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, ecoleri@ucdavis.edu

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

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.IPSN’13, April 8–11, 2013, Philadelphia, Pennsylvania, USA.Copyright 2013 ACM 978-1-4503-1959-1/13/04 ...$15.00.

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.

103

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].

104

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

105

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

106

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.

107

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.

108

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

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.

9. REFERENCES[1] M. Arraigada, M. Partl, S. Angelone, and F. Martinez.

Evaluation of accelerometers to determine pavementdeflections under traffic loads. Materials andStructures, 42:779–790, 2009.

[2] R. Bajwa, R. Rajagopal, P. Varaiya, and R. Kavaler.In-pavement wireless sensor network for vehicleclassification. In Information Processing in SensorNetworks (IPSN), 2011 10th International Conferenceon, pages 85 –96, april 2011.

[3] P. Burnos, J. Gajda, P. Piwowar, R. Sroka,

M. Stencel, and T. Żegleń. Accurate weighing ofmoving vehicles. Metrology and Measurement Systems,14(4):507–516, 2007.

[4] R. Bushman and A. Pratt. Weigh in motiontechnology–economics and performance. InPresentation on the North American TravelMonitoring Exhibition and Conference (NATMEC).Charlotte, North Carolina, 1998.

[5] D. Cebon. Handbook of Vehicle-Road Interaction.Swets and Zeitlinger Publishers, 1999.

[6] M. Ceriotti, L. Mottola, G. Picco, A. Murphy,S. Guna, M. Corra, M. Pozzi, D. Zonta, and P. Zanon.Monitoring heritage buildings with wireless sensornetworks: The Torre Aquila deployment. InInformation Processing in Sensor Networks, 2009.IPSN 2009. International Conference on, pages277–288. IEEE, 2009.

[7] S. Y. Cheung, S. Coleri, B. Dundar, S. Ganesh, C.-W.Tan, and P. Varaiya. Traffic measurement and vehicleclassification with single magnetic sensor.Transportation Research Record: Journal of theTransportation Research Board, 1917:173–181, 2006.

[8] Colibrys, Inc, accelero.us@colibrys.com. MEMSCapacitive Accelerometers Datasheet MS9000.D.

[9] A. Designation. E 1318-94, standard specifications forhighway weigh-in-motion (wim) systems with userrequirements and test methods. American Society forTesting and Materials, 1994.

[10] Federal Highway Administration, U.S. Department ofTransportation. Traffic Monitoring Guide, May 2001.

[11] M. C. Fehler. Seismic Wave Propagation andScattering in the Heterogenous Earth. Springer, 2009.

[12] M. Gindy, H. H. Nassif, and J. Velde. Bridgedisplacement estimates from measured accelerationrecords. Transportation Research Record: Journal ofthe Transportation Research Board, 2028(-1):136–145,2007.

[13] A. Haoui, R. Kavaler, and P. Varaiya. Wirelessmagnetic sensors for traffic surveillance.Transportation Research C, 16(3):294–306, 2008.

[14] S. Kim, S. Pakzad, D. Culler, J. Demmel, G. Fenves,S. Glaser, and M. Turon. Health monitoring of civilinfrastructures using wireless sensor networks. In IPSN’07: Proceedings of the 6th international conference onInformation processing in sensor networks, pages254–263, New York, NY, USA, 2007. ACM.

[15] A. N. Knaian. A wireless sensor network for smartroadbeds and intelligent transportation systems.Master’s thesis, Massachusetts Institute of Technology,2000.

[16] M. Li and Y. Liu. Underground structure monitoringwith wireless sensor networks. In Proceedings of the6th international conference on Information processingin sensor networks, pages 69–78. ACM, 2007.

[17] C. Liu, L. Guo, J. Li, and X. Chen. Weigh-in-motion(wim) sensor based on em resonant measurements. InAntennas and Propagation Society InternationalSymposium, 2007 IEEE, pages 561–564. IEEE, 2007.

[18] R. B. Malla, A. Sen, and N. W. Garrick. A specialfiber optic sensor for measuring wheel loads of vehicleson highways. Sensors, 8(4):2551–2568, 2008.

[19] C. Merzbacher, A. Kersey, and E. Friebele. Fiber opticsensors in concrete structures: a review. Smartmaterials and structures, 5:196, 1996.

[20] D. Parl, N. Buch, and K. Chatti. Effective layertemperature prediction model and temperaturecorrection via falling weight deflectometer deflections.Transportation Research Record: Journal of theTransportation Research Board, 1764:97–111, 2001.

[21] R. Rajagopal. Large Monitoring Systems: DataAnalysis, Deployment and Design. PhD thesis,University of California, Berkeley, 2009.

[22] H. Sawant, J. Tan, and Q. Yang. A sensor networkedapproach for intelligent transportation systems. InIntelligent Robots and Systems, 2004. (IROS 2004).Proceedings. 2004 IEEE/RSJ International Conferenceon, volume 2, pages 1796 – 1801 vol.2, 2004.

[23] Sensys Networks, Inc, 2650 9th Street, Berkeley CA94710. The Sensys WirelessTM Vehicle DetectionSystem, 1.1 edition.

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

HistoryItem_V1 TrimAndShift Range: all pages Trim: fix size 8.500 x 11.000 inches / 215.9 x 279.4 mm Shift: move down by 23.83 points Normalise (advanced option): 'original'

32 D:20130222145938 792.0000 US Letter Blank 612.0000

Tall 1 0 No 795 352 Fixed Down 23.8320 0.0000 Both AllDoc

CurrentAVDoc

Uniform 0.0000 Top

QITE_QuiteImposingPlus2 Quite Imposing Plus 2 2.0 Quite Imposing Plus 2 1

11 12 11 12

1

HistoryItem_V1 TrimAndShift Range: all pages Trim: fix size 8.500 x 11.000 inches / 215.9 x 279.4 mm Shift: move left by 7.20 points Normalise (advanced option): 'original'

32 D:20130222145938 792.0000 US Letter Blank 612.0000

Tall 1 0 No 795 352 Fixed Left 7.2000 0.0000 Both AllDoc

CurrentAVDoc

Uniform 0.0000 Top

QITE_QuiteImposingPlus2 Quite Imposing Plus 2 2.0 Quite Imposing Plus 2 1

11 12 11 12

1

HistoryList_V1 qi2base