traffic sensing methodology combining influence line...

Research ArticleTraffic Sensing Methodology Combining Influence Line Theoryand Computer Vision Techniques for Girder Bridges

Xudong Jian1 Ye Xia 2 Jose A Lozano-Galant3 and Limin Sun1

1State Key Laboratory for Disaster Reduction in Civil Engineering Tongji University Shanghai 200092 China2Department of Bridge Engineering Tongji University Shanghai 200092 China3Department of Civil Engineering University of Castilla-La Mancha Ciudad Real 13071 Spain

Correspondence should be addressed to Ye Xia yxiatongjieducn

Received 22 January 2019 Revised 8 March 2019 Accepted 7 May 2019 Published 27 May 2019

Guest Editor Samir Mustapha

Copyright copy 2019 Xudong Jian et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Collecting the information of traffic load especially heavy trucks is crucial for bridge statistical analysis safety evaluation andmaintenance strategies This paper presents a traffic sensing methodology that combines a deep learning based computer visiontechnique with the influence line theory Theoretical background and derivations are introduced from both aspects of structuralanalysis and computer vision techniques In addition to evaluate the effectiveness and accuracy of the proposed traffic sensingmethod through field tests a systematic analysis is performed on a continuous box-girder bridge The obtained results show thatthe proposed method can automatically identify the vehicle load and speed with promising efficiency and accuracy and mostimportantly cost-effectiveness All these features make the proposed methodology a desirable bridge weigh-in-motion systemespecially for bridges already equipped with structural health monitoring system

1 Introduction

Modern bridges are mainly constructed for traffic purposesAccordingly collecting the information of traffic includingvehicle weight velocity quantity type and spatiotemporaldistribution is crucial for bridge design refinement safetyevaluation and maintenance strategies [1ndash3] To this end anumber of studies on traffic information identification havebeen conducted Among these methods the bridge-weigh-in-motion (BWIM) technique is highlighted [4 5]

The concepts behind BWIM techniques were initiallyproposed by Moses [6] who used an instrumented bridgeas the weighing scale to estimate vehicle weights Comparedwith other weigh-in-motion (WIM) techniques such as thepavement-based WIM systems [7 8] BWIM techniques arecost-efficient durable and unbiased as they are not impactedby repeated axle loads and do not require interrupting thetraffic to cut the pavement All these advantages have madeBWIM a preferable tool to weigh vehicles especially heavytrucks attracting many follow-up research and engineeringapplications Up to date this research topic has progressedsignificantly in aspects as diverse as the identification results

such as time-history moving load identification [9ndash11] or thetypes of sensors such as portable accelerometers [12]

One of the most simple and practical BWIM techniquesverified by field tests is the gross vehicle weight (GVW)This identification method is based on the static influencelinesurface theory which is already applied by Moses inhis earliest research [13] However key problems arise inobtaining accurate results when multiple vehicles cross thebridge deck simultaneously or move transversely [14] In thisscenario combining supplemental vehicles position infor-mation and the influence surface instead of influence linemight help to mitigate the problem To position the vehicleson the bridge traffic sensors such as radar road tubes andembedded axle detectors are recommended by Snyder et al[15] Lamentably these sensors are too costly for its massiveinstallation in actual structures Alternatively Xiao et al [16]and Yamaguchi et al [17] innovatively utilized the longitu-dinal ribs strains of an orthotropic steel bridge to detect thetransverse position of vehicle axles Unfortunately concretebridges without ribs are insensitive to single axle loadsmaking this method ineffective for this kind of structuresYu et al [18] proposed a novel BWIM algorithm that was

HindawiJournal of SensorsVolume 2019 Article ID 3409525 15 pageshttpsdoiorg10115520193409525

2 Journal of Sensors

able to identify the lateral position of a single vehicle on abridge by using only seven strain gauges installed transverselyat the bottom of the beams That paper however admittedthat identifying the presence of multiple-vehicle is still one ofthe main challenges faced by BWIM technology

To address the multiple-vehicle presence challenge usingvisual information is an innovative and feasible solutionon the basis that a large number of bridges have beenequipped with surveillance cameras for traffic monitoring oflate years In fact the rich visual information recorded by thesurveillance cameras enables obtaining the exact position ofthe vehicles on the bridge deck with nothing but a commonwebcam Chen et al [19] proposed an identification approachfor the spatiotemporal distribution of traffic loads on bridgesusing the information from the pavement-based WIM andbackground subtraction technique This approach relies onhigh quality video image which limits its range of applicationAnother disadvantage of this method is the fact that it isnonsemantic which means deep information contained inthe video image such as type and axle number of vehiclesis difficult to obtain Similar problems also exist in studiesaiming to detect vehicle axles using traditional computervision techniques [1 20]

In recent years deep learning methods have dramaticallyimproved the state of the art in visual object detection andrecognition with amazing efficiency and robustness [21]Inspired by the tremendous advance of computer vision tech-niques this paper presents a traffic information identificationmethodology in combination with influence line theory anddeep learning based computer vision techniques

This paper is organized as follows Firstly the theo-retical background of both aspects of structural analysisand computer vision techniques is presented Next fieldtests on a box-girder bridge were conducted to evaluate theproposed methodology in various aspects Finally both theadvantages and the potential engineering applications of themethodology are discussed

2 Structural Analysis

21 Bridge Response Analysis One of the most concerningtraffic information is vehicle weight To estimate the vehi-cle weight BWIM technology traditionally uses the bridgestrainsTherefore bridge structural strain analysis is essentialin the process of vehicle weight identification

Most BWIM systems are applied on girder bridges withsmall or medium span due to its structural simplicityCompared with long-span bridges middle-small span girderbridges perform linear elasticity under normal operationmaking them ideal weighing scales to estimate vehicleweights Moreover load effects on such bridges are relativelysimple which can be expressed as follows

120576119887119903119894119889119892119890 = 120576119890119899V119894119903119900119899119898119890119899119905 + 120576V119890ℎ119894119888119897119890 (1)

120576V119890ℎ119894119888119897119890 = 120576119889119910119899119886119898119894119888 + 120576119904119905119886119905119894119888 (2)

where 120576119887119903119894119889119892119890 is the directly measured bridge strain 120576119890119899V119894119903119900119899119898119890119899119905is the bridge strain caused by environmental factors such astemperature wind slight earth pulse and creep of concrete

120576V119890ℎ119894119888119897119890 is the bridge strain induced by vehicles which includesdynamic 120576119889119910119899119886119898119894119888 and static 120576119904119905119886119905119894119888 components

According to the influence theory the static component120576119904119905119886119905119894119888 is to be extracted from 120576119887119903119894119889119892119890 by filtering 120576119890119899V119894119903119900119899119898119890119899119905and 120576119889119910119899119886119898119894119888 for the purpose of traffic load identification Inthis paper the filtering process is divided into two steps (i)the 120576119887119903119894119889119892119890 time-history curve is robustly smoothed to get120576119890119899V119894119903119900119899119898119890119899119905 and subtract 120576119890119899V119894119903119900119899119898119890119899119905 from 120576119887119903119894119889119892119890 to get 120576V119890ℎ119894119888119897119890and (ii) the 120576V119890ℎ119894119888119897119890 time-history curve is smoothed to get thedesired 120576119904119905119886119905119894119888 The whole procedure is shown in Figure 1 forintuitive illustration

To achieve the filtering process in time domain a localregression algorithm named locally weighted scatterplotsmoothing (LOWESS) is used Chief attractions of thisalgorithm are the accuracy and convenience It is not requiredto specify a global function of any form to fit a model to thedata only to fit segments of the data so that satisfactory localaccuracy is achieved According to Cleveland and Devlin[22] the basic principle of the LOWESS is expressed asfollows

First of all the LOWESS belongs to the regression analy-sis which aims to fit the mathematical relationship betweentwo sequences 119909119894 and 119910119894 In this paper 119909119894 is considered as thetime sequence 119905119894 while 119910119894 is the bridge strain data sequence120576119894

The LOWESS adopts the polynomial regression modelexpression of which is [23]

120576119894 = 1205730 + 1205731119905119894 + 12057321199052119894 + sdot sdot sdot + 120573119889119905119889119894 + 120576119894 =119889

sum119895=0

120573119895119905119895119894 + 120579119894(119894 = 1 2 119899)

(3)

where 120573119895 is the coefficient of the polynomial regressionmodel119889 is the order of the polynomial 120579119894 is the randomerrorand 119899 is the length of local sequence segment For LOWESStaking 119889 = 2 should almost always provide adequate smoothand computational efficiency

To get appropriate coefficient 120573119895(119905119894) of the polynomial theLOWESS chooses weighted least squares estimate methodwhichmeans 120573119895(119905119894) are the values that minimize the followingfunction

119864 =119899

sum119896=1

119908119896 (119905119894) (120576119896 minus 1205730 minus 1205731119905119896 minus sdot sdot sdot minus 120573119889119905119889119896)2 (4)

where 119908119896(119905119894) are weights defined for all 119905119896(119896 = 1 119899)The tri-cube weight function is adopted to provide adequatesmooth results

Thus 120573119895(119905119894) can be obtained by

120597119864120597120573 = 0 (5)

Finally smoothing results are

120576119894 ==119889

sum119895=0

120573119895 (119905119894) 119905119895119894 (119894 = 1 2 119899) (6)

where 120576119894 is the smoothed strain sequence

Journal of Sensors 3

Step1 Step2

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

Strain Time-History

Strain Time-History

Strain Time-History

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

(a) bridge

(b) environment(d) dynamic

(c) vehicle (e) static

minus10

0

10

20

Scal

ed S

trai

n (

)

minus10

0

10

20

Scal

ed S

trai

n (

)

minus5

0

5

Scal

ed S

trai

n (

)

Figure 1 Procedure of the vehicle induced static strain extraction

After preselecting 119889 the order of the polynomial and119908119896(119905119894) the weight function the only parameter left to bedefined is the length of local sequence segment 119899 Thisparameter can be chosen on the basis of the data propertiesIn this paper 119899 is selected as 50 when smoothing the 120576V119890ℎ119894119888119897119890time-history curve Because the longest vibration period ofgirder bridges is less than 1s and the sampling frequencyof strain sensors in this research is fixed at 50Hz whichmeans that 50 data points are recorded perminute Choosingthe length of the data sequence segment as 50 for locallysmoothing is enough to filter the 120576119889119910119899119886119898119894119888 from the 120576V119890ℎ119894119888119897119890hence Similarly 119899 = 500 can be assumed for smoothing the120576119887119903119894119889119892119890 time-history curve when a vehicle crosses a bridge withsmall ormedium span In these cases the frequency is usuallywithin 10s

The LOWESS algorithm is capable of smoothing the120576V119890ℎ119894119888119897119890 time-history curve to get the desired 120576119904119905119886119905119894119888 Howeverusing LOWESS to smoothing 120576119887119903119894119889119892119890might not be satisfactoryenough Compared with 120576119889119910119899119886119898119894119888 strain variation caused byvehicle weight is much more significant Thus the apparentpeaks will distort the smoothed results as shown in Figure 2

To prevent seriously deviant data from distortingthe smoothed results robust locally weighted regression(RLOWESS) algorithm was proposed on the basis ofLOWESS [24] Based on the size of the residual 119890119896 = 120576119896 minus 120576119896a different set of weights 120575119896 sdot 119908119896(119905119894) is defined for each (119905119894 120576119894)as

120575119896 =

[1 minus (1198901198966119904)2]2

for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 lt 1

0 for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 ge 1

(7)

bridgeenvironment

minus150

minus145

minus140

minus135

minus130

minus125

Scal

ed S

trai

n (

)

275 280 285 290

LOWESS

RLOWESS

295270Time (s)

Figure 2 Normal strain signal collected from the web of a concretebox girder bridge

where 120575119896 is the robust factor of weights 119890119896 = 120576119896 minus 120576119896 isthe smoothing residual and 119904 is the median of the |119890119896| Byintroducing 120575119896 large residuals result in small weights andsmall residuals result in large weights In this way distortionproduced by seriously deviant data points can be effectivelymitigated as shown in Figure 2

22 Influence Line Calibration Bridge influence lines can beused to weigh vehicles and they are vital tools for BWIManalysis In fact obtaining an adequate accuracy of theinfluence line is critical for the BWIM system to achieve


Linear curve Cubic curve

A

P

B C D E

M

y

Chosen section

S2

S3S1

IS2

IS3 S4

IS4

IS1

Figure 3 Diagram of the kinematic method aiming to obtain the influence line of section 1198781

convincing results According to previous studies on BWIMthere are two methods to obtain the influence line of a bridgeOne is the theoretical simulation method [6 25 26] andthe other is the calibration method carried out in field tests[8 27]

Apparently numerical simulation is unable to fully repro-duce the mechanical behavior of a real bridge To fill this gapa method fitting strain influence line with measured straindata from field calibration tests is presented in this paperThemethod includes the following two steps

Step 1 (theoretically derive the shape of the influence line)In the first step the theoretical shape of the strain influenceline of the analyzed girder bridge is obtained According tothe structural mechanics one of the most common methodsto obtain the influence line of a chosen beam section is thekinematic one [28]

Normal strain of the chosen bridge cross-section is usedto weigh vehicles in this work As it is well known the Euler-Bernoulli beam theory states that the normal strain of thechosen cross-section of a beam under vertical loads is pro-portional to its bending moment According to TimoshenkoandGere [29] the proportional relationship can be expressedas

120576 = 119872119910119864119868 (8)

where 120576 is the normal strain of a point on the chosen beamcross-section119872 is the bendingmoment at that cross-section119910 is the distance between the point and the neutral axis of thecross-section 119864 is the elastic modulus of the beam materialand 119868 is the moment of inertia of the cross-section

Equation (8) indicates that for a fixed point on the chosenbeam cross-section the normal strain 120576 of that point isproportional to the bending moment119872 at the cross-sectionThus the shape of strain influence line of a fixed point issimilar to that of the bending moment influence line at thechosen cross-section where the fixed point is located In otherwords it can be said that the two influence lines are scaled

To illustrate the kinematic method a four-span contin-uous beam presented in Figure 3 with nodes from A to Eis considered This method assumes that an element of thebeam at the chosen cross-section like 1198781 section in Figure 3is replaced with an ideal hinge It allows relative rotationbetween the two portions of the beam and a system with onedegree of freedom is obtained in this manner If a load 119875 is

applied at any point on themovable system for equilibrium apair of two equal and opposite bendingmoments119872 is neededat the hinge Meanwhile virtual displacement of the movablesystem will be produced by the loads For the left movableportion 1198601198781 the displacement curve is linear and for theright structure portion 1198781-E the displacement curve is a cubic[29] as shown in Figure 3

According to the principle of virtual work the sum ofcorresponding virtual work of load 119875 and the couple 119872equates zero that is

119872 sdot 120575120579 minus 119875 sdot 119910 = 0 997888rarr119872 = 119875 sdot 119910120575120579

(9)

where 120575120579 is the total angular displacement between the twoparts of the beam and 119910 is the vertical displacement ofthe point where load P is applied Thus 119910120575120579 refers to theinfluence coefficients for bending moment at the chosensection 1198781 and the diagramof structural displacement has theshape of the influence line

Step 2 (calibrating the derived influence line with field testsdata) In the second step numerical values of the straininfluence line are calibrated from field test data Figure 3illustrates how the influence line can be numerically fittedafter introducing the realmeasurements (I) obtained in a fieldtest at points 1198781 1198782 1198783 and 1198784 (that is to say 1198681198781 1198681198782 1198681198783 and1198681198784)

The calibration approach begins with arranging a cali-bration truck with known weight to cross the instrumentedbridge for several times as Figure 4(a) shows

Since bridges are usually long relative to the spacingof vehicle axles gross vehicle weight is more importantthan individual axle load [30] Besides for the linear elasticstructures the mechanics principle of superposition worksConsidering this the vehicle load can be simplified as aconcentrated load 119875 which is written as

119875 = 119882 sdot g (10)

where 119882 is the vehicle weight and g is the gravitationalacceleration

According to the influence line theory there will bean extreme on the strain time history curve recorded bya fixed strain sensor when a moving load passes a bridgespan For a four-span continuous girder bridge passed by the


Truck with known weightStrain sensor

S2 S3S1 S4

(a) Diagram of field calibration tests

Strain Time-History

Extremum

157 159153 155 161151Time (s)

minus10

0

10

20

Scal

ed S

trai

n (

)

IS2

IS3

IS4

IS1

(b) Strain time history collected in tests

Linear FittingCubic Fitting

A B C D E

Chosen section

S2

S3S1

S4IW1

IW2

IW3

IW4

Strain Influence Line of Section S1

6932 101 1330Longitudinal Length (m)

minus05

0

05

1

15

Influ

ence

Val

ue (

middotto

n-1)

(c) Calibrated influence line of the chosen section

Figure 4 Procedure of the influence line calibration

calibration truck the 120576119904119905119886119905119894119888 time-history curve of a fixed pointon bridge has four extremes as shown in Figure 4(b) Thedeflections 1198681199041 1198681199042 1198681199043 and 1198681199044 occur when the calibrationtruck passes cross-section 1198781 1198782 1198783 and 1198784Then it is feasibleto numerically fit the strain influence line of a desired pointon the chosen section with nine points AsimE and 1198781 sim 1198784 inFigure 3 of which the coordinates are determined

Finally the strain influence line is normalized to obtainthe direct relationship between vehicle weight and bridge forBWIM application convenience The normalization equationis as follows

119868119882 = 119868119878119882 (11)

where 119868119882 is the static strain caused by per unit vehicleweight and 119868119878 is the obtained value of the strain influenceline An example of calibrated strain influence line is shownin Figure 4(c) In this figure four static strain values perunit vehicle weight (1198681199081 1198681199082 1198681199083 and 1198681199084) are consideredAs discussed previously the polynomial order for fittingpurposes depends on the order of the displacement curve

This calibration procedure of influence lines has a numberof advantages such as low calculation operation simplicityand no need to close traffic enabling convenient recalibrationif the mechanical performances of the instrumented bridgechange [31] However it is noteworthy that the usage of influ-ence line instead of influence surface [32] is a simplificationfor real bridges because vehicles may move transversely onbridge But this simplification is still acceptable under theassumption that heavy trucks this research focuses on seldomchange the traffic lane when crossing the bridge

3 Computer Vision Technique

31 Deep Learning Approach Convolution neural network(CNN) is one of the most notable deep learning approachesemployed for object detection classification and segmenta-tion tasks [33] Here learning means that CNN automaticallylearns useful features from the training data and distinguishesthe target object and the others based on these featuresActually that is how humans recognize objects The CNN istherefore classified as artificial intelligence (AI) method Thelearning ability is a qualitative leap over traditional manualfeature extraction methods and can thus drastically reducethe workload of operation Besides the intelligent characteralso improves the robustness and generalization capacitybecause of the invariance to complex background geometricdistortion and illumination

Due to such advantages newCNNbased computer visionalgorithms with better performance have been unceasinglyproposed and most of them are open source This researchapplies the most advanced algorithm named YOLO V3 tofulfill the vehicle recognition tasks for its multi-scale anddeeper feature extraction capacity as well as the fastestrecognition speed up to date [34] The application procedurehas the following three steps

Step 1 (preparing training data sets) As stated previouslyCNN based computer vision algorithms will not work with-out effective training Thus training data sets need to beprepared for the YOLOV3 algorithm at firstThe preparatorywork includes singling out segment of videos in whichvehicles exist and manually labelling cars trucks and wheels


(a) Manual labeling

0

02

04

06

Erro

r Rat

e

5000 100000Iterations

(b) Error curve in the training process

Figure 5 Preparation procedure of YOLO V3 algorithm

(a) Multi-vehicle overlap (b) Illumination change (c) Axle segmentation

Figure 6 Vehicle recognition results for different scenarios

in every video frame as shown in Figure 5(a) In this paper atotal of 1000 video images with the same camera visual angleare selected as the training set and different types of objectsincluding cars trucks and wheels are labelled in each image

Step 2 (training CNN of YOLO V3) CNN is essentially a setof weight coefficients capable of recognize objects using thepixel data of an image Errors are inevitable in the process ofrecognition and training CNN intends to obtain the optimalweight coefficients that minimizes the errors To that endthe gradient descent method [33] is used in this optimizationproblemThis technique states

120597119890120597119908119894 le 119903 (12)

where 119890 is the recognition error119908119894 are the CNNweights and119903 is the convergence threshold

Numerical iteration is required to achieve (12) and theiteration process is shown in Figure 5(b) In this researchiteration times are set to 10000 in the six-hour trainingprocess accelerated by a NVIDIA 1080Ti GPU

Step 3 (applying YOLO V3) After a well-trained CNN isobtained the YOLO V3 is used to recognize vehicles inreal time Recognition results in this research were quitesatisfactory in the different scenarios shown in Figure 6 Itis remarkable that the closely spaced wheels are successfully

recognized as shown in Figure 6(c) proving the splendidrecognition capability of the YOLO V3 algorithm The rec-ognized pixel coordinates of the detection box are collectedfor further vehicle positioning tasks

Vehicle overlap and insufficient illumination might pro-duce inevitable recognition errors Diversifying neural net-work training sets and utilizing infrared camera at dark nightwill help to improve the recognition accuracy

32 Coordinate Transformation After the successful recog-nition by YOLO V3 algorithm precise position of vehicleshas to be determined To address this problem coordinatesystems are established as illustrated in Figure 7 [35] and acoordinate transformation method is proposed in this workThere are two coordinate systems in the process of coordinatetransformation namely camera pixel coordinate in the videoimage as shown in Figure 7(a) and space coordinate in thereal world as shown in Figure 7(b) The relations betweenthem are shown in Figures 7(c) and 7(d) respectively wherethe parameters with same marks are equal Based on therelations the spatial coordinate of a point 1198751015840(1199091015840 1199101015840) on pixelplane can be transferred into P(x y z) as follows

119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x

(a) Camera pixel coordinate system

Lane1Lane2

Lane3

Vehicle

Webcam

yx

z

(b) Space coordinate system

O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]

P Image of the Object

y

x

P

(c) Camera imaging spatial model

Similar Triangles

P

x

f

z

O

Pixel plane

x

P

(d) Camera imaging planarmodel

Figure 7 Coordinate systems

where119891 is the focal length of the camera and 119905 is the similaritycoefficient between the two similar triangles

In the space coordinate the bridge deck can be consideredas a spatial plane represented by the following equation

119860119909 + 119861119910 + 119862119911 + 119863 = 0 (14)where x y z are the spatial coordinates of the observed objectsuch as a truck and A B C D are unknown parametersdetermining the bridge deck plane equation If the bridgeslope is negligible which is the usual case x and 119910 directlydetermine position of vehicles on the bridge deck Thenvehicle coordinates on the deck are attainable after obtainingA B C and D

Instinctively both location and orientation of thewebcamare needed to obtain parameters A B C and 119863 However anumber of field conditions such as heavy traffic flow makeit difficult to obtain this information To solve this problemthis paper proposes a method to obtain A B C D directlyfrom the video image without knowing the camera locationandor its orientation The proposed method only needs twolines of equal space length in the image For example lines1198751101584011987521015840 and 1198753101584011987541015840 in Figure 8 have the equal length of 375mThe coordinates of their endpoints can be measured directlyfrom the image

375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)

Figure 8 Diagram for A B C D calculation from two referencelines 11987511015840-11987521015840 and 11987531015840-11987541015840

According to Figure 8 the relations between both linescan be written as follows

Δ1199091 = 11990911015840 minus 11990921015840Δ1199101 = 11991011015840 minus 11991021015840Δ1199092 = 11990931015840 minus 11990941015840Δ1199102 = 11991031015840 minus 11991041015840

radicΔ11990912 + Δ11991012 sdot 1199051 = radicΔ11990922 + Δ11991022 sdot 1199052 = 119871

(15)


x

y

O

Truck1Truck2

Lane1 Lane2

(a) Trajectory in image

Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)

0 375minus375Transverse Length (m)

(b) Trajectory on bridge deck

Figure 9 Recognized vehicle trajectory

where (11990911015840 11991011015840) (11990921015840 11991021015840) (11990931015840 11991031015840) and (11990941015840 11991041015840) are thecoordinates of the endpoints 11987511015840 11987521015840 11987531015840 and 11987541015840 1199051 and 1199052are similarity coefficients of the lines and L is the line lengthWith (15) parameter 119905 of the two lines can be separatelycalculated then spatial coordinates of the four endpointsare obtained with (13) Substituting coordinates of the fourendpoints of the two equal length lines into (14) the fourunknowns A B C and 119863 can be directly obtained

Themain advantage of this method is its simplicity whilethe trade-off is the loss of accuracy assuming that parameter119905 is equal for endpoints 11987511015840 and 11987521015840 as well as 11987531015840 and 11987541015840which is true when the selected lines are far enough from thecamera and the line length is short Another noticeable errorsource comes from the camera imaging distortion which iscomplicated and will not be discussed in this paper Figure 9depicts vehicle trajectory tracked by the aforementionedmethod

4 Field Tests

41 Test Setup In order to verify the applicability ofthe proposed traffic information identification methodol-ogy in real structures field tests were conducted on a32m+37m+32m+32m continuous concrete box girder bridgeof Baoding-Duping Highway China There are three trafficlanes on the bridge in total and each of them is 375m wideAmong these traffic lines lane3 is an emergency lane wherevehicles are prohibited to drive under normal conditions Thebridge is slightly curved with a bending radius of 2600m anda central angle of 293∘ thus the curvature effects are negli-gible in the analysis A structural health monitoring systemcomprising a pavement-based WIM system six resistance-type strain sensors and a webcam is installed on this bridgeAll the discussed information is shown in Figure 10

In the field tests the normal strain data were collectedby the six resistance-type strain sensors mounted on themid-span section of the first span and stored in an onlineserver Video recorded by thewebcam is also available on line

providing a basis for long-term online application Vehicleweight and velocity recognized by pavement-based WIMsystem are used as contrast to evaluate the accuracy of thisproposed methodology

42 Calibration Tests First of all field calibration tests ason the lanes presented in Figure 10(b) were implementedfollowing the method mentioned in Section 22 up frontTo do so an ordinary truck weighing 1486t as shown inFigure 11 was arranged to drive on the tested bridge for fourtimes Detailed test conditions are shown in Table 1 Lane3was ignored for the calibration because it is an emergencylane where vehicles are prohibited to drive under normalconditions

Figure 12 shows the influence line calibration results of theldquoS6rdquo strain sensor in Figure 10(b) Differences between test1and test2 as well as test3 and test4 are slight which verifiesthe feasibility and reliability of the proposed influence linecalibrationmethod It is also observed that the influence valueof traffic lane1 is larger than that of lane2 as strain sensor ldquoS6rdquois located closer to lane1

43 Strain Data Processing Next strain data collected by sixresistance-type strain sensors shown in Figure 10 is pro-cessed with the LOWESS algorithm mentioned in Section 21of this paper Taking a segment of the processed strain timehistory shown in Figure 13(a) as an example an obviouslinear relationship between data peak values of strain sensorsmounted on the same box web is observed in Figure 13(b)The linear relationship confirms the plane section assumptionof Euler-Bernoulli beam theory mentioned in (8) above andthus validates the effectiveness of the strain data processingmethod

44 GVW Calculation The gross vehicle weight (GVW) canbe calculated by combining the calibrated strain influenceline the processed bridge strains and the vehicle positionBasically there are only three elementary vehicle distribution


32000

16000 16000 15000

87900

Resistance Type Strain Sensor times 6 Pavement-based WIM Webcam

Unit mm

Traffic Direction

2

(a) Elevation view of the tested bridge

Span1 (Instrumented)

Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3

Instrumented cross-section

112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times

(b) Diagram of the tested bridge and the instrumented section

Figure 10 Bridge for field tests

Table 1 Conditions of calibration tests

Test1 Test2 Test3 Test4Weight 1486t 1486t 1486t 1486tVelocity 60kmh 80kmh 60kmh 80kmhLane Lane1 Lane1 Lane2 Lane2

scenarios presented in Figure 14 They are single vehiclein Figure 14(a) one-by-one vehicles on the same lane inFigure 14(b) and side-by-side vehicles on different lanes inFigure 14(c)

For the first single vehicle scenario it is simple to calculateweight of the vehicle through the following equation

119882 = 119878119901119890119886119896119868119901119890119886119896 (16)

where 119878119901119890119886119896 is the peak value of vehicle induced static strainsignal 119868119901119890119886119896 is the peak value of the calibrated strain influenceline and119882 is the GVW of the vehicle

For the second one-by-one vehicles scenario GVW of thefirst front vehicle can still be calculated through (16) Then

GVW of the rear vehicles can be calculated after subtractingeffects of the front vehiclewhoseGVW is already knownThisprocess is written as

119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)

where 119878119901119890119886119896119903119890119886119903 is the peak value of the rear vehicle induced staticstrain signal 119868119891119903119900119899119905 is the strain influence value related to theposition of the front vehicle which can be obtained with theaid of the aforementioned computer vision technique119882119891119903119900119899119905is the GVW of the front vehicle calculated through (16) 119868119901119890119886119896119903119890119886119903is the peak value of the calibrated strain influence line of


Table 2 Statistics of the relative errors compared with pavement-basedWIM

Sensor Mean of errors () Standard deviation of errors ()S1 352 374S2 -36 187S3 -28 208S4 386 252S5 -18 124S6 -52 116

360 ton

55 m

1126 ton

Figure 11 Calibration truck

traffic lane where the rear vehicle drives and 119882119903119890119886119903 is theGVW of the rear vehicle

It is important to highlight that using (16) to calculate theweight of the front vehicle in the one-by-one vehicle queue isnot applicable to circumstances when the rear vehicle entersthe bridge before the front vehicle passes the instrumentedbridge cross-section because 119878119901119890119886119896 in (16) involves the effectsof the rear vehicle under such circumstances Fortunately thisproblem does not exist in this research for a sizeable safetymargin no less than 30m between front and rear vehicles isdemanded when driving on highways in China The distancebetween the instrumented cross-section and the start pointof the bridge however is only 16m

Challenge arises when two vehicles driving side by sidehowever In this scenario one strain signal peak correspondsto two indistinguishable vehicles which makes the aboveGVW calculation methods ineffective

Finally a segment of 15 minutesrsquo strain signal and videowhen there are no side-by-side trucks is analyzed Cars areignored and weights of a total of 61 trucks are calculatedStatistics of the relative errors compared with the resultsrecognized by the pavement-based WIM system are listed inTable 2 Plots of the GVW results of the six sensors S1simS6 arealso shown in Figure 15 in which each point corresponds toa vehicle In this figure the further away the point is from thebaseline the larger the error is

According to the GVW calculation results though errorsof several vehicles are unpleasantly significant accuracy ofthe rest is still acceptable except results based on strainsensors named S1 and S4 Close distance to the sectionneutralaxis of S1 and S4 explains their significant errors Becauseunder the plane section assumption the closer the strainsensor is to the neutral axis the smaller its strain value

making the relative error larger in contrast To avoid thisproblem BWIM sensors should be installed far from thesection neutral axis for higher accuracy

45 VehicleVelocity Calculation Theoretically instantaneousvelocities of vehicles can be calculated through (18) with therecognized vehicle position in each video frame and fixedtime interval between frames

V = Δ119878Δ119905 (18)

where v is the vehicle velocity and Δ119878 is the vehicle displace-ment within a period of time Δ119905

However calculated instantaneous velocities of vehiclesappear to fluctuate drastically Average vehicle velocity inthree seconds which means Δ119905 = 3s is calculated instead ofinstantaneously and the calculation results are quite accurateas shown in Figure 16 The mean value of errors is -08 thestandard deviation of errors is 92 and the maximum valueof errors is 231

46 Vehicle Type and Axle Recognition Identification ofclosely spaced axles including tandem axles is a key factorto ensure accurate classification of the passing vehicles Real-time traffic characterization on a bridge is beneficial for assetmanagers and bridge owners because it provides statisticaldata about the configurations of the passing vehicles Thenothing-on-road (NOR) technique is generally utilized toobtain the information about the axles with sensors locatedunderneath the bridge girder [36 37]

As a supplement this paper obtains information aboutvehicle type and number of axles with visual informationprovided by only a webcam Figures 6(a) and 6(c) show thatthe well-trained YOLO V3 algorithm is capable of directlyrecognizing vehicle types and the number of axles similarlyto humans The vehicle type recognition accuracy is 100and the axle recognition results of 61 trucks (including 6trucks with 2 axles) and 50 cars in the field tests are shownin Figure 17 which is still quite satisfactory compared withthe pavement-based WIM Errors are inevitable because ofvehicle overlap limited visual angle of the webcam andillumination conditions For instance if cars are obscuredby trucks with large size or the illumination is rather dimwheels of cars will thus not be recognized For instance if carsare obscured by trucks with larger size or the illumination israther dim carswheelswill thus not be recognizedThat is thereasonwhy the computer visionmademistakesThis problem


Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)

32 69 101 1330Longitudinal Length (m)

(a) Results of test1 and test2

Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)


(b) Results of test3 and test4

Figure 12 Influence line calibration results

Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

(a) Processed strain time-history curve

Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)

S2 S4S1 S5 S6S3Sensor Name

(b) Values of peaks

Figure 13 Strain data processing results

(a) Single vehicle (b) One-by-one vehicles (c) Side-by-side vehicles

Figure 14 Scenarios of vehicle distribution on bridge


0 40 60 8020 100Pavement-based WIM (t)

0

20

40

60

80

100

BWIM

(t)

BaselineS1

(a) GVW results based on S1 data


0

20

40

60

80

100

BWIM

(t)

BaselineS2

(b) GVW results based on S2 data


0

20

40

60

80

100

BWIM

(t)

BaselineS3

(c) GVW results based on S3 data


0

20

40

60

80

100BW

IM (t

)

BaselineS4

(d) GVW results based on S4 data


0

20

40

60

80

100

BWIM

(t)

BaselineS5

(e) GVW results based on S5 data


0

20

40

60

80

100

BWIM

(t)

BaselineS6

(f) GVW results based on S6 data

Figure 15 GVW calculation results for the six strain sensors S1simS6


0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV

Figure 16 Vehicle velocity results

56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s

5 6 7 82Number of Axles

WIM

CV

Figure 17 Axle recognition results

did not appear in the pavement-based WIM as illustrated inFigure 17

To prevent these errors the visual angle of the webcamcan be adjusted to observe the vehicle wheels more clearlyAnother way to improve the quality of the vision is using aninfrared camera to prevent dim illumination

47 Error Analysis Although the recognition accuracy isacceptable error analysis is imperative for further improve-ment To the authorrsquos knowledge the following two reasonsmay account for calculation errors illustrated in Figure 18(i) vehicle deviation from the traffic lane and (ii) vehiclepositioning errors of the computer vision technique

It is noted that vehicles on a bridge do not drive on thetraffic lane strictly in some cases but in this research onlyinfluence lines of traffic lanes are utilized This assumptionleads to significant errors when the vehicle deviates from the

traffic lane severely as presented in Figure 18(a) To reducethis kind of error the influence line can be substituted by theinfluence surface

Another error source is inaccurate vehicle detection asshown in Figure 18(b) where multiple vehicles overlap inthe image and leads to positioning errors Particular labellingaiming at this phenomenon and diversifying the training setsfor the deep neural network will help tomitigate the problem

5 Conclusions

A traffic sensing methodology has been proposed in thispaper in combination with influence line theory and com-puter vision technique Field tests were conducted to evaluatethe proposed methodology in various aspects The mainconclusions of this work might be listed as follows

(1) The identification of vehicle positions especially ontransverse direction when passing a bridge is quitecritical to solve multiple-vehicle problem for BWIMsystems This paper introduces for the first timedeep learning based computer vision technique toobtain the exact position of vehicles on bridges andsuccessfully solves one-by-one vehicles scenario ofmultiple-vehicle problems for BWIM research withan average weighing error within 5

(2) The time series smoothing algorithm LOWESS isan effective tool to extract static component fromdirectly measured bridge responses Then influenceline or influence surface of a real bridge can be easilycalibrated for BWIM purpose

(3) Verified by field tests the deep learning based com-puter vision technique is highly stable and efficientto recognize vehicles on bridges in real time mannerTherefore it is proven to be a promising technique fortraffic sensing

(4) The proposed traffic sensing methodology is capableof identifying vehicle weight velocity type axlenumber and time-spatial distribution on small andmedium span girder bridges in a cost-effective wayespecially for those bridges already equipped withstructure health monitoring systems and surveillancecameras

Data Availability

Thevideo and testing data used to support the findings of thisstudy are included within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This paper is supported by the National Key RampD Pro-gram of China (2017YFC1500605) Science and TechnologyCommission of Shanghai Municipality (17DZ1204300 and


(a) Vehicle deviation from traffic lane (b) Inaccurate vehicle detection

Figure 18 Major error sources

18DZ1201203) and the Fundamental Research Funds for theCentral Universities

References

[1] R Zaurin and F N Catbas ldquoIntegration of computer imagingand sensor data for structural health monitoring of bridgesrdquoSmart Materials and Structures vol 19 no 1 Article ID 0150192009

[2] B Wei C Zuo X He L Jiang and T Wang ldquoEffects of verticalground motions on seismic vulnerabilities of a continuoustrack-bridge system of high-speed railwayrdquo Soil Dynamics andEarthquake Engineering vol 115 pp 281ndash290 2018

[3] B Wei T Yang L Jiang and X He ldquoEffects of uncertain char-acteristic periods of ground motions on seismic vulnerabilitiesof a continuous trackndashbridge system of high-speed railwayrdquoBulletin of Earthquake Engineering vol 16 no 9 pp 3739ndash37692018

[4] Y Yu C S Cai and L Deng ldquoState-of-the-art review onbridge weigh-in-motion technologyrdquo Advances in StructuralEngineering vol 19 no 9 pp 1514ndash1530 2016

[5] M Lydon S E Taylor D Robinson AMufti and E J O BrienldquoRecent developments in bridge weigh in motion (B-WIM)rdquoJournal of Civil Structural Health Monitoring vol 6 no 1 pp69ndash81 2016

[6] F Moses ldquoWeigh-in-motion system using instrumentedbridgesrdquo Journal of Transportation Engineering vol 105 no 31979

[7] J Zhang Y Lu Z Lu C Liu G Sun and Z Li ldquoA newsmart traffic monitoring method using embedded cement-based piezoelectric sensorsrdquo Smart Materials and Structuresvol 24 no 2 Article ID 025023 2015

[8] H Zhao N Uddin X Shao P Zhu and C Tan ldquoField-calibrated influence lines for improved axle weight identifi-cation with a bridge weigh-in-motion systemrdquo Structure andInfrastructure Engineering vol 11 no 6 pp 721ndash743 2015

[9] C D Pan L Yu andH L Liu ldquoIdentification of moving vehicleforces on bridge structures via moving average Tikhonovregularizationrdquo Smart Materials and Structures vol 26 no 8Article ID 085041 2017

[10] Z Chen T H T Chan and A Nguyen ldquoMoving force identi-fication based on modified preconditioned conjugate gradient

methodrdquo Journal of Sound and Vibration vol 423 pp 100ndash1172018

[11] C-D Pan L Yu H-L Liu Z-P Chen andW-F Luo ldquoMovingforce identification based on redundant concatenated dictio-nary and weighted l1-norm regularizationrdquoMechanical Systemsand Signal Processing vol 98 pp 32ndash49 2018

[12] H Sekiya K Kubota and C Miki ldquoSimplified portablebridge weigh-in-motion system using accelerometersrdquo Journalof Bridge Engineering vol 23 no 1 Article ID 04017124 2017

[13] X Q Zhu and S S Law ldquoRecent developments in inverseproblems of vehiclebridge interaction dynamicsrdquo Journal ofCivil Structural Health Monitoring vol 6 no 1 pp 107ndash1282016

[14] F Schmidt B Jacob C Servant and Y Marchadour ldquoExperi-mentation of a bridge WIM system in France and applicationsfor bridge monitoring and overload detectionrdquo in Proceedingsof the International Conference on Weigh-In-Motion ICWIM6p 8p 2012

[15] R E Snyder and F Moses ldquoApplication of in-motion weighingusing instrumented bridgesrdquo Transportation Research Recordvol 1048 pp 83ndash88 1985

[16] Z-G Xiao K Yamada J Inoue and K Yamaguchi ldquoMeasure-ment of truck axle weights by instrumenting longitudinal ribsof orthotropic bridgerdquo Journal of Bridge Engineering vol 11 no5 pp 526ndash532 2006

[17] E Yamaguchi S-I Kawamura K Matuso Y Matsuki andY Naito ldquoBridge-weigh-in-motion by two-span continuousbridge with skew and heavy-truck flow in Fukuoka area JapanrdquoAdvances in Structural Engineering vol 12 no 1 pp 115ndash1252009

[18] Y Yu C S Cai and L Deng ldquoNothing-on-road bridge weigh-in-motion considering the transverse position of the vehiclerdquoStructure and Infrastructure Engineering vol 14 no 8 pp 1108ndash1122 2018

[19] Z Chen H Li Y Bao N Li and Y Jin ldquoIdentification ofspatio-temporal distribution of vehicle loads on long-spanbridges using computer vision technologyrdquo Structural Controland Health Monitoring vol 23 no 3 pp 517ndash534 2016

[20] J F Frenze A Video-Based Method for the Detection of TruckAxles National Institute for Advanced Transportation Technol-ogy University of Idaho 2002


[21] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[22] W S Cleveland and S J Devlin ldquoLocally weighted regressionan approach to regression analysis by local fittingrdquo Journal ofthe American Statistical Association vol 83 no 403 pp 596ndash610 1988

[23] D A Freedman Statistical Models eory and Practice Cam-bridge University Press 2009

[24] W S Cleveland ldquoRobust locally weighted regression andsmoothing scatterplotsrdquo Journal of the American StatisticalAssociation vol 74 no 368 pp 829ndash836 1979

[25] A Znidaric and W Baumgartner ldquoBridge weigh-in-motionsystems-an overviewrdquo in Proceedings of the Second EuropeanConference on Weigh-In-Motion of Road Vehicles Lisbon Por-tugal 1998

[26] P McNulty and E J OrsquoBrien ldquoTesting of bridge weigh-in-motion system in a sub-arctic climaterdquo Journal of Testing andEvaluation vol 31 no 6 pp 497ndash506 2003

[27] E J OBrien M J Quilligan and R Karoumi ldquoCalculating aninfluence line from direct measurementsrdquo Proceedings of theInstitution of Civil Engineers Bridge Engineering vol 159 noBE1 pp 31ndash34 2006

[28] S P Timoshenko and D H Young eory of StructuresMcGraw-Hill 1965

[29] S P Timoshenko and J M Gere Mechanics of Materials vanNordstrand Reinhold Company New York NY USA

[30] F Moses ldquoInstrumentation for weighing truck-in-motion forhighway bridge loadsrdquo Final Report FHWA-OH-83-001 1983

[31] Y L Ding H W Zhao and A Q Li ldquoTemperature effectson strain influence lines and dynamic load factors in a steel-truss arch railway bridge using adaptive FIR filteringrdquo Journalof Performance of Constructed Facilities vol 31 no 4 Article ID04017024 2017

[32] M Quilligan Bridge weigh-in motion development of a 2-Dmulti-vehicle algorithm [Doctoral thesis] Byggvetenskap 2003

[33] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquoNeural Networks vol 61 pp 85ndash117 2015

[34] J Redmon and A Farhadi ldquoYolov3 an incremental improve-mentrdquo 2018 httpsarxivorgabs180402767

[35] G Xu and Z Zhang Epipolar Geometry in Stereo Motion andObject Recognition A Unified Approach Springer 1996

[36] H Kalhori M M Alamdari X Zhu B Samali and SMustapha ldquoNon-intrusive schemes for speed and axle iden-tification in bridge-weigh-in-motion systemsrdquo MeasurementScience and Technology vol 28 no 2 Article ID 025102 2017

[37] H Kalhori M M Alamdari X Zhu and B Samali ldquoNothing-on-road axle detection strategies in bridge-weigh-in-motion fora cable-stayed bridge case studyrdquo Journal of Bridge Engineeringvol 23 no 8 Article ID 05018006 2018

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able to identify the lateral position of a single vehicle on abridge by using only seven strain gauges installed transverselyat the bottom of the beams That paper however admittedthat identifying the presence of multiple-vehicle is still one ofthe main challenges faced by BWIM technology

To address the multiple-vehicle presence challenge usingvisual information is an innovative and feasible solutionon the basis that a large number of bridges have beenequipped with surveillance cameras for traffic monitoring oflate years In fact the rich visual information recorded by thesurveillance cameras enables obtaining the exact position ofthe vehicles on the bridge deck with nothing but a commonwebcam Chen et al [19] proposed an identification approachfor the spatiotemporal distribution of traffic loads on bridgesusing the information from the pavement-based WIM andbackground subtraction technique This approach relies onhigh quality video image which limits its range of applicationAnother disadvantage of this method is the fact that it isnonsemantic which means deep information contained inthe video image such as type and axle number of vehiclesis difficult to obtain Similar problems also exist in studiesaiming to detect vehicle axles using traditional computervision techniques [1 20]

In recent years deep learning methods have dramaticallyimproved the state of the art in visual object detection andrecognition with amazing efficiency and robustness [21]Inspired by the tremendous advance of computer vision tech-niques this paper presents a traffic information identificationmethodology in combination with influence line theory anddeep learning based computer vision techniques

This paper is organized as follows Firstly the theo-retical background of both aspects of structural analysisand computer vision techniques is presented Next fieldtests on a box-girder bridge were conducted to evaluate theproposed methodology in various aspects Finally both theadvantages and the potential engineering applications of themethodology are discussed

2 Structural Analysis

21 Bridge Response Analysis One of the most concerningtraffic information is vehicle weight To estimate the vehi-cle weight BWIM technology traditionally uses the bridgestrainsTherefore bridge structural strain analysis is essentialin the process of vehicle weight identification

Most BWIM systems are applied on girder bridges withsmall or medium span due to its structural simplicityCompared with long-span bridges middle-small span girderbridges perform linear elasticity under normal operationmaking them ideal weighing scales to estimate vehicleweights Moreover load effects on such bridges are relativelysimple which can be expressed as follows

120576119887119903119894119889119892119890 = 120576119890119899V119894119903119900119899119898119890119899119905 + 120576V119890ℎ119894119888119897119890 (1)

120576V119890ℎ119894119888119897119890 = 120576119889119910119899119886119898119894119888 + 120576119904119905119886119905119894119888 (2)

where 120576119887119903119894119889119892119890 is the directly measured bridge strain 120576119890119899V119894119903119900119899119898119890119899119905is the bridge strain caused by environmental factors such astemperature wind slight earth pulse and creep of concrete

120576V119890ℎ119894119888119897119890 is the bridge strain induced by vehicles which includesdynamic 120576119889119910119899119886119898119894119888 and static 120576119904119905119886119905119894119888 components

According to the influence theory the static component120576119904119905119886119905119894119888 is to be extracted from 120576119887119903119894119889119892119890 by filtering 120576119890119899V119894119903119900119899119898119890119899119905and 120576119889119910119899119886119898119894119888 for the purpose of traffic load identification Inthis paper the filtering process is divided into two steps (i)the 120576119887119903119894119889119892119890 time-history curve is robustly smoothed to get120576119890119899V119894119903119900119899119898119890119899119905 and subtract 120576119890119899V119894119903119900119899119898119890119899119905 from 120576119887119903119894119889119892119890 to get 120576V119890ℎ119894119888119897119890and (ii) the 120576V119890ℎ119894119888119897119890 time-history curve is smoothed to get thedesired 120576119904119905119886119905119894119888 The whole procedure is shown in Figure 1 forintuitive illustration

To achieve the filtering process in time domain a localregression algorithm named locally weighted scatterplotsmoothing (LOWESS) is used Chief attractions of thisalgorithm are the accuracy and convenience It is not requiredto specify a global function of any form to fit a model to thedata only to fit segments of the data so that satisfactory localaccuracy is achieved According to Cleveland and Devlin[22] the basic principle of the LOWESS is expressed asfollows

First of all the LOWESS belongs to the regression analy-sis which aims to fit the mathematical relationship betweentwo sequences 119909119894 and 119910119894 In this paper 119909119894 is considered as thetime sequence 119905119894 while 119910119894 is the bridge strain data sequence120576119894

The LOWESS adopts the polynomial regression modelexpression of which is [23]

120576119894 = 1205730 + 1205731119905119894 + 12057321199052119894 + sdot sdot sdot + 120573119889119905119889119894 + 120576119894 =119889

sum119895=0

120573119895119905119895119894 + 120579119894(119894 = 1 2 119899)

(3)

where 120573119895 is the coefficient of the polynomial regressionmodel119889 is the order of the polynomial 120579119894 is the randomerrorand 119899 is the length of local sequence segment For LOWESStaking 119889 = 2 should almost always provide adequate smoothand computational efficiency

To get appropriate coefficient 120573119895(119905119894) of the polynomial theLOWESS chooses weighted least squares estimate methodwhichmeans 120573119895(119905119894) are the values that minimize the followingfunction

119864 =119899

sum119896=1

119908119896 (119905119894) (120576119896 minus 1205730 minus 1205731119905119896 minus sdot sdot sdot minus 120573119889119905119889119896)2 (4)

where 119908119896(119905119894) are weights defined for all 119905119896(119896 = 1 119899)The tri-cube weight function is adopted to provide adequatesmooth results

Thus 120573119895(119905119894) can be obtained by

120597119864120597120573 = 0 (5)

Finally smoothing results are

120576119894 ==119889

sum119895=0

120573119895 (119905119894) 119905119895119894 (119894 = 1 2 119899) (6)

where 120576119894 is the smoothed strain sequence


Step1 Step2

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

Strain Time-History

Strain Time-History

Strain Time-History

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

(a) bridge



minus10

0

10

20

Scal

ed S

trai

n (

)

minus10

0

10

20

Scal

ed S

trai

n (

)

minus5

0

5

Scal

ed S

trai

n (

)





120575119896 =

[1 minus (1198901198966119904)2]2

for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 lt 1

0 for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 ge 1

(7)

bridgeenvironment

minus150

minus145

minus140

minus135

minus130

minus125

Scal

ed S

trai

n (

)

275 280 285 290

LOWESS

RLOWESS

295270Time (s)






A

P

B C D E

M

y

Chosen section

S2

S3S1

IS2

IS3 S4

IS4

IS1






120576 = 119872119910119864119868 (8)







(9)





119875 = 119882 sdot g (10)





S2 S3S1 S4


Strain Time-History

Extremum

157 159153 155 161151Time (s)

minus10

0

10

20

Scal

ed S

trai

n (

)

IS2

IS3

IS4

IS1



A B C D E

Chosen section

S2

S3S1

S4IW1

IW2

IW3

IW4



minus05

0

05

1

15

Influ

ence

Val

ue (

middotto

n-1)





119868119882 = 119868119878119882 (11)








(a) Manual labeling

0

02

04

06

Erro

r Rat

e








120597119890120597119908119894 le 119903 (12)







119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Step1 Step2

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

Strain Time-History

Strain Time-History

Strain Time-History

Strain Time-History

minus150

minus140

minus130

minus120

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

275 280 285 290 295270Time (s)

(a) bridge



minus10

0

10

20

Scal

ed S

trai

n (

)

minus10

0

10

20

Scal

ed S

trai

n (

)

minus5

0

5

Scal

ed S

trai

n (

)





120575119896 =

[1 minus (1198901198966119904)2]2

for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 lt 1

0 for100381610038161003816100381610038161003816100381611989011989661199041003816100381610038161003816100381610038161003816 ge 1

(7)

bridgeenvironment

minus150

minus145

minus140

minus135

minus130

minus125

Scal

ed S

trai

n (

)

275 280 285 290

LOWESS

RLOWESS

295270Time (s)






A

P

B C D E

M

y

Chosen section

S2

S3S1

IS2

IS3 S4

IS4

IS1






120576 = 119872119910119864119868 (8)







(9)





119875 = 119882 sdot g (10)





S2 S3S1 S4


Strain Time-History

Extremum

157 159153 155 161151Time (s)

minus10

0

10

20

Scal

ed S

trai

n (

)

IS2

IS3

IS4

IS1



A B C D E

Chosen section

S2

S3S1

S4IW1

IW2

IW3

IW4



minus05

0

05

1

15

Influ

ence

Val

ue (

middotto

n-1)





119868119882 = 119868119878119882 (11)








(a) Manual labeling

0

02

04

06

Erro

r Rat

e








120597119890120597119908119894 le 119903 (12)







119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




A

P

B C D E

M

y

Chosen section

S2

S3S1

IS2

IS3 S4

IS4

IS1






120576 = 119872119910119864119868 (8)







(9)





119875 = 119882 sdot g (10)





S2 S3S1 S4


Strain Time-History

Extremum

157 159153 155 161151Time (s)

minus10

0

10

20

Scal

ed S

trai

n (

)

IS2

IS3

IS4

IS1



A B C D E

Chosen section

S2

S3S1

S4IW1

IW2

IW3

IW4



minus05

0

05

1

15

Influ

ence

Val

ue (

middotto

n-1)





119868119882 = 119868119878119882 (11)








(a) Manual labeling

0

02

04

06

Erro

r Rat

e








120597119890120597119908119894 le 119903 (12)







119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




S2 S3S1 S4


Strain Time-History

Extremum

157 159153 155 161151Time (s)

minus10

0

10

20

Scal

ed S

trai

n (

)

IS2

IS3

IS4

IS1



A B C D E

Chosen section

S2

S3S1

S4IW1

IW2

IW3

IW4



minus05

0

05

1

15

Influ

ence

Val

ue (

middotto

n-1)





119868119882 = 119868119878119882 (11)








(a) Manual labeling

0

02

04

06

Erro

r Rat

e








120597119890120597119908119894 le 119903 (12)







119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



(a) Manual labeling

0

02

04

06

Erro

r Rat

e








120597119890120597119908119894 le 119903 (12)







119909 = 1199091015840 sdot 119905119910 = 1199101015840 sdot 119905119911 = 119891 sdot 119905

(13)


O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



O

y

x


Lane1Lane2

Lane3

Vehicle

Webcam

yx

z


O

P Observed Object

zyx

P[x y z]

O Optical Center

Pixel plane

Focal Length f

[x y]


y

x

P


Similar Triangles

P

x

f

z

O

Pixel plane

x

P







375m

375m

P1(x1

y1)

P3(x3

y3)

P4(x4

y4)

P2(x2

y2)





(15)


x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



x

y

O

Truck1Truck2

Lane1 Lane2


Truck1Truck2

0

32

69

101

133

Long

itudi

nal L

engt

h (m

)






4 Field Tests









32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



32000

16000 16000 15000

87900


Unit mm

Traffic Direction

2



Span 2

Span 3

Start line

End line

32m

37m

32m32m

Pavement-based WIM

Span 4

LANE1

LANE 1

LANE2 LANE3


112503750

LANE 2

Unit mmX

LANE 3

37503750

S1S2S3

S4900400300 S5

S62times







119882 = 119878119901119890119886119896119868119901119890119886119896 (16)




119882119903119890119886119903 = 119878119901119890119886119896119903119890119886119903 minus 119868119891119903119900119899119905 sdot 119882119891119903119900119899119905119868119901119890119886119896119903119890119886119903

(17)





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





360 ton

55 m

1126 ton









V = Δ119878Δ119905 (18)






Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Test1Test2Baseline

minus1

0

1

2

3In

fluen

ce V

alue

(middot

ton-1

)



Test3Test4Baseline

minus1

0

1

2

3

Influ

ence

Val

ue (

middotto

n-1)




Strain Time-History

S1

Peak1 Peak3Peak2

S2S3

S4S5S6

minus50

0

50

100

Scal

ed S

trai

n (

)

275 280 285 290 295270Time (s)


Peak1

Peak3Peak2

0

20

40

60

80

100

Scal

ed S

trai

n Pe

ak (

)


(b) Values of peaks






0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

20

40

60

80

100

BWIM

(t)

BaselineS1



0

20

40

60

80

100

BWIM

(t)

BaselineS2



0

20

40

60

80

100

BWIM

(t)

BaselineS3



0

20

40

60

80

100BW

IM (t

)

BaselineS4



0

20

40

60

80

100

BWIM

(t)

BaselineS5



0

20

40

60

80

100

BWIM

(t)

BaselineS6




0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

20

40

60

80

100

120C

ompu

ter V

ision

(km

h)

20 40 60 80 100 1200Pavement WIM (kmh)

BaselineCV


56 54

55 49

3 2 10 0 00

20

40

60

Num

ber o

f Veh

icle

s


WIM

CV








5 Conclusions






Data Availability




Acknowledgments






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






References










































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


traffic sensing methodology combining influence line...

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