andaxle spacing are estimated using
the Axle Detection (ADET)algorithm described in [2].
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2.3 ChallengesThe system needs to overcome several
challenges:
Measurement: The road pavement is designed to experi-ence very
small vibrations from vehicle movement [5]. Thevibration sensor
must measure these small vibrations whilebeing immune to the high
environment noise arising fromvehicle sound and traffic in
neighboring lanes.
Modeling: The relationship between applied axle load andpavement
vibrations is not well-understood. Most pavementmodels relate
pavement deflection to applied load, but es-timating pavement
deflection from acceleration is a chal-lenging problem in itself.
Moreover, the response is highlydependent on pavement temperature
and speed of the ve-hicle, and these variables must be properly
accounted for.Another challenge is to estimate static load from
dynamicload, as discussed before.
Signal processing: The pavement response at any giventime and
location is an accumulated response due to all ve-hicles in the
vicinity, therefore response due to other vehi-cles needs to be
filtered out. An even harder challenge isto extract the pavement
response due to each axle becauseat any given time, all the axles
of a vehicle are affectingsensor measurements. Additionally, the
signal processingalgorithms have to be simple enough for real-time
executionand efficient enough to conserve energy for a longer
lifetime.
Design: The sensors should be well coupled to the pave-ment and
robust enough to withstand the tire forces. Thesystem should also
be insensitive to vehicle wander. It shouldbe cost-effective and
convenient to install and maintain, andhave a lifetime of at least
4 years [4].
2.4 Related workWe identify four areas related to this work:
applications of
wireless sensor networks (WSN) in transportation, applica-tions
of sensor networks in infrastructure monitoring, weigh-in-motion
sensor technologies, and algorithms that estimatepavement
displacement from acceleration.
Applications of WSNs in transportation have been grow-ing. WSNs
have been used for vehicle detection using mag-netic sensors [7,
15, 23], classification of vehicles in differentcategories [2], and
increasing road safety by intervehicularinformation sharing [22].
Much less has been done in termsof monitoring the response of road
infrastructure itself.
Monitoring large infrastructures using accelerometer sen-sor
networks has been studied for structural monitoring ofbridges [14],
buildings [6] and underground structures suchas caves [16]. Wired
embedded sensors in concrete struc-tures have been investigated
[19] but usually require com-plex installation procedures and have
limited lifetime if usedin roads.
WIM technologies have not advanced much in the lastdecade and
focus has shifted on using multiple WIM sensorsto improve system
accuracy, as opposed to requiring special-material pavement near
the sensors [10, 3]. A novel WIMsensor based on perturbation theory
of microwave resonantcavities is presented in [17], and a special
fiber optic sen-sor based on measuring light loss under mechanical
stressis discussed in [18]. However, both sensors were tested in
acontrolled laboratory setting, and challenges regarding
roadinstallation and sensor durability under heavy loads werenot
addressed.
Estimating pavement deflection (or displacement)
fromacceleration is a challenging problem in itself. Simple dou-ble
integration amplifies the low frequency noise leading toa large
unpredictable drift [6]. Popular techniques for driftcorrection
include fitting some polynomial during the silentperiods to
estimate drift, and subtracting it from the calcu-lated
displacement to correct it [12, 1]. However, correctedsignals are
highly sensitive to the choice of the drift poly-nomial, and these
techniques do not perform as well for lowSNR measurements.
3. WIRELESS WIM SYSTEM
Figure 2: Wireless WIM system: The accelerometerand magnetometer
sensors report data to the accesspoint. The data is stored locally
on hard drives andcan be transferred remotely via a cellular modem
[2].
Figure 2 shows the schematic of the proposed system.There are
four components: vibration sensors, vehicle detec-tion sensors,
access point (AP), and a pan-tilt-zoom (PTZ)camera (not shown)
connected to the AP. The vibration andvehicle detection sensors are
installed in the pavement asshown whereas the rest of the equipment
is mounted on a15ft pole on the side of the road. The vibration and
vehicledetection sensors follow a TDMA schedule to transmit
theirdata to the AP. The camera captures images of vehicles
tovalidate that the sensor data corresponds to the correct
ve-hicles. For accurate time stamps on the data, the sensors,the
AP, and the camera are periodically synchronized to acommon Network
Time Protocol (NTP) server. Data fromthe site can be collected 24x7
and the AP saves all this datalocally. The data can be retrieved
through a local WiFi con-nection to the AP or remotely via a
cellular connection. Infact, the entire system can be monitored and
controlled thisway. We now describe the network components and
theircommunication protocol.
3.1 Sensor network componentsWireless vibration sensor. Figure 3
shows the block di-agram for the sensor. Vibrations from the
pavement areconverted to analog voltage by a MEMS accelerometer
onboard [8]. The voltage signal is then passed through a
filterstage. The output of the filter stage is sampled at 512 Hz
bya 12-bit ADC included in MSP430 microprocessor. The col-lected
samples are then transmitted via the radio transceiverusing a TDMA
based, low power consuming protocol. Alongwith each packet of
acceleration data, the vibration sensoralso sends out a temperature
reading using the on-board
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analog temperature sensor. The average current consump-tion of
the vibration sensor is 1.96 mA in active mode and 35µA in idle
mode. Using a 7200 mAhr battery, the respectivelifetimes are around
5 months and 23 years respectively. Fordata collection purposes,
lifetime is sufficient and techniquessuch as in-sensor processing
(Section 7) can extend this forother applications.
Figure 3: Block Diagram of the vibration sensor [2].
Simulations reported in [21] revealed that the sensor musthave a
resolution of 500 µg at a bandwidth of 50 Hz. Thehighway
environment is extremely noisy, and noise fromsound alone is a few
mg if the sensor is not properly iso-lated. Another problem is that
vehicles in the neighboringlanes cause pavement vibrations and
corrupt our measure-ments. In order to estimate the load of a given
vehicle, weneed the pavement vibrations corresponding to that
vehiclealone. Any measured vibrations due to another vehicle
willcontribute to error in our load estimates.
Filtering signals above 50Hz with a steep filter can elimi-nate
sound noise significantly. It was shown in [2] that a lowpass
filter with frequency response H(jω) = 1
(1+ jω50
)2(1+ jω500
)
successfully isolates the sensor from most of the sound.
More-over, the sensor case shown in Figure 5 attenuates sound
be-fore it reaches the accelerometer, providing more isolation.
To provide isolation from traffic in neighboring lanes,
thesensors are placed towards the middle of the lane. Pave-ment
vibrations are maximum at the location of appliedload and magnitude
decreases exponentially away from thatlocation [11]. Center
placement maximizes the distance ofneighboring-lane vehicles from
the sensors, thus minimizinglane-to-lane interference.
Vehicle detection sensor. A wireless magnetic sensor isused to
infer the presence of a vehicle by measuring changesin the local
magnetic field. The sensor transmits the arrivaltime ta and
departure time td of a vehicle as it arrives atthe sensor and
traverses it. Multiple sensors are combinedto estimate speed. These
sensors have a lifetime of over 10years [13].
Pan-tilt-zoom (PTZ) camera. The PTZ camera takesvehicle images
from the side of the road and transmits themto the AP using a wired
connection. The power to the cam-era and AP is provided through
Caltrans controller box onthe side of the road.
Access point (AP). Figure 4 shows the schematic of the
access point. This equipment provides remote control
andobservation of the WSN. The AP contains: (i) A processorwith
attached radio and 2TB hard drive storage; (ii) a powercontroller
that controls power to each connected device; (iii)an ethernet hub
through which a local area network (LAN)is setup for devices to
communicate with each other; (iv) a3G modem that acts as a gateway
to the wide area network(WAN) and enables remote access to the
system; and (v) aWi-Fi bridge and an ethernet data port for local
access tothe system. Once a remote computer is connected to the
AP,it can communicate to any of the connected devices throughthe
LAN. It can, for instance, use the power controller toturn on/off
individual components in the box, send com-mands to the sensors via
the radio, change the settings ofthe PTZ camera, and start
collecting video and sensor dataremotely.
Figure 4: Schematic of the access point.
3.2 Communication protocolWe focus on the communication protocol
followed by the
wireless sensor nodes and the AP. Other components followwidely
used standard protocols and are not discussed here.The sensors
follow a TDMA protocol that uses headers verysimilar to IEEE
802.15.4 MAC layer. Time is divided intomultiple frames with each
frame about 125 ms long. Eachframe is further divided into 64 time
slots, numbered 0 to 63,most of which can be used by the sensor
nodes to transmitdata. Timeslot 0 is used by the AP to send clock
synchro-nization information and other commands to the sensors.The
AP assigns every node unique time slots and a networkaddress (or
node ID) to communicate with it. This sched-ule enables individual
nodes to stay awake for the minimumamount of time and prevents
packet collisions. There arethree major applications of this
protocol: synchronization,sensor management, and firmware
update.
Synchronization. This application ensures clock synchro-nization
of all nodes within 60 µs. Sync packets are sent bythe AP on a
periodic basis with very low jitter. Nodes mustfirst synchronize
their clocks before transmitting. When asensor node first starts,
it listens to sync packets every 125ms. It learns the difference
between its clock and the AP’sclock, and over time improves its
estimate of the AP’s clock.As the estimate improves, the node
converges to a steadystate in which it listens for a sync packet
only once in 30
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s. If a node loses sync, it repeats the above process to
getsynchronized again. In addition to sending clock informa-tion,
the sync application is also used to send commands toindividual
sensors like change mode, set RF channel, resetsensor .
Sensor management. This is the most important applica-tion for
both sensors. For the vibration sensor, the applica-tion controls
when to turn on the accelerometer and relatedcircuitry, when to
sample, and when to wake up the radioto transmit the data
collected. There are two main modesin this application: idle mode
and raw data mode. In idlemode, the accelerometer and related
conditioning circuitryare turned off by disabling the voltage
regulator that powersthis part of the circuit. Even the
microcontroller and the ra-dio transceiver are put in a low power
consuming state mostof the time. Once every 30 seconds, the
microcontroller andthe transceiver wake up and acquire the sync
packet. Inraw data mode, the accelerometer and related circuitry
areturned on. The microcontroller wakes up every 1/512 sec-onds and
samples the analog output from the accelerometerunit, as shown in
Figure 3. In addition to waking up forthe sync packet, the
transceiver wakes up right before itsallotted timeslots to send the
sampled data. Due to chal-lenging environment of highways, sensors
frequently sufferfrom packet loses. To fix this problem, we
transmit everypacket twice after a slight delay.
For the detection sensor, the application is similar. Thekey
difference is that instead of the raw data mode thereis a vehicle
detect mode. The magnetometer is constantlysampled at 128 Hz,
followed by in-sensor processing to de-termine if the vehicle is
present or not. Only in case of adetection is any data transmitted,
as opposed to the vibra-tion sensor which continuously transmits
raw data. Sincethe data throughput from detection sensors is very
small,each packet is retransmitted until an acknowledgement
isreceived from the AP.
The AP receives data from each sensor, appends useful
in-formation such as the timestamp, Received Signal
StrengthIndicator (RSSI), the Link Quality Indicator (LQI),
andrecords it into a file that can be processed offline.
Firmware update. This application allows reprogram-ming the
entire flash memory of a sensor node over the air,via the AP. Using
this mode, any future upgrades in the sen-sor firmware can be made
remotely and since no lane closuresare needed, it considerably
reduces maintenance costs.
3.3 System designIn order to overcome the measurement challenges
described
in Section 2.3, sensor casing, system layout, and
installationprocedure need to be selected carefully.
Sensor casing. In order to withstand large forces in a
harshenvironment, the sensors must be packaged for durabilitybefore
installation. The circuit board and the battery areplaced in a hard
plastic casing as shown in Figure 5. Thecasing is then filled with
fused silica and sealed air tight.This protects the electronics
from rain water, oil spills etcon the road and further attenuates
interference from sound.
System layout. Figure 6 shows the selected layout. Thevehicle
detection sensors are set in the standard recommendedconfiguration.
There are four arrays of vibration sensors in-
Figure 5: Packaging of the sensors in a sealedcase [2].
Figure 6: System layout: detection sensors reportvehicle
detection time and multiple array of vibra-tion sensors report
pavement acceleration for loadestimation [2].
stalled 15 ft apart, with five sensors in each array. The
sensorlayout is designed to minimize lane-to-lane interference
andmaximize the in-lane signal-to-noise ratio. The pavementresponse
at the sensor location reduces exponentially withthe distance
between the sensor and applied force [11]. Thuswe minimize the
interference from neighboring lane vehiclesby placing the sensors
in the middle of each lane as thismaximizes the distance between
the sensors and neighbor-ing lane vehicles. An additional important
benefit is thatthis placement minimizes the effect of vehicle
wander. Theleft and right wheels of a vehicle contribute additively
to sen-sor measurements. Vehicles moving off-centered in the
lanewill have one wheel closer to the sensors than the
other.Therefore, reduction in measurements from one wheel
arecompensated by the other to ensure that their sum remainsalmost
constant.
Installation procedure. In order to minimize the systemcost, the
installation procedure must be quick and simple.
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To install a sensor in the pavement, we drill a 4-inch di-ameter
hole, approximately 2 1
4inches deep at the desired
location. The sensor is placed in the hole, properly leveledwith
the earth’s surface, and the hole is sealed with fast-drying epoxy
[23], as shown in Figure 7. Each sensor can beinstalled in the road
in less than 10 mins. The AP and thePTZ camera are mounted on a
15ft high pole on the side ofthe road, and don’t require any lane
closures.
4. EXPERIMENTAL SETUP
Figure 7: Installation procedure for embedding thesensors in the
pavement [2].
This section describes deployment challenges and data
col-lection procedure used to test our system.
Deployment challenges. A test system was installed onI-80 W in
Pinole, CA, about 300 ft away from an exist-ing WIM station. This
WIM station, operated by Caltrans,measures and records weights for
every passing truck whichwe planned to use as ground truth for
training and test-ing our system. However, the data provided by
this stationturned out to be inaccurate (Figure 18). Renting
individualtrucks for testing, on the other hand, is extremely
expensive.Fortunately, we were able to collect ground truth data
froma static weigh station in Cordelia, CA but it required
exten-sive coordination with local and state agencies, and
posedadditional challenges. Each truck had to be stopped andweighed
individually, and required the presence of a Califor-nia Highway
Patrol (CHP) officer. Moreover, the station islocated about 25
miles upstream from the wireless WIM inPinole, and some of the
trucks take alternative routes andnever arrive at our site.
Identification of trucks that reachour site is also very
challenging, given the volume of trucksthat go over the wireless
WIM every day. The trucks alsocannot be directed to drive in our
installation lane and oftentraveled in neighboring lanes. All these
factors limited thesize of our final dataset.
Data collection. Randomly selected class 9 trucks wereweighed
individually at the static weigh station. These truckshave 3 axles,
1 single axle and 2 tandem axles. Class 9 truckswere chosen because
these are the most common trucks onhighways and other truck classes
are made up of differentcombinations of these two axle types. For
truck identifica-tion, pictures of each truck were taken at the
station andmatched with images collected by the road-side PTZ
cam-era of the wireless WIM. Timestamps provided by the PTZcamera
are then used to extract data reported by the sen-sors:
• Speed data. Timestamps from the camera images arematched with
the detection sensor timestamps to getthe data corresponding to the
truck. Each vehicle de-tection sensor reports both the time of
arrival andtime of departure of the truck. A pair of sensors (i,
j)installed at a fixed known distance (dij) apart from
each other are used to estimate speed. Given the ar-rival times
tai and taj at the two sensors i and j, the
speed v is given by v =dij
|taj−tai|. The speed can then
be used to estimate the length (L) of the vehicle asL = v(tdj −
taj), where tdj is the departure time re-ported by sensor j. These
measurements have beenshown to be accurate in practice [13].
• Acceleration data. The arrival and departure timesreported by
detection sensors are used to estimate thetime window during which
the truck passed each arrayof vibration sensors. This time window
is then usedto extract the corresponding acceleration reported
byeach sensor.
• Temperature data. Temperature readings reported byvibration
sensors around the time of vehicle’s arrivalare averaged to get a
single estimate of pavement tem-perature around that time.
The collected ground truth data is a very good represen-tation
of the distribution of loads, speeds, and pavementtemperatures for
this site. Axle weights range from 10,000to 35,000 lbs, speeds vary
from 15 to 65 mph, and pavementtemperature from 15 to 40◦C. In
fact, most common WIMstandards use only a couple of pre-weighed
vehicles at dif-ferent speeds to verify WIM performance [10, 9]. In
orderto test the system under different environmental conditions,we
collected data on three different days over a span of sixmonths.
Most WIM standards finish their testing on a sin-gle day. In
addition to the ground truth from static weighstation, we also
obtained loads reported by the nearby WIMstation. This data
provides a useful one-on-one comparisonbetween our system and an
operational WIM system cur-rently used by the government.
Figure 8: Euler beam model for vehicle-pavementinteraction
[5].
5. LOAD ESTIMATIONIn this section, we propose a model for
vehicle-pavement
interaction that directly relates pavement acceleration,
ve-hicle speed, and pavement temperature to applied axle load.We
then describe the procedure used to extract pavement re-sponse due
to individual axles from the measured response.We end the section
by describing how the model is calibratedfor load estimation.
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5.1 Pavement-vehicle interaction modelWe start by describing the
model for pavement accelera-
tion (and displacement) at a constant temperature, and
thenexplain how measurements can be properly compensated
fortemperature variation. The simplest vehicle-pavement
in-teraction model is a composite one dimensional Euler beamresting
on an elastic Winkler foundation as shown in Fig-ure 8 [5, 21]. The
vehicle is modeled as a moving forcemodulated by its suspension
system. A typical pavement re-sponse due to a moving load is shown
in Figure 9. As an axleapproaches the pavement is pushed down, but
it returns toits original location after the axle has passed. The
responseof the pavement at any fixed location can be approximatedas
y(t) = FΦ(vt) [21], where y(t) is the vertical displace-ment or
deflection of the pavement, and the function Φ(·)mainly depends on
the structural and material properties ofthe pavement. The model is
linear in F , and vehicle speedv just scales the function Φ(·) in
time. This is a simplifyingassumption, and in general Φ(·) has some
dependency on vand unknown suspension frequencies of the vehicle
[21].
Figure 9: Example of pavement deflection due totwo-axle truck
moving at 50 km/h. Image takenfrom [1].
Based on typical measured responses (Figure 9) and the-ory
developed in [5, 21], we assume that the shape of pave-ment
response due to a single axle load is closely approx-imated by a
Gaussian function. Φ(vt), in our model, canbe interpreted as the
pavement response due to a unit forcemoving at speed v. Let η be
the amplitude of pavementresponse for a unit force, then Φ(t) and
y(t) can be writtenas:
Φ(t) = ηe−t2
2σ20 ,
y(t) = FΦ(vt),
= Fηe−v2t2
2σ20 ,
y(t) = Fηe−t22σ2 . (1)
The last step is obtained by assuming σ = σ0v
, where σ0 isthe width of pavement response due to a unit force,
whichdepends on pavement properties. Since we measure acceler-ation
and not displacement, we can convert the model intoa more
appropriate form,
a(t) = ÿ(t) = F Φ̈(vt),
= −Fη v2
σ20
(1− t
2
σ2
)e
−t22σ2 .
Now, let Ψ(t, σ) = −(
1− t2
σ2
)e
−t22σ2 and α = Fηv
2
σ20, and we
have the following relation for pavement acceleration due toa
single axle load:
a(t) = αΨ(t, σ).
From the definition of α, we see that
F =σ20η
α
v2= β
α
v2, (2)
y(t) = ασ20v2e
−t22σ2 = ασ2e
−t22σ2 .
The last step is obtained by combining Equations (2) and(1). The
unknowns α and σ can be estimated from themeasured acceleration
(Section 5.2), but β depends on axletype (single or tandem) and
pavement properties, and needsto be calibrated using trucks of
known weights (Section 5.3).For a K axle truck, with the ith axle
arriving at the sensor attime µi and applying a force fi, the
response can be writtenas the superposition of individual axle
responses (ai(t))i.e.
ai(t) = αiΨ(t− µi, σi), (3)
a(t) =
K∑i=1
αiΨ(t− µi, σi). (4)
Using a non-linear curve fitting procedure, described in
Sec-tion 5.2, we estimate αi, µi, and σi for each axle. Oncethese
have been estimated, each axle can be treated sepa-rately to
estimate quantities like individual axle loads (Fi)and pavement
displacement (yi(t)) due to each axle,
Fi = βiαiv2,
yi(t) = αiσ2i e
−(t−µi)2
2σ2i . (5)
Figure 10: Percentage change in pavement responsewith
temperature. For the same applied load, pave-ment acceleration (or
displacement) increases withincreasing temperature.
Temperature compensation. The above model is validfor a constant
temperature but pavement response for asphalt-concrete layer is
highly dependent on temperature. Usingthe thickness of different
layers and material parameters for
109
-
the pavement at this site, we developed a layered elastic
the-ory (LET) model to simulate the effect of temperature onthe
pavement response [20]. Figure 10 shows how the pave-ment
acceleration changes with temperature according tothe LET model.
The plot shows that pavement responsecan change over 15% with
changes in temperature aloneand proper temperature compensation is
needed for accu-rate load estimation.
Let τ(T ) be the ratio of the modeled response at 25◦Cand at
temperature T . To compensate for temperature, wenormalize all our
measurements to the reference tempera-ture of 25◦C as a(t, T =
25◦C) = a(t, T )τ(T ), where τ(T ) iscalculated using the LET
model. It can be seen from Equa-tion (4) that αi(T = 25) = αi(T
)τ(T ), and accordingly
Fi = βiαiv2τ(T ). (6)
5.2 Extracting individual axle responseIn order to extract
individual axle response, we follow a
two stage process. In the first stage, measurements frommultiple
sensors are combined to get an average pavementresponse for the
whole vehicle. In the second stage, we fitthis response to the
model described by Equation (4) andestimate αi, µi, and σi for each
axle.
Figure 11: Top plot shows the raw acceleration sig-nal measured
by the reference sensor. Bottom plotshows the average pavement
response am(t) and thefitted response a(t). There are 3 mexican-hat
func-tions in a(t) (at 0.6, 0.8, and 1.2 s resp.), each
corre-sponding to an axle. The response due to last axleis well
isolated from the others but the response forthe first two axles is
not isolated.
Average pavement response. The average pavement re-sponse
requires aligning the measurements from each sensor.Each signal is
first passed through a low pass filter to filterout high frequency
noise. The highest amplitude signal isthen designated as the
reference signal, and signals from allother sensors are
time-shifted to align with the reference sig-nal. Let akm(t) be the
time-shifted signal for the k
th sensor,and I the number of available sensors. Then the
average
pavement acceleration am(t) can be estimated as:
am(t) =1
I
I∑k=1
akm(t).
Figure 11 shows an example of the raw acceleration datafrom a
sensor, and the average pavement response am(t).The improvement
from filtering and combining signals canbe easily seen in the plot.
Figure 11 also highlights anotherimportant challenge in estimating
individual axle loads. Re-sponse due to each axle needs to be
decoupled and extractedfrom am(t). Because of high speeds and
relatively short axlespacings, the trailing axles of a truck arrive
at the sensor be-fore the pavement has relaxed from the first
axle’s load. Toextract each ai(t) from am(t), we use the following
algo-rithm.
Curve fitting algorithm. Let a(t) be the modeled re-sponse of a
K axle truck, given by Equation (4). Let �(t) bethe error between
the measured and modeled response forthe truck at time t i.e. �(t)
= (am(t) − a(t)). We can nowwrite the measured response as:
am(t) =
K∑i=1
αiΨ(t− µi, σi) + �(t). (7)
We estimate the unknown parameters {αi}Ki=1, {σi}Ki=1
and{µi}Ki=1 by minimizing the mean square error i.e.
(α∗i , σ∗i , µ∗i ) = arg min
αi,σi,µi
∫ ∞−∞
(am(t)− a(t))2dt,
(α∗i , σ∗i , µ∗i ) = arg min
αi,σi,µi
∫ ∞−∞
(am(t)−K∑i=1
αiΨ(t− µi, σi))2dt.
(8)
This is a non-linear least-squares problem that can be
solvedusing standard techniques. Once the fit is performed,
accel-eration and displacement corresponding to each axle can
becalculated using Equations (3) and (5). Figure 11 shows anexample
of how good the modeled response fits the measure-ments.
5.3 Model calibrationBefore individual axle loads can be
estimated using Equa-
tion (6), the parameter βi needs to be calibrated. In general,βi
is site specific and can depend on axle type but a set
ofpre-weighed trucks can be used to estimate it. Let N be thenumber
of trucks used in the training data, f̂ni be the loadestimate for
the ith axle of nth truck, fni be the true weight,vn be the speed,
α
ni be the corresponding fitted parameter
α∗i , and eni be the percentage error associated with the
load
estimates. The optimal βi can be calculated by minimizing
110
-
the mean-square percentage errors for the load estimates,
f̂ni = βiαniv2nτ(T ), (9)
eni =βiαniv2nτ(T )− fnifni
× 100,
= (βiαnifni v
2n
τ(T )− 1)× 100,
β∗i = arg minβ
1
N
N∑i=1
(eni )2,
β∗i = arg minβ
N∑i=1
(βαnifni v
2n
τ(T )− 1)2. (10)
Equation (10) is a standard linear least squares problem andcan
be solved for β∗i . Once β
∗i is known, individual axle loads
can be estimated using Equation (9).
6. RESULTS AND DISCUSSIONThe results discussed in this section
serve three goals: ver-
ify that the proposed model fits the data well, evaluate
theaccuracy of wireless WIM, and understand the effect of dy-namic
component of load on system accuracy.
Figure 12: Plot shows the estimated weights againstthe ground
truth static weights.
Model verification. We calibrate the model using the en-tire set
of trucks and examine how closely it explains thedata. Figure 12
compares the axle weights estimated by oursystem with their true
weights. The estimated loads trackthe true loads very closely (R2 =
0.99) but there is one inter-esting observation. The error in klbs1
increases as the trueweight increases. This is, however, by design
as percent-age errors (eni ) are more important for WIM systems,
andwe calibrate the system to minimize the percentage errors.If
error in klbs is minimized, the lighter axles will tend tohave much
higher percentage errors. Figure 13 shows the es-timated
probability distribution function of errors for eachaxle. The means
and standard deviations associated withthese bell-shaped curves are
summarized in Table 1.
1klb, also known as kip, is a non-SI unit of force and
equals1000 pounds-force.
Figure 13: Plot shows the probability distributionof percentage
errors in load estimates for each axleand the entire vehicle.
Figure 14: Plot shows the percentage error in loadestimates
against truck speeds. Errors are statisti-cally uncorrelated to
speed.
Figure 14 shows the percentage errors in load estimates
atdifferent truck speeds. The errors are uncorrelated to
speed,implying that the 1
v2term in the model captures the speed
dependence of the pavement response pretty well.Figure 15 shows
the percentage errors of load estimates
at different pavement temperatures. The errors are uncor-related
to temperature and compensation τ(T ) captures theeffect of
pavement temperature well. Figure 16 shows thatthe errors are much
higher when no temperature compensa-tion is used (i.e. τ(T ) = 1 ∀T
). Consistent with pavementmodels [20], without temperature
compensation loads areoverestimated at higher temperatures and
underestimatedestimated at lower temperatures. This is because
pave-ment response for any load is higher at higher
temperatures.Quantitatively, the errors for both scenarios are
provided inTable 1. Clearly, temperature compensation is a very
crucialstep in our load estimation algorithm.
Wireless WIM accuracy. For the results above, we usethe entire
dataset for training our system. For a more re-alistic evaluation
of the system accuracy, we now run 1000
111
-
Table 1: Effect of pavement temperature on load es-timation.
Errors in total weight estimates are below8.2% at a confidence
level of 95% when tempera-ture compensation is applied. When no
tempera-ture compensation is used, the 95% error bound ontotal
weight estimate increases to 11.3%.
Temperature compensation No compensationMean Std of Mean Std
of
Error (%) errors (%) Error (%) errors (%)Axle 1 -0.27 5.25 -0.44
6.66Axle 2 -0.22 4.75 -0.39 6.27Axle 3 -0.33 5.81 -0.43 6.63Total
-0.19 4.09 -0.33 5.61
Figure 15: Plot shows the percentage error in loadestimates
against pavement temperature when mea-surements are compensated for
temperature varia-tion.
different training and testing trials. In each trial, we
ran-domly select 26 out of 52 trucks for estimating β∗i and useit
for estimating loads of trucks in the testing set. To judgeeach
trial, we now define a widely used performance mea-sure for WIM
systems, called the LTPP error. The Long-Term Pavement Performance
(LTPP) specification definesthe WIM system error as the 95%
confidence bound on er-ror, assuming a normal distribution of
errors. Let µme andσme be the mean and standard deviation of test
set errors forthe mth trial. The LTPP error (λm) for the m
th trial canbe calculated as
λm = max{|µme − 1.96σme |, |µme + 1.96σme |}.
Table 2 contains the mean LTPP error (λ̄) from the 1000trials
and the maximum allowed errors by the LTPP stan-dard. The mean LTPP
error in each case is less than theallowed error. Figure 17 shows
the cumulative distributionof λm. The LTPP error is less than the
maximum allowederror for majority of the trials.
We now provide a one-on-one comparison of wireless WIMwith the
nearby WIM station. Figure 18 shows the per-centage errors in loads
reported by the Caltrans station.Due to technical difficulties,
weights from this station werenot available for one of our testing
days, thus reducing thedataset for comparison to 31 trucks. Table 2
compares the
Figure 16: Plot shows the percentage error in loadestimates
against pavement temperature when tem-perature compensation is not
applied. Errors in-crease with increase in temperature.
Figure 17: Plot shows cumulative distribution forthe LTPP errors
from the 1000 trials. Majority oftrials pass the LTPP specification
for allowed errors.
accuracy of both systems. The wireless WIM clearly out-performs
the conventional WIM in every category. The con-ventional WIM meets
the required LTPP accuracy levels foronly axle 1, and fails in all
other cases. It is worth notic-ing in Figure 19 that even a single
lane of wireless WIMoutperforms the conventional WIM (except for
Axle 1).
Effect of dynamic component. Road roughness and thevehicle
suspension system cause the applied load F to bedifferent from the
static load Fs that we are interested in es-timating. In general,
the instantaneous applied load can bewritten as F = Fs+Fd
∑i cos(ωit), where ωi depends on the
suspension system and Fd is usually within 30% of Fs [5].To
reduce the error (F − Fs) or the dynamic component,we average
measurements from multiple arrays. Figure 19shows how the LTPP
error decreases when the number ofarrays increase. Each array
essentially measures the staticload with some uncertainty, and by
averaging multiple mea-surements we reduce the amount of
uncertainty in our load
112
-
Table 2: Comparison of mean LTPP errors betweenour system and
the nearby conventional WIM. Theerrors for the conventional WIM are
much higherthan the errors allowed by the LTPP standard.
Wireless Conventional MaximumWIM error WIM error allowed
error
Axle 1 11.29 18.67 20Axle 2 10.07 26.49 15Axle 3 12.44 37.35
15Total 8.76 23.23 10
Figure 18: Plot shows errors in load estimates forthe nearby WIM
system. These are much higherthan expected and fail to meet the
LTPP standard.
estimate. Adding more arrays to the system could improvethe
system accuracy, but the system achieves the requiredLTPP accuracy
with 4 arrays.
7. CONCLUSIONS AND FUTURE WORKConclusions. A wireless WIM system
that uses pavementvibrations to estimate axle loads was built and
tested inthis study. The wireless vibration sensor designed for
thissystem is capable of measuring very small pavement vibra-tions
in an extremely noisy environment. A new pavement-vehicle
interaction model that relates applied load to pave-ment
vibrations, temperature, and speed of the vehicle wasalso developed
and evaluated. The system was tested on areal highway and passed
the WIM accuracy standards. Thesystem achieved the required
accuracy of 15% for individ-ual axle loads and 10% for total load,
and outperformed anearby conventional WIM system. As part of load
estima-tion, the system also estimates the pavement deflection,
andtherefore can be used for long-term pavement monitoring.
Future work. Even though we have provided a proof-of-concept for
the wireless WIM, more work needs to be donebefore the system can
be widely used. The following aresome avenues for future work.
• In-sensor processing. As mentioned in Section 3.1,the lifetime
of the vibration sensors is only 5 months
Figure 19: Plot shows that errors in static loadsdecrease as the
number of arrays increase. The morethe number of arrays, the better
we filter out thedynamic component.
because they continuously transmit all the raw data.One
efficient way to reduce the current consumptionof the sensor is to
only send out processed data. Thiscan be done by implementing a
version of the fittingalgorithm inside the sensor and only sending
the fittedcoefficients. This should immediately increase the
life-time of the sensor to a few years. The challenge, how-ever, is
to preserve the accuracy of the system whilereducing the current
consumption. To learn about thetrade-off between current
consumption and system ac-curacy, we simulated the in-sensor
processing of data.Instead of combining the raw data from all
sensorsand then using the fitting algorithm, we apply the fit-ting
algorithm to individual sensor data and averagethe fitted
coefficients to get the average pavement re-sponse. The load
estimates based on this procedureare shown in Figure 20. The LTPP
errors were 10.33,12.09, 12.36, and 9.45 percent respectively for
axle 1,2, 3, and the total weight. These are very similar toour
previous results and still pass the accuracy lev-els defined by the
LTPP specification. The in-sensorfitting algorithm needs to be
implemented and tested.
• Testing on different pavements. Pavement re-sponse is highly
dependent on pavement’s structuraland material properties. More
tests need to be doneusing different kinds of pavements to
understand theeffect of pavement properties on the load
estimationprocedure.
• Pavement monitoring. We plan on working withpavement engineers
to use this system as a pavementmonitoring tool. Long-term pavement
monitoring sys-tems are practically non-existent currently but
manyinteresting problems can be studied using such sys-tems.
8. ACKNOWLEDGEMENTSWe would like to thank the California
Department of Trans-
portation for letting us install the system near their oper-
113
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Figure 20: Expected results of load estimation afterin-sensor
processing. The results are very similar toFigure 12
ational WIM, and California Highway Patrol at Cordeliafor
helping us collect ground truth data for trucks. Specialthanks to
Ben Wild for his contributions to the load esti-mation algorithm.
This project was funded by the NationalScience Foundation under
Award Number IIP-0945919.
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114
IntroductionWeigh-In-MotionProblem statementProposed solution:
Wireless WIMChallengesRelated work
Wireless WIM systemSensor network componentsCommunication
protocolSystem design
Experimental SetupLoad estimationPavement-vehicle interaction
modelExtracting individual axle responseModel calibration
Results and discussionConclusions and future
workAcknowledgementsReferences
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