Research ArticleReliability Assessment for PSC Box-Girder Bridges Based onSHM Strain Measurements

Chuang Chen1 ZonglinWang2 Yinhui Wang1 TaoWang1 and Zheng Luo1

1School of Civil Engineering and Architecture Ningbo Institute of Technology Zhejiang University Ningbo 315100 China2School of Transportation Science and Engineering Harbin Institute of Technology Harbin 150090 China

Correspondence should be addressed to Chuang Chen chuang0925hotmailcom

Received 2 January 2017 Revised 19 April 2017 Accepted 21 May 2017 Published 10 July 2017

Academic Editor Emad Elbeltagi

Copyright copy 2017 Chuang Chen 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

A reliability assessment method for prestressed concrete (PSC) continuous box-girder bridges based on structural healthmonitoring (SHM) strainmeasurements was proposed First due to the fact thatmeasured strain was compositive and the variationperiods of its components were different a series of limit state equations under normal use limit state were given Then a linearfitting method was used to determine the relationship between the ambient temperature and the measured strain which wasaimed at extracting the vehicle load effect and the temperature load effect from the measured strain Finally according to theequivalent normalization method the load effects unsatisfying the normal distribution by probability density function fitting weretransformed and the daily failure probabilities of monitored positions were calculated for evaluating the safety state of the girderThe results show that (1) the top plate of the box girder is more sensitive than the bottom plate to the high temperature (2) thedaily and seasonal strain variations induced by uniform temperature reveal an inconsistent tendency to the seasonal variation formid-span cross sections and (3) the generalized extreme value distribution is recommended for temperature gradient stress andvehicle induced stress fitting for box-girder bridges

1 Introduction

Typically the structural health monitoring (SHM) technol-ogy is commonly considered as an efficient and effective toolacquiring the in-service behavior for structures during theirlife cycles [1] Strain measurement as the most commonand important part of the SHM system is usually used tomonitor changes of critical points and sections of bridges [2ndash5] Many researchers have tried to utilize the short-term andlong-term monitoring strain responses to evaluate the stateof bridges [6ndash8] Moreover the strain is used as an importantdetective parameter to identify damage and cracks in timeseries [9] Strain responses are responsible for solving thefatigue assessment problem for the steel bridge [10]

However for concrete structures the strain is a com-plicated comprehensive variable determined not only bydeformation but also by the ambient excitation variation(temperature wind) and the property variation of the mate-rials (concrete shrinkage and creep) [8] The prestressedforce plays a very important role in strain measurement

during the long-term monitoring All these factors makestrainmeasurement as an evaluation parameter very difficultdirectly reflecting structure performanceMoreover concretebridges are usually subjected to the thermal effect whichis normally caused by the temperature difference betweenthe bridges and ambient environment where solar radiationprimarily leads to daily and seasonal temperature variation[11] The nonlinear temperature distribution will lead totensile stress along the depth of the sections and also leadto strain difference between the areas outside and inside thebox girder which are considered to be responsible for thermalcracks and damage [12]

The reliability methodology incorporation with SHMmeasurements to identify the damage and assess the con-dition of bridges was proposed in recent years [13] It hasmainly solved the randomness problem which greatly affectsprecisely evaluating the performance of bridges by usingprobability statistic methodology Frangopol et al [7] and Liuet al [14 15] have realized the reliability assessment of compo-nents on real bridges based on the long-termmonitored data

HindawiJournal of SensorsVolume 2017 Article ID 8613659 13 pageshttpsdoiorg10115520178613659

2 Journal of Sensors

of SHM systems Additionally Li et al [16] and Xia et al [17]have applied the reliability analysis method for the conditionassessment of TsingMa Bridge Liu et al [18] combined finiteelement analysis and radial basis function neural networkwithMonte-Carlo importance sampling method establishinga hybrid algorithm for reliability assessment of long-spanprestressed concrete cable-stayed bridges Wang et al [19]compared three extreme value selection methods of vehicleload and their results show that the different method forchoosing the vehicle response may affect the reliability ofbridges Liu at al have developed a holistic reliability assess-ment framework considering the cable breakage incidentfor the long-span cable bridge However applications of thereliability method on concrete box-girder bridges using themeasurements from SHM systems are limited to date

The bridge is commonly subjected to plenty of loadswith high degree of randomness Therefore how to use thisrandom load responses from the SHM system to assess safetycondition is amain issueThe reliabilitymethod utilizes prob-abilistic methodology solving the load effects randomnessand provides a new solution for assessing the safety conditionof concrete box-girder bridges In this study a reliabilityassessment method for PSC continuous box-girder bridgesbased on SHMstrainmeasurementswas first proposedThena reliability calculation case based on strain measurementsof a long-term SHM system of a prestress concrete (PSC)continuous box-girder bridge was presented According tothe stress characteristics and load reference period in theoperation stage of concrete box-girder bridge limit stateequations under normal using limit state were given due tothe measured compositive strain and the different variationperiods of its components The probability density functionfitting of the load effect dissatisfying the normal distribu-tion was transformed according to equivalent normalizationmethod (JC method) The daily failure probabilities of moni-tored positions were calculated for assessment of this bridgeThis study provides a methodology of reliability assessmentfor concrete box-girder bridges which has simultaneouslytaken into account the vehicle load effect and the temperatureload effect

2 Reliability Evaluation Method

21 Component Analysis of Measured Strain Responses Forconcrete box-girder bridges in order to attain long-termdata credibly in order to reduce the influence of the externalenvironment on data and to improve the service life of sen-sors the monitoring system including used sensors is usuallyarranged on interior of the box girder Therefore for long-term measured responses for example strain monitoringdata can be expressed as

120582119872 = 120582119879 + 120582EF + 120582IF + 120582119862 + 120582119873 + 120582119874 (1)

where 120582119872 is measured strain 120582119879 is temperature producedstrain 120582EF are external forces producing strain for concretecontinuous box-girder bridge which mainly refer to vehicleload producing strain 120582IF are internal forces including deadload and prestressed load producing strain 120582119862 is creep and

shrinkage strain 120582119873 is measured noise and 120582119874 are accidentalactions producing strain

From formula (1) long-term monitoring strain responseis comprehensive while its components have different timescale Researches show that (1) temperature of bridge struc-ture is usually affected by external environment factorssuch as geographical conditions and intensity of solar radi-ation The surface temperature of the box-girder changesat the same time scale as atmospheric temperature Dailytemperature difference annual temperature difference andabrupt temperature drop are the biggest factors affectingbridge structures Obviously (1) the unit of daily temperaturedifference and annual temperature difference are one day andone year for time scales respectivelyThe abrupt temperaturedrop on time scale has its randomness which completes overa few days (2) when a vehicle passes through a bridge theduration is very short lasting several minutes so the minuteis considered as the time scale (3) Concrete shrinkage andcreep last the whole lifetime of the structure for years andthe variation in general uses the month as time scale alreadysatisfying accuracy requirement (4) the variation of the deadload and prestress will occur for a long time during bridgeoperating process so considering the month as time scalealso has enough accuracy and (5) noise influence is a randomanduncertainty processwhich can be considered as a randomvariable and the time scale distribution is in a wide range Asa result in daily time scale for the bridge structure conditionassessment one only needs to consider the influences oftemperature difference vehicle load and noise

22 Normal Use Limit State Equation For the bridge withinfrequent traffic the role of environmental factors may begreater than the effect of the vehicle loadTherefore conditionassessing is focused on the performance of the normal useduring the whole lifetime of bridges During normal use pro-cess of concrete continuous box-girder bridges on daily timescale daily temperature difference and the vehicle load playmain roles in bridge condition assessment Specifically dailyuniform temperature variation mainly produces expansiondeformation along the beam direction and vertical tempera-ture gradient mainly produces temperature subinternal forceacross cross sections The overall longitudinal deformationis not useful for the box girder As we all know verticaltemperature gradient stress will take responsibility for thetemperature cracks on the concrete box girder Thereforeduring the benchmark period of the concrete box-girderbridge structure the concrete tensile strength standard valuecan be considered as the resistance in the normal use limitstate equation The load effects are dead load vehicle loadand temperature gradient stress respectively These threekinds of load effects are independent of each other so asto establish the in-service concrete continuous box-girderbridges cross section limit state equation as

119866 = 119885119878 (119909 119905) + 1205930 (119909 119905) 119885119863 (119909 119905)minus (1 + 1205761) 1205931 (119909 119905) 119885119881 (119909 119905)minus (1 + 1205762) 1205932 (119909 119905) 119885119879 (119909 119905)

(2)

Journal of Sensors 3

where119885119878(119909 119905) is the concrete tensile strength standard value119885119863(119909 119905) is the dead load effect after the bridge completed119885119881(119909 119905) is the measured vehicle load effect 119885119879(119909 119905) is themeasured temperature gradient load effect 1205930(119909 119905) is thetime variation function of the dead load effect 1205931(119909 119905) isthe time variation function of the vehicle load effect and1205932(119909 119905) is the time variation function of the temperaturegradient effect The time variation functions can be used topredict the response of the future 1205761 and 1205762 are monitoringerrors respectively assuming that they satisfy the normaldistribution 119873(0 120590) The reliability index of the limit stateequation is shown as follows

120573 = 120572119878 + 120572119863 minus 120572119881 minus 120572119879radic1205752119878 + 1205752119863 + 1205752119881 + 1205752119879

(3)

where 120572119878 is themean of the concrete tensile strength standardvalues 120572119863 is the mean stress caused by dead load 120572119881 isthe mean stress caused by vehicle load 120572119879 is the meanstress caused by temperature gradient load 120575119878 is the standarddeviation of concrete tensile strength standard values 120575119863 isthe standard deviation stress caused by dead load 120575119881 is thestandard deviation stress caused by vehicle load and 120575119879 isthe standard deviation stress caused by temperature gradientload

Under the effect of the vehicle load according to the flatsection assumption the top plate of the box girder alongthe longitudinal presents compression stress and the bottomplate presents tensile stress Therefore when calculating thetop plate reliability index according to the most unfavorableprinciple the vehicle load effect is not counted Underthe effect of the temperature gradient load tension andcompression both act on the top plate and the bottom plateTherefore the limit state equation (6) can be representedaccording to the most unfavorable load combination onlytaking into account the temperature gradient load effect as

119866119879 = 119885119878 (119909 119905) + 1205930 (119909 119905) 119885119863 (119909 119905)minus (1 + 1205762) 1205932 (119909 119905) 119885119879 (119909 119905)

(4)

Correspondingly the reliability index can be rewritten as

120573119879 =120572119878 + 120572119863 minus 120572119879radic1205752119878 + 1205752119863 + 1205752119879

(5)

When calculating the reliability index of the bottomplateonly vehicle load effect is taken into account because of thetemperature gradient load producing compression stress sothe limit state equation can be represented as

119866119881 = 119885119878 (119909 119905) + 1205930 (119909 119905) 119885119863 (119909 119905)minus (1 + 1205761) 1205931 (119909 119905) 119885119881 (119909 119905)

(6)

Then the reliability index can be described as

120573119881 =120572119878 + 120572119863 minus 120572119881radic1205752119878 + 1205752119863 + 1205752119881

(7)

According to the previous analysis a method whichis used to evaluate the condition of concrete box-girderbridges based on strainmeasurements is proposed where theevaluation process is illustrated in Figure 1

3 A Case for Reliability Calculation

31 Fu Sui Bridge and Its SHM System Description Theprestress concrete continuous box-girder bridge is locatedat Heilongjiang province (N47∘1410158404010158401015840 E131∘5810158401110158401015840) of main-land of China (shown in Figure 2) The bridge is 1170m longand is composed of six 150m long main spans and two 85mlong side spans The vertical heights of supporting sectionsand mid-span sections are 9m and 35m respectively Cast-in-place cantilever posttensioned construction method wasadopted for the single-cell box girder Each cantilever armwas 74m in length which was divided into 19 segments (0to 18) The entire construction process lasted for three yearsfrom 2008 to 2011

In order to detect the damage and evaluate the long-term static and dynamic performances under the influencesof traffic and ambient environment a long-term SHM systemwas designed and implemented on this bridge The systemwas composed of a hydrostatic leveling subsystem (HLS) afiber Bragg grating (FBG) sensor subsystem a data acquisi-tion and transmission subsystem a master control center aremote control center data analysis and processing softwareand a power supply system (Figure 3) Detailed informationof SHM system can be found elsewhere [20 21]

Sensor positions of the SHM system are shown in Fig-ure 4 There are two types of the sensor for the monitoringsystem Fiber Bragg grating sensors were applied to monitortemperature strain and vibration Inductance type sensorwas applied for displacement Totally 24 self-adaptive strainsensors which were usually installed on inner surface ofthe top plate and the bottom plate were distributed on sixsections of the box girder A temperature sensor was appliedto every strain section In section T (as shown in Figure 4) sixtemperature sensors were applied to monitor the inside andoutside temperature variation of the girder The field sensordistribution of section B is presented in Figure 5

32 Monitoring Strain and Temperature From May 2012 toApril 2013 strainmeasurements were presented to investigatethe relationship with the temperature For concrete box-girder bridges temperature distribution on bridge compo-nents can be described as the uniform temperature and thetemperature gradient

The uniform temperature variation can only cause theexpansion and compression along the girder in length How-ever the temperature gradient variation normally inducesthe girder bending deformations which is considered as themain reason of local cracking [22] For a continuous bridgeonly one bearing support fixed can eventually restrict thegirder against the longitudinal and lateral movements Underthe uniform temperature load the girder can freely expandand compress in longitudinal direction However uniformtemperature-induced distortion may be restricted due to

4 Journal of Sensors

Original monitoringstrain response

Vehicle loadresponse

Temperaturetrend term

Eliminating theoverall temperature

effect

Selecting themaximums over

the threshold

Trend term separationmethod based on EMD

Tension andcompression zone

judgment

Tension zonejudgment

The top plate tension

The bottomplate tension

The bottom plate tension The top plate

compression

Do not calculate thereliability index

according to the mostunfavorable principle

JC method JC method JC method

Distribution fitting and

the standard deviation 휎V

calculating the mean 휇V and

훽T =훼S + 훼D minus 훼T

radic훿2S + 훿2

D + 훿2T

훽 =훼S + 훼D minus 훼V minus 훼T

radic훿2S + 훿2

D + 훿2V + 훿2

T

훽V =훼S + 훼D minus 훼V

radic훿2S + 훿2

D + 훿2V

Distribution fitting and

the standard deviation 휎T

calculating the mean 휇T and

Figure 1 Flow chart of reliability index calculation

Figure 2 The view of the bridge

friction force existence in other supports In the early stage ofthe uniform temperature load it can be imaged that the girderexpansion movement may not happen But it may exceed thebearing sliding friction force along with the expanding forceaccumulating Finally the girder longitudinal movementhappensThe entire processing can be described as an energyaccumulation and releasing cycle

321 Uniform Temperature-Induced Strain Generally longi-tudinal strain measurement in accordance with the longitu-dinal deformation of the girder presents the approximatelylinear relation with the uniform temperature variation Strain

measurements and one-day temperature variation inside andoutside the box-girder are presented in Figure 5

Figure 6 shows that the outside temperature magnitude isusually much bigger than the inside temperature magnitudeThe strain variation represents positive correlation with theoutside temperature of box girder in spite of whether insummer or winter In summer the strain also increases to themaximum value when the temperature reaches the highestvalue (at 16 pm) Similarly the peak presents at 13 pm inwinter and the strain may lag for a while to arrive at itspeak Overall the strain changes the same as the outsidetemperature variation in daily measurement Therefore alinear regression analysis was carried out using the outsidetemperature measurements and the strain measurements ofsection D The regression results are shown in Figures 7 and8

Figures 7 and 8 show the daily strain linear regressionwith the outside temperature variation One-day strain mea-surements of section D were selected from summer in 2012and winter in 2013 respectively From these figures it can beseen that the linear regression slopes even when all are fromthe same section were different from each other regardlessof the season difference It is one evidence of temperaturegradient which is a common property existing in box-girderbridges

Journal of Sensors 5

OE

GPRS

ComputerUser

Database

Power station

Currentcable

CurrentlineRS485

Displacement sensor

Optical fiberacquisitioninstrument

Accelerationsensor

Temperaturesensor

Strainsensor

Opticalfiber

Opticalfiber

OpticalfiberOptical

fiber

Opticalcable

OpticalcableOptical

cable

Data line Data line

Figure 3 SHM system of Fu Sui bridge

Section A

P1 P2 P3 P4 P5 P6 P7 P8 P9

AA1

AS1~AS4AD1AT1 CD1

CS1~CS4

CT1BA1

BS1~BS4BD1BT1

DA1

DS1~DS4DD1DT1

EA1

ES1~ES4ED1ET1 FS1~FS4

FT1

CT1CS1

CS3

CS4

CS2

Displacement sensor (DS)Temperature sensor (TS)Strain sensor (SS) Acceleration sensor (AS)

DS3DS2DT1DS1 DS4

ES2 ES3ET1ES4ES1

Section BSection C

Section D Section ESuibin Town Fujin City

Section T

Figure 4 Elevation and positions of sensors

Linear regression coefficients between the outside tem-perature and strain measurements and their 1198772 values arepresented in Table 1 It can be observed that 1198772 valuesare all effective except for two values (the DS1 and DS4in summer) which means that linear regression method issuitable for describing the relationship between the outsidetemperature and strain measurements The slope magnitude119886 (120583120576∘C) can reflect the strain sensitivity to the outsidetemperature variation In summer the slopes of the top plateare much bigger than the ones of the bottom plate which

means that the top plate is more sensitive to the uniformtemperature variation This suggests that high temperature ismore effective on the top plate However in winter the slopesof the bottomplate growmuchbigger which suggests that lowtemperature can produce strain more easily on the bottomplate

Figure 9 shows one-day mean-temperature variationinside and outside the box-girder from May 2012 to April2013

6 Journal of Sensors

Table 1 Linear regression coefficients between temperature and strain measurements and their 1198772 values

Sensor Time 119886 1198772DS1 (on bottom plate)

Summer (2012621)

1452 06067DS2 (on top plate) 219 08750DS3 (on top plate) 3038 09121DS4 (on bottom plate) 1049 05573DS1 (on bottom plate)

Winter (2013121)

204 09078DS2 (on top plate) 1897 09304DS3 (on top plate) 2242 08277DS4 (on bottom plate) 1714 07966lowast119910 = 119886119909 where 119910means strain and 119909means temperature variation 1198772 means coefficient of determination

Accelerationsensor Strain sensor on the top plate

Strain sensor on the bottom plate

Current line

Displacement sensor

BS2 BS3

BS1

BA1

BT1

BS4

Fiber

D2

RS485 line

Figure 5 Sensors distribution of section B

Figure 9 shows the temperature variation outside andinside the box girder Generally the temperature measure-ments are consistent with the seasonal climate feature at thebridge site where the daily temperature difference is verybig both in summer and in winter Overall the ambienttemperature can drop from 30∘C (in summer) down tominus20∘C(in winter)The temperature variation not only influences theproperty of concrete but also redistributes the internal forcesand changes the boundary conditions of bridges

Figure 10 shows the strain variation from May in 2012to May in 2013 The curve decreasing means the tensilestrain and the curve increasingmeans the compressive strainIt is interesting that the seasonal strain variation presentsa negative correlation with the uniform temperature intime series which is contrary to the daily strain variationtrend with the temperature The main reason is that theseasonal temperature can generate the longitude expansionand compression along the deck especially for this kind ofcontinuous concrete bridges with the extremely long deckMeanwhile the bridge has no longitude restrictions whichmakes the longitude expansion and compression occur freelyTherefore in winter the deformation of the mid-section ofthe continuous bridge goes down which can cause the tensilestrain on the mid-section in summer the deformation ofthe mid-section goes up so the strain of the mid-section iscompressive and keeps on decreasing From Figure 9 four

strain sensors arranged on section D all present consistencywith the above theory Therefore the seasonal temperaturevariation is more effective on the strain of concrete bridges incold region

322 Temperature Gradient Induced Strain Difference Inparticular concrete box-girder bridges normally producetemperature gradient stress along the vertical cross sectionsdue to solar radiation and abrupt temperature droppingThisproperty currently is considered as one of the main reasonswhich induce the cracking and local damage for concrete box-girder bridges One-day strain measurements of section D onJune 21 are shown in Figure 11

The sampling frequency of the monitoring system is 60times per hour Δ1198781 and Δ1198782 are the strain difference betweenthe top plate and the bottom plate of the mid-span crosssection The strain of the top plate happens earlier than thebottom plate reaching the peak at around 16 pm then thestrain of bottom plate reaches the peak at about 19 pm Itdemonstrates that the solar energy needs a couple of hourstransferring along the vertical cross section from the top plateto the bottom plate When the strain rises up before reachingthe peak the strain differences Δ1198781 and Δ1198782 between topand bottom plates are positive which means the top plateis tensile relative to the bottom plate although its amplitudekeeps on decreasing after the strain reaches the peak itdrops quickly without the solar energy while the strain of thebottom plate goes down relatively slowly then the Δ1198781 andΔ1198782 difference directions turn to be negative which meansthe bottom plate is tensile It can been seen that the strain ofthe top plate declines faster than the bottom plate Thereforethe solar energy transfer lag is responsible for generatingvertical temperature gradient stress in cross sections Withdaily temperature gradient effect recycle the cross sectionspotentially can have cracks and be damaged

33 Temperature-Induced Response Separation Uniformtemperature strain response is usually considered as atrend term in original measurements A number of trendterm separation methods have been developed such asempirical mode decomposition (EMD) method low passfiltering method wavelet method least square methodand average slope method In this study EMD method wasadopted to separate the temperature trend term A more

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Sensors 3

where119885119878(119909 119905) is the concrete tensile strength standard value119885119863(119909 119905) is the dead load effect after the bridge completed119885119881(119909 119905) is the measured vehicle load effect 119885119879(119909 119905) is themeasured temperature gradient load effect 1205930(119909 119905) is thetime variation function of the dead load effect 1205931(119909 119905) isthe time variation function of the vehicle load effect and1205932(119909 119905) is the time variation function of the temperaturegradient effect The time variation functions can be used topredict the response of the future 1205761 and 1205762 are monitoringerrors respectively assuming that they satisfy the normaldistribution 119873(0 120590) The reliability index of the limit stateequation is shown as follows

120573 = 120572119878 + 120572119863 minus 120572119881 minus 120572119879radic1205752119878 + 1205752119863 + 1205752119881 + 1205752119879

(3)

where 120572119878 is themean of the concrete tensile strength standardvalues 120572119863 is the mean stress caused by dead load 120572119881 isthe mean stress caused by vehicle load 120572119879 is the meanstress caused by temperature gradient load 120575119878 is the standarddeviation of concrete tensile strength standard values 120575119863 isthe standard deviation stress caused by dead load 120575119881 is thestandard deviation stress caused by vehicle load and 120575119879 isthe standard deviation stress caused by temperature gradientload

Under the effect of the vehicle load according to the flatsection assumption the top plate of the box girder alongthe longitudinal presents compression stress and the bottomplate presents tensile stress Therefore when calculating thetop plate reliability index according to the most unfavorableprinciple the vehicle load effect is not counted Underthe effect of the temperature gradient load tension andcompression both act on the top plate and the bottom plateTherefore the limit state equation (6) can be representedaccording to the most unfavorable load combination onlytaking into account the temperature gradient load effect as

119866119879 = 119885119878 (119909 119905) + 1205930 (119909 119905) 119885119863 (119909 119905)minus (1 + 1205762) 1205932 (119909 119905) 119885119879 (119909 119905)

(4)

Correspondingly the reliability index can be rewritten as

120573119879 =120572119878 + 120572119863 minus 120572119879radic1205752119878 + 1205752119863 + 1205752119879

(5)

When calculating the reliability index of the bottomplateonly vehicle load effect is taken into account because of thetemperature gradient load producing compression stress sothe limit state equation can be represented as

119866119881 = 119885119878 (119909 119905) + 1205930 (119909 119905) 119885119863 (119909 119905)minus (1 + 1205761) 1205931 (119909 119905) 119885119881 (119909 119905)

(6)

Then the reliability index can be described as

120573119881 =120572119878 + 120572119863 minus 120572119881radic1205752119878 + 1205752119863 + 1205752119881

(7)

According to the previous analysis a method whichis used to evaluate the condition of concrete box-girderbridges based on strainmeasurements is proposed where theevaluation process is illustrated in Figure 1

3 A Case for Reliability Calculation

31 Fu Sui Bridge and Its SHM System Description Theprestress concrete continuous box-girder bridge is locatedat Heilongjiang province (N47∘1410158404010158401015840 E131∘5810158401110158401015840) of main-land of China (shown in Figure 2) The bridge is 1170m longand is composed of six 150m long main spans and two 85mlong side spans The vertical heights of supporting sectionsand mid-span sections are 9m and 35m respectively Cast-in-place cantilever posttensioned construction method wasadopted for the single-cell box girder Each cantilever armwas 74m in length which was divided into 19 segments (0to 18) The entire construction process lasted for three yearsfrom 2008 to 2011

In order to detect the damage and evaluate the long-term static and dynamic performances under the influencesof traffic and ambient environment a long-term SHM systemwas designed and implemented on this bridge The systemwas composed of a hydrostatic leveling subsystem (HLS) afiber Bragg grating (FBG) sensor subsystem a data acquisi-tion and transmission subsystem a master control center aremote control center data analysis and processing softwareand a power supply system (Figure 3) Detailed informationof SHM system can be found elsewhere [20 21]

Sensor positions of the SHM system are shown in Fig-ure 4 There are two types of the sensor for the monitoringsystem Fiber Bragg grating sensors were applied to monitortemperature strain and vibration Inductance type sensorwas applied for displacement Totally 24 self-adaptive strainsensors which were usually installed on inner surface ofthe top plate and the bottom plate were distributed on sixsections of the box girder A temperature sensor was appliedto every strain section In section T (as shown in Figure 4) sixtemperature sensors were applied to monitor the inside andoutside temperature variation of the girder The field sensordistribution of section B is presented in Figure 5

32 Monitoring Strain and Temperature From May 2012 toApril 2013 strainmeasurements were presented to investigatethe relationship with the temperature For concrete box-girder bridges temperature distribution on bridge compo-nents can be described as the uniform temperature and thetemperature gradient

The uniform temperature variation can only cause theexpansion and compression along the girder in length How-ever the temperature gradient variation normally inducesthe girder bending deformations which is considered as themain reason of local cracking [22] For a continuous bridgeonly one bearing support fixed can eventually restrict thegirder against the longitudinal and lateral movements Underthe uniform temperature load the girder can freely expandand compress in longitudinal direction However uniformtemperature-induced distortion may be restricted due to

4 Journal of Sensors

Original monitoringstrain response

Vehicle loadresponse

Temperaturetrend term

Eliminating theoverall temperature

effect

Selecting themaximums over

the threshold

Trend term separationmethod based on EMD

Tension andcompression zone

judgment

Tension zonejudgment

The top plate tension

The bottomplate tension

The bottom plate tension The top plate

compression

Do not calculate thereliability index

according to the mostunfavorable principle

JC method JC method JC method

Distribution fitting and

the standard deviation 휎V

calculating the mean 휇V and

훽T =훼S + 훼D minus 훼T

radic훿2S + 훿2

D + 훿2T

훽 =훼S + 훼D minus 훼V minus 훼T

radic훿2S + 훿2

D + 훿2V + 훿2

T

훽V =훼S + 훼D minus 훼V

radic훿2S + 훿2

D + 훿2V

Distribution fitting and

the standard deviation 휎T

calculating the mean 휇T and

Figure 1 Flow chart of reliability index calculation

Figure 2 The view of the bridge

friction force existence in other supports In the early stage ofthe uniform temperature load it can be imaged that the girderexpansion movement may not happen But it may exceed thebearing sliding friction force along with the expanding forceaccumulating Finally the girder longitudinal movementhappensThe entire processing can be described as an energyaccumulation and releasing cycle

321 Uniform Temperature-Induced Strain Generally longi-tudinal strain measurement in accordance with the longitu-dinal deformation of the girder presents the approximatelylinear relation with the uniform temperature variation Strain

measurements and one-day temperature variation inside andoutside the box-girder are presented in Figure 5

Figure 6 shows that the outside temperature magnitude isusually much bigger than the inside temperature magnitudeThe strain variation represents positive correlation with theoutside temperature of box girder in spite of whether insummer or winter In summer the strain also increases to themaximum value when the temperature reaches the highestvalue (at 16 pm) Similarly the peak presents at 13 pm inwinter and the strain may lag for a while to arrive at itspeak Overall the strain changes the same as the outsidetemperature variation in daily measurement Therefore alinear regression analysis was carried out using the outsidetemperature measurements and the strain measurements ofsection D The regression results are shown in Figures 7 and8

Figures 7 and 8 show the daily strain linear regressionwith the outside temperature variation One-day strain mea-surements of section D were selected from summer in 2012and winter in 2013 respectively From these figures it can beseen that the linear regression slopes even when all are fromthe same section were different from each other regardlessof the season difference It is one evidence of temperaturegradient which is a common property existing in box-girderbridges

Journal of Sensors 5

OE

GPRS

ComputerUser

Database

Power station

Currentcable

CurrentlineRS485

Displacement sensor

Optical fiberacquisitioninstrument

Accelerationsensor

Temperaturesensor

Strainsensor

Opticalfiber

Opticalfiber

OpticalfiberOptical

fiber

Opticalcable

OpticalcableOptical

cable

Data line Data line

Figure 3 SHM system of Fu Sui bridge

Section A

P1 P2 P3 P4 P5 P6 P7 P8 P9

AA1

AS1~AS4AD1AT1 CD1

CS1~CS4

CT1BA1

BS1~BS4BD1BT1

DA1

DS1~DS4DD1DT1

EA1

ES1~ES4ED1ET1 FS1~FS4

FT1

CT1CS1

CS3

CS4

CS2

Displacement sensor (DS)Temperature sensor (TS)Strain sensor (SS) Acceleration sensor (AS)

DS3DS2DT1DS1 DS4

ES2 ES3ET1ES4ES1

Section BSection C

Section D Section ESuibin Town Fujin City

Section T

Figure 4 Elevation and positions of sensors

Linear regression coefficients between the outside tem-perature and strain measurements and their 1198772 values arepresented in Table 1 It can be observed that 1198772 valuesare all effective except for two values (the DS1 and DS4in summer) which means that linear regression method issuitable for describing the relationship between the outsidetemperature and strain measurements The slope magnitude119886 (120583120576∘C) can reflect the strain sensitivity to the outsidetemperature variation In summer the slopes of the top plateare much bigger than the ones of the bottom plate which

means that the top plate is more sensitive to the uniformtemperature variation This suggests that high temperature ismore effective on the top plate However in winter the slopesof the bottomplate growmuchbigger which suggests that lowtemperature can produce strain more easily on the bottomplate

Figure 9 shows one-day mean-temperature variationinside and outside the box-girder from May 2012 to April2013

6 Journal of Sensors

Table 1 Linear regression coefficients between temperature and strain measurements and their 1198772 values

Sensor Time 119886 1198772DS1 (on bottom plate)

Summer (2012621)

1452 06067DS2 (on top plate) 219 08750DS3 (on top plate) 3038 09121DS4 (on bottom plate) 1049 05573DS1 (on bottom plate)

Winter (2013121)

204 09078DS2 (on top plate) 1897 09304DS3 (on top plate) 2242 08277DS4 (on bottom plate) 1714 07966lowast119910 = 119886119909 where 119910means strain and 119909means temperature variation 1198772 means coefficient of determination

Accelerationsensor Strain sensor on the top plate

Strain sensor on the bottom plate

Current line

Displacement sensor

BS2 BS3

BS1

BA1

BT1

BS4

Fiber

D2

RS485 line

Figure 5 Sensors distribution of section B

Figure 9 shows the temperature variation outside andinside the box girder Generally the temperature measure-ments are consistent with the seasonal climate feature at thebridge site where the daily temperature difference is verybig both in summer and in winter Overall the ambienttemperature can drop from 30∘C (in summer) down tominus20∘C(in winter)The temperature variation not only influences theproperty of concrete but also redistributes the internal forcesand changes the boundary conditions of bridges

Figure 10 shows the strain variation from May in 2012to May in 2013 The curve decreasing means the tensilestrain and the curve increasingmeans the compressive strainIt is interesting that the seasonal strain variation presentsa negative correlation with the uniform temperature intime series which is contrary to the daily strain variationtrend with the temperature The main reason is that theseasonal temperature can generate the longitude expansionand compression along the deck especially for this kind ofcontinuous concrete bridges with the extremely long deckMeanwhile the bridge has no longitude restrictions whichmakes the longitude expansion and compression occur freelyTherefore in winter the deformation of the mid-section ofthe continuous bridge goes down which can cause the tensilestrain on the mid-section in summer the deformation ofthe mid-section goes up so the strain of the mid-section iscompressive and keeps on decreasing From Figure 9 four

strain sensors arranged on section D all present consistencywith the above theory Therefore the seasonal temperaturevariation is more effective on the strain of concrete bridges incold region

322 Temperature Gradient Induced Strain Difference Inparticular concrete box-girder bridges normally producetemperature gradient stress along the vertical cross sectionsdue to solar radiation and abrupt temperature droppingThisproperty currently is considered as one of the main reasonswhich induce the cracking and local damage for concrete box-girder bridges One-day strain measurements of section D onJune 21 are shown in Figure 11

The sampling frequency of the monitoring system is 60times per hour Δ1198781 and Δ1198782 are the strain difference betweenthe top plate and the bottom plate of the mid-span crosssection The strain of the top plate happens earlier than thebottom plate reaching the peak at around 16 pm then thestrain of bottom plate reaches the peak at about 19 pm Itdemonstrates that the solar energy needs a couple of hourstransferring along the vertical cross section from the top plateto the bottom plate When the strain rises up before reachingthe peak the strain differences Δ1198781 and Δ1198782 between topand bottom plates are positive which means the top plateis tensile relative to the bottom plate although its amplitudekeeps on decreasing after the strain reaches the peak itdrops quickly without the solar energy while the strain of thebottom plate goes down relatively slowly then the Δ1198781 andΔ1198782 difference directions turn to be negative which meansthe bottom plate is tensile It can been seen that the strain ofthe top plate declines faster than the bottom plate Thereforethe solar energy transfer lag is responsible for generatingvertical temperature gradient stress in cross sections Withdaily temperature gradient effect recycle the cross sectionspotentially can have cracks and be damaged

33 Temperature-Induced Response Separation Uniformtemperature strain response is usually considered as atrend term in original measurements A number of trendterm separation methods have been developed such asempirical mode decomposition (EMD) method low passfiltering method wavelet method least square methodand average slope method In this study EMD method wasadopted to separate the temperature trend term A more

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Sensors

Original monitoringstrain response

Vehicle loadresponse

Temperaturetrend term

Eliminating theoverall temperature

effect

Selecting themaximums over

the threshold

Trend term separationmethod based on EMD

Tension andcompression zone

judgment

Tension zonejudgment

The top plate tension

The bottomplate tension

The bottom plate tension The top plate

compression

Do not calculate thereliability index

according to the mostunfavorable principle

JC method JC method JC method

Distribution fitting and

the standard deviation 휎V

calculating the mean 휇V and

훽T =훼S + 훼D minus 훼T

radic훿2S + 훿2

D + 훿2T

훽 =훼S + 훼D minus 훼V minus 훼T

radic훿2S + 훿2

D + 훿2V + 훿2

T

훽V =훼S + 훼D minus 훼V

radic훿2S + 훿2

D + 훿2V

Distribution fitting and

the standard deviation 휎T

calculating the mean 휇T and

Figure 1 Flow chart of reliability index calculation

Figure 2 The view of the bridge

friction force existence in other supports In the early stage ofthe uniform temperature load it can be imaged that the girderexpansion movement may not happen But it may exceed thebearing sliding friction force along with the expanding forceaccumulating Finally the girder longitudinal movementhappensThe entire processing can be described as an energyaccumulation and releasing cycle

321 Uniform Temperature-Induced Strain Generally longi-tudinal strain measurement in accordance with the longitu-dinal deformation of the girder presents the approximatelylinear relation with the uniform temperature variation Strain

measurements and one-day temperature variation inside andoutside the box-girder are presented in Figure 5

Figure 6 shows that the outside temperature magnitude isusually much bigger than the inside temperature magnitudeThe strain variation represents positive correlation with theoutside temperature of box girder in spite of whether insummer or winter In summer the strain also increases to themaximum value when the temperature reaches the highestvalue (at 16 pm) Similarly the peak presents at 13 pm inwinter and the strain may lag for a while to arrive at itspeak Overall the strain changes the same as the outsidetemperature variation in daily measurement Therefore alinear regression analysis was carried out using the outsidetemperature measurements and the strain measurements ofsection D The regression results are shown in Figures 7 and8

Figures 7 and 8 show the daily strain linear regressionwith the outside temperature variation One-day strain mea-surements of section D were selected from summer in 2012and winter in 2013 respectively From these figures it can beseen that the linear regression slopes even when all are fromthe same section were different from each other regardlessof the season difference It is one evidence of temperaturegradient which is a common property existing in box-girderbridges

Journal of Sensors 5

OE

GPRS

ComputerUser

Database

Power station

Currentcable

CurrentlineRS485

Displacement sensor

Optical fiberacquisitioninstrument

Accelerationsensor

Temperaturesensor

Strainsensor

Opticalfiber

Opticalfiber

OpticalfiberOptical

fiber

Opticalcable

OpticalcableOptical

cable

Data line Data line

Figure 3 SHM system of Fu Sui bridge

Section A

P1 P2 P3 P4 P5 P6 P7 P8 P9

AA1

AS1~AS4AD1AT1 CD1

CS1~CS4

CT1BA1

BS1~BS4BD1BT1

DA1

DS1~DS4DD1DT1

EA1

ES1~ES4ED1ET1 FS1~FS4

FT1

CT1CS1

CS3

CS4

CS2

Displacement sensor (DS)Temperature sensor (TS)Strain sensor (SS) Acceleration sensor (AS)

DS3DS2DT1DS1 DS4

ES2 ES3ET1ES4ES1

Section BSection C

Section D Section ESuibin Town Fujin City

Section T

Figure 4 Elevation and positions of sensors

Linear regression coefficients between the outside tem-perature and strain measurements and their 1198772 values arepresented in Table 1 It can be observed that 1198772 valuesare all effective except for two values (the DS1 and DS4in summer) which means that linear regression method issuitable for describing the relationship between the outsidetemperature and strain measurements The slope magnitude119886 (120583120576∘C) can reflect the strain sensitivity to the outsidetemperature variation In summer the slopes of the top plateare much bigger than the ones of the bottom plate which

means that the top plate is more sensitive to the uniformtemperature variation This suggests that high temperature ismore effective on the top plate However in winter the slopesof the bottomplate growmuchbigger which suggests that lowtemperature can produce strain more easily on the bottomplate

Figure 9 shows one-day mean-temperature variationinside and outside the box-girder from May 2012 to April2013

6 Journal of Sensors

Table 1 Linear regression coefficients between temperature and strain measurements and their 1198772 values

Sensor Time 119886 1198772DS1 (on bottom plate)

Summer (2012621)

1452 06067DS2 (on top plate) 219 08750DS3 (on top plate) 3038 09121DS4 (on bottom plate) 1049 05573DS1 (on bottom plate)

Winter (2013121)

204 09078DS2 (on top plate) 1897 09304DS3 (on top plate) 2242 08277DS4 (on bottom plate) 1714 07966lowast119910 = 119886119909 where 119910means strain and 119909means temperature variation 1198772 means coefficient of determination

Accelerationsensor Strain sensor on the top plate

Strain sensor on the bottom plate

Current line

Displacement sensor

BS2 BS3

BS1

BA1

BT1

BS4

Fiber

D2

RS485 line

Figure 5 Sensors distribution of section B

Figure 9 shows the temperature variation outside andinside the box girder Generally the temperature measure-ments are consistent with the seasonal climate feature at thebridge site where the daily temperature difference is verybig both in summer and in winter Overall the ambienttemperature can drop from 30∘C (in summer) down tominus20∘C(in winter)The temperature variation not only influences theproperty of concrete but also redistributes the internal forcesand changes the boundary conditions of bridges

Figure 10 shows the strain variation from May in 2012to May in 2013 The curve decreasing means the tensilestrain and the curve increasingmeans the compressive strainIt is interesting that the seasonal strain variation presentsa negative correlation with the uniform temperature intime series which is contrary to the daily strain variationtrend with the temperature The main reason is that theseasonal temperature can generate the longitude expansionand compression along the deck especially for this kind ofcontinuous concrete bridges with the extremely long deckMeanwhile the bridge has no longitude restrictions whichmakes the longitude expansion and compression occur freelyTherefore in winter the deformation of the mid-section ofthe continuous bridge goes down which can cause the tensilestrain on the mid-section in summer the deformation ofthe mid-section goes up so the strain of the mid-section iscompressive and keeps on decreasing From Figure 9 four

strain sensors arranged on section D all present consistencywith the above theory Therefore the seasonal temperaturevariation is more effective on the strain of concrete bridges incold region

322 Temperature Gradient Induced Strain Difference Inparticular concrete box-girder bridges normally producetemperature gradient stress along the vertical cross sectionsdue to solar radiation and abrupt temperature droppingThisproperty currently is considered as one of the main reasonswhich induce the cracking and local damage for concrete box-girder bridges One-day strain measurements of section D onJune 21 are shown in Figure 11

The sampling frequency of the monitoring system is 60times per hour Δ1198781 and Δ1198782 are the strain difference betweenthe top plate and the bottom plate of the mid-span crosssection The strain of the top plate happens earlier than thebottom plate reaching the peak at around 16 pm then thestrain of bottom plate reaches the peak at about 19 pm Itdemonstrates that the solar energy needs a couple of hourstransferring along the vertical cross section from the top plateto the bottom plate When the strain rises up before reachingthe peak the strain differences Δ1198781 and Δ1198782 between topand bottom plates are positive which means the top plateis tensile relative to the bottom plate although its amplitudekeeps on decreasing after the strain reaches the peak itdrops quickly without the solar energy while the strain of thebottom plate goes down relatively slowly then the Δ1198781 andΔ1198782 difference directions turn to be negative which meansthe bottom plate is tensile It can been seen that the strain ofthe top plate declines faster than the bottom plate Thereforethe solar energy transfer lag is responsible for generatingvertical temperature gradient stress in cross sections Withdaily temperature gradient effect recycle the cross sectionspotentially can have cracks and be damaged

33 Temperature-Induced Response Separation Uniformtemperature strain response is usually considered as atrend term in original measurements A number of trendterm separation methods have been developed such asempirical mode decomposition (EMD) method low passfiltering method wavelet method least square methodand average slope method In this study EMD method wasadopted to separate the temperature trend term A more

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 5

OE

GPRS

ComputerUser

Database

Power station

Currentcable

CurrentlineRS485

Displacement sensor

Optical fiberacquisitioninstrument

Accelerationsensor

Temperaturesensor

Strainsensor

Opticalfiber

Opticalfiber

OpticalfiberOptical

fiber

Opticalcable

OpticalcableOptical

cable

Data line Data line

Figure 3 SHM system of Fu Sui bridge

Section A

P1 P2 P3 P4 P5 P6 P7 P8 P9

AA1

AS1~AS4AD1AT1 CD1

CS1~CS4

CT1BA1

BS1~BS4BD1BT1

DA1

DS1~DS4DD1DT1

EA1

ES1~ES4ED1ET1 FS1~FS4

FT1

CT1CS1

CS3

CS4

CS2

Displacement sensor (DS)Temperature sensor (TS)Strain sensor (SS) Acceleration sensor (AS)

DS3DS2DT1DS1 DS4

ES2 ES3ET1ES4ES1

Section BSection C

Section D Section ESuibin Town Fujin City

Section T

Figure 4 Elevation and positions of sensors

Linear regression coefficients between the outside tem-perature and strain measurements and their 1198772 values arepresented in Table 1 It can be observed that 1198772 valuesare all effective except for two values (the DS1 and DS4in summer) which means that linear regression method issuitable for describing the relationship between the outsidetemperature and strain measurements The slope magnitude119886 (120583120576∘C) can reflect the strain sensitivity to the outsidetemperature variation In summer the slopes of the top plateare much bigger than the ones of the bottom plate which

means that the top plate is more sensitive to the uniformtemperature variation This suggests that high temperature ismore effective on the top plate However in winter the slopesof the bottomplate growmuchbigger which suggests that lowtemperature can produce strain more easily on the bottomplate

Figure 9 shows one-day mean-temperature variationinside and outside the box-girder from May 2012 to April2013

6 Journal of Sensors

Table 1 Linear regression coefficients between temperature and strain measurements and their 1198772 values

Sensor Time 119886 1198772DS1 (on bottom plate)

Summer (2012621)

1452 06067DS2 (on top plate) 219 08750DS3 (on top plate) 3038 09121DS4 (on bottom plate) 1049 05573DS1 (on bottom plate)

Winter (2013121)

204 09078DS2 (on top plate) 1897 09304DS3 (on top plate) 2242 08277DS4 (on bottom plate) 1714 07966lowast119910 = 119886119909 where 119910means strain and 119909means temperature variation 1198772 means coefficient of determination

Accelerationsensor Strain sensor on the top plate

Strain sensor on the bottom plate

Current line

Displacement sensor

BS2 BS3

BS1

BA1

BT1

BS4

Fiber

D2

RS485 line

Figure 5 Sensors distribution of section B

Figure 9 shows the temperature variation outside andinside the box girder Generally the temperature measure-ments are consistent with the seasonal climate feature at thebridge site where the daily temperature difference is verybig both in summer and in winter Overall the ambienttemperature can drop from 30∘C (in summer) down tominus20∘C(in winter)The temperature variation not only influences theproperty of concrete but also redistributes the internal forcesand changes the boundary conditions of bridges

Figure 10 shows the strain variation from May in 2012to May in 2013 The curve decreasing means the tensilestrain and the curve increasingmeans the compressive strainIt is interesting that the seasonal strain variation presentsa negative correlation with the uniform temperature intime series which is contrary to the daily strain variationtrend with the temperature The main reason is that theseasonal temperature can generate the longitude expansionand compression along the deck especially for this kind ofcontinuous concrete bridges with the extremely long deckMeanwhile the bridge has no longitude restrictions whichmakes the longitude expansion and compression occur freelyTherefore in winter the deformation of the mid-section ofthe continuous bridge goes down which can cause the tensilestrain on the mid-section in summer the deformation ofthe mid-section goes up so the strain of the mid-section iscompressive and keeps on decreasing From Figure 9 four

strain sensors arranged on section D all present consistencywith the above theory Therefore the seasonal temperaturevariation is more effective on the strain of concrete bridges incold region

322 Temperature Gradient Induced Strain Difference Inparticular concrete box-girder bridges normally producetemperature gradient stress along the vertical cross sectionsdue to solar radiation and abrupt temperature droppingThisproperty currently is considered as one of the main reasonswhich induce the cracking and local damage for concrete box-girder bridges One-day strain measurements of section D onJune 21 are shown in Figure 11

The sampling frequency of the monitoring system is 60times per hour Δ1198781 and Δ1198782 are the strain difference betweenthe top plate and the bottom plate of the mid-span crosssection The strain of the top plate happens earlier than thebottom plate reaching the peak at around 16 pm then thestrain of bottom plate reaches the peak at about 19 pm Itdemonstrates that the solar energy needs a couple of hourstransferring along the vertical cross section from the top plateto the bottom plate When the strain rises up before reachingthe peak the strain differences Δ1198781 and Δ1198782 between topand bottom plates are positive which means the top plateis tensile relative to the bottom plate although its amplitudekeeps on decreasing after the strain reaches the peak itdrops quickly without the solar energy while the strain of thebottom plate goes down relatively slowly then the Δ1198781 andΔ1198782 difference directions turn to be negative which meansthe bottom plate is tensile It can been seen that the strain ofthe top plate declines faster than the bottom plate Thereforethe solar energy transfer lag is responsible for generatingvertical temperature gradient stress in cross sections Withdaily temperature gradient effect recycle the cross sectionspotentially can have cracks and be damaged

33 Temperature-Induced Response Separation Uniformtemperature strain response is usually considered as atrend term in original measurements A number of trendterm separation methods have been developed such asempirical mode decomposition (EMD) method low passfiltering method wavelet method least square methodand average slope method In this study EMD method wasadopted to separate the temperature trend term A more

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

6 Journal of Sensors

Table 1 Linear regression coefficients between temperature and strain measurements and their 1198772 values

Sensor Time 119886 1198772DS1 (on bottom plate)

Summer (2012621)

1452 06067DS2 (on top plate) 219 08750DS3 (on top plate) 3038 09121DS4 (on bottom plate) 1049 05573DS1 (on bottom plate)

Winter (2013121)

204 09078DS2 (on top plate) 1897 09304DS3 (on top plate) 2242 08277DS4 (on bottom plate) 1714 07966lowast119910 = 119886119909 where 119910means strain and 119909means temperature variation 1198772 means coefficient of determination

Accelerationsensor Strain sensor on the top plate

Strain sensor on the bottom plate

Current line

Displacement sensor

BS2 BS3

BS1

BA1

BT1

BS4

Fiber

D2

RS485 line

Figure 5 Sensors distribution of section B

Figure 9 shows the temperature variation outside andinside the box girder Generally the temperature measure-ments are consistent with the seasonal climate feature at thebridge site where the daily temperature difference is verybig both in summer and in winter Overall the ambienttemperature can drop from 30∘C (in summer) down tominus20∘C(in winter)The temperature variation not only influences theproperty of concrete but also redistributes the internal forcesand changes the boundary conditions of bridges

Figure 10 shows the strain variation from May in 2012to May in 2013 The curve decreasing means the tensilestrain and the curve increasingmeans the compressive strainIt is interesting that the seasonal strain variation presentsa negative correlation with the uniform temperature intime series which is contrary to the daily strain variationtrend with the temperature The main reason is that theseasonal temperature can generate the longitude expansionand compression along the deck especially for this kind ofcontinuous concrete bridges with the extremely long deckMeanwhile the bridge has no longitude restrictions whichmakes the longitude expansion and compression occur freelyTherefore in winter the deformation of the mid-section ofthe continuous bridge goes down which can cause the tensilestrain on the mid-section in summer the deformation ofthe mid-section goes up so the strain of the mid-section iscompressive and keeps on decreasing From Figure 9 four

strain sensors arranged on section D all present consistencywith the above theory Therefore the seasonal temperaturevariation is more effective on the strain of concrete bridges incold region

322 Temperature Gradient Induced Strain Difference Inparticular concrete box-girder bridges normally producetemperature gradient stress along the vertical cross sectionsdue to solar radiation and abrupt temperature droppingThisproperty currently is considered as one of the main reasonswhich induce the cracking and local damage for concrete box-girder bridges One-day strain measurements of section D onJune 21 are shown in Figure 11

The sampling frequency of the monitoring system is 60times per hour Δ1198781 and Δ1198782 are the strain difference betweenthe top plate and the bottom plate of the mid-span crosssection The strain of the top plate happens earlier than thebottom plate reaching the peak at around 16 pm then thestrain of bottom plate reaches the peak at about 19 pm Itdemonstrates that the solar energy needs a couple of hourstransferring along the vertical cross section from the top plateto the bottom plate When the strain rises up before reachingthe peak the strain differences Δ1198781 and Δ1198782 between topand bottom plates are positive which means the top plateis tensile relative to the bottom plate although its amplitudekeeps on decreasing after the strain reaches the peak itdrops quickly without the solar energy while the strain of thebottom plate goes down relatively slowly then the Δ1198781 andΔ1198782 difference directions turn to be negative which meansthe bottom plate is tensile It can been seen that the strain ofthe top plate declines faster than the bottom plate Thereforethe solar energy transfer lag is responsible for generatingvertical temperature gradient stress in cross sections Withdaily temperature gradient effect recycle the cross sectionspotentially can have cracks and be damaged

33 Temperature-Induced Response Separation Uniformtemperature strain response is usually considered as atrend term in original measurements A number of trendterm separation methods have been developed such asempirical mode decomposition (EMD) method low passfiltering method wavelet method least square methodand average slope method In this study EMD method wasadopted to separate the temperature trend term A more

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 7

Outside box girderInside box girderDS2

400 800 1200 1600 2000 000000Time (H)

minus120

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

minus20

minus10

0

10

20

30

40

Tem

pera

ture

(∘C)

(a) One-day measured strain and temperature on Jun 21 2012

Outside box girderInside box girderDS2

minus50

minus40

minus30

minus20

minus10

0

Tem

pera

ture

(∘C)

400 800 1200 1600 2000 000000Time (H)

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)

(b) One-day measured strain and temperature on Jan 21 2013

Figure 6 One-day measured strain and temperature

Linear fitting95 boundsDS1 strains

minus20

minus10

0

10

20

Stra

in (휇

휀)

20 4 6minus2minus4minus6

Temperature (∘C)

(a) Linear fitting of DS1

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(b) Linear fitting of DS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(c) Linear fitting of DS3

minus20

minus10

0

10

20

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4minus6

Temperature (∘C)

(d) Linear fitting of DS4

Figure 7 One-day strain linear regression of four sensors on section D on 21 June 2012

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Sensors

minus10

minus5

0

5

10

15St

rain

(휇휀)

Linear fitting95 boundsDS1 strains

20 4 6minus2minus4

Temperature (∘C)

(a) Linear fitting of DS1

minus10

minus5

0

5

10

Stra

in (휇

휀)

Linear fitting95 boundsDS2 strains

20 4 6minus2minus4

Temperature (∘C)

(b) Linear fitting of DS2

minus15

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS3 strains

20 4 6minus2minus4

Temperature (∘C)

(c) Linear fitting of DS3

minus10

minus5

0

5

10

15

Stra

in (휇

휀)

Linear fitting95 boundsDS4 strains

20 4 6minus2minus4

Temperature (∘C)

(d) Linear fitting of DS4

Figure 8 One-day strain linear regression of four sensors on section D on 21 January 2013

OutsideInside

minus20

0

20

40

Tem

pera

ture

(∘C)

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

Figure 9 One-year temperature variation for Fu Sui Bridge

efficient EMD method was developed rather than directlyusing EMD method to decompose the original signal Fora long-term monitoring dynamic signal a large amount ofdata was directly decomposed into intrinsic mode functions

2012

-06

2012

-07

2012

-08

2012

-09

2012

-10

2012

-11

2013

-01

2013

-02

2013

-03

2013

-04

2013

-05

2013

-06

2012

-05

Time (M)

DS1DS2

DS3DS4

minus200

minus150

minus100

minus50

0

50

Stra

in (휇

휀)

Figure 10 One-year strain variation of section D

(IMFs) that the whole iterative calculation process will takeup a lot of CPU memory and time Therefore a solutionwas to cut the whole signal into several subsections byone-day signal length Each subsection was operated for

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 9

ΔS1ΔS1

ΔS2

ΔS2

minus20

minus10

0

10

20

Stra

in (휇

휀)

400 800 1200 1600 2000 000000Time (H)

DS1DS2

DS3DS4

Figure 11 One-day monitoring strain responses of section D onJune 21 2012 lowastΔ1198781 Δ1198782 = the strain difference between the top plateand the bottom plate

downsampling obtaining a new signal to be dealt with by theEMD method After this process a residual in accordancewith the trend term was prepared for upsampling withthe cubic spline interpolation method which was aimed atrestoring the residual to original length As a result one-daytrend term was obtained Then the overall trend term canmerge sequentially all the subsection trend term signalstogether This method can greatly and effectively reduce thecalculation cost and time cost for trend term extraction oflong-term monitoring data

Original monitoring strain responses of DS3 and DS4were shown in Figure 12 with the data selected from June 14to June 23 2012 Through the separation trend term methodpreviously mentioned the signals after deleting the trendterm are shown in Figure 13 and trend terms are shown inFigure 14

34 Probability Density Function Fitting In order to calculatethe reliability index probability density distribution functionof each load effect in the limit state equation needs to beattained firstly Researches show that the concrete tensilestrength standard value and the dead load both satisfy thenormal distribution According to the equivalent normal-ization method one should estimate the distribution of thevehicle load effect and the temperature gradient load effectIf they do not satisfy the normal distribution equivalentnormalization process may be needed to make effects satisfynormal distribution

During the whole monitoring process it is assumed thatthe concrete material property satisfied Hookersquos Law namely120590 = 119864 sdot 120576 where 120590 and 120576 were the stress and measured strainand 119864 was the modulus of elasticity which was adopted as41 times 104MPa (the average value of the measured concretemodulus of elasticity on the 28th day) Thus the measuredstrain can be transformed to stress instead

341 Probability Density Function Fitting of TemperatureGradient Load Stress A probability density function fittingwas carried out with extracted temperature trend term strainFirstly a preprocessing procedure was operated on the trend

term by resetting the daily relative zero starting points at thesame moment when the temperature-induced strain in topplate and in bottom plate was varying almost consistently Inthis case 0 amwas chosen to be the starting point of the dailytrend term The purpose of resetting the zero starting pointwas to eliminate the influence of the cumulative effectThere-fore the one-day trend termwas only affected by the intradaytemperature variation According to the assumption that thecross section had the same longitudinal deformation underthe overall temperature load the relative strain between thetop plate and the bottom plate can eliminate this uniformtemperature-induced strain and the difference values can beconsidered as the temperature gradient strain

Probability density function (PDF) fitting results of thetemperature gradient stress are depicted in Figure 15 Gen-eralized extreme value (GEV) distribution is used to fit thehistogram of the relative stress of DS4-DS3 The temperaturegradient stress presents randomness and approximativelysatisfies the GEV distribution

342 Probability Density Function Fitting of Vehicle LoadStress Currently there are two basic methods to use thevehicle load stress values for calculation The first methoddirectly applies the monitoring vehicle load response forstructure reliability assessment Another method only usesextreme values of the vehicle load stress For vehicle loadstress extremum selection there are also two options (1) con-sidering the daily maximum as the monitoring extremum(2) taking all the monitoring extremums which are biggerthan the threshold In this case a threshold was set and allthe extremums bigger than the threshold were selected forthe probability density distribution function fitting Throughthe analysis of the measured vehicle load stress responses itwas found that the absolute values less than 006MPa werenoise In addition 025MPa and 030MPa were decided asthresholds for DS3 and DS4 respectively

Four kinds of the PDF distribution fitting were carriedout for the vehicle load stress responses of DS3 and DS4which were shown in Figure 16 The maximum likelihoodmethod was used to compare the fitting results of these fourdistributions From the calculation results GEV distributionfitting was better than others So in this case the vehicleload stress response was considered as satisfying the GEVdistribution

35 Failure Probability Results and Discussion The failureprobability of the monitoring position was calculated as theflow (Figure 11) The distributions of temperature gradientload stress and vehicle load stress have been given accordingto the previous fitting The vehicle load stress and thetemperature gradient load stress of the monitoring positionsare combined with the most unfavorable principle for thebridgeThe different combination selects the suitable formulato calculate the reliability index which generally has a certainrelationship with the failure probability The combinationsand their suitable formulas are shown inTable 2 In particularJC method requires that the random parameters all satisfy

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Sensors

Table 2 Calculation combination of reliability index

Combination Vehicle load stress Temperature gradient load stress Reliability index calculation formula1 DS3 lt 0 Top plate tension DS4-DS3 lt 0 Top plate tension (5)2 DS4 gt 0 Bottom plate tension DS4-DS3 gt 0 Bottom plate tension (3)3 DS4 gt 0 Bottom plate tension DS4-DS3 lt 0 Top plate tension (5) (7)

DS3

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) Strain response of DS3DS4

615 616 617 618 619 620 621 622 623614Time (D)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

Stra

in (휇

휀)(b) Strain response of DS4

Figure 12 Strain time history signals of section D

DS3

minus30

minus20

minus10

0

10

20

Stra

in (휇

휀)

615 616 617 618 619 620 621 622 623614Time (D)

(a) DS3 signal after deleting the trend termDS4

615 616 617 618 619 620 621 622 623614Time (D)

minus10

minus5

0

5

10

15

20

25

Stra

in (휇

휀)

(b) DS4 signal after deleting the trend term

Figure 13 Strain signals after deleting the trend term

DS4

DS1DS2

DS3

623621 622620619618616 617615614Time (D)

minus60

minus40

minus20

0

20

40

60

Stra

in (휇

휀)

Figure 14 Trend terms of strain responses

the normal distributionThat is the reason why the measure-ments with abnormal distributions such as vehicle load stress

and temperature gradient load stress were conducted for thetransformation through equivalent normalization

In this case the concrete tensile strength standard valuewas 265MPa with the variable coefficient of 015 It isdifficult to directly measure the dead load stress mean valuein completed bridge state Thus the finite element analysiscalculated dead load stress mean value was used instead andits variable coefficient was adopted for 00462 The vehicleload stress and temperature gradient stress were used in thefield measured data to calculate the real mean values andstandard deviations According to calculated reliability indexflow shown in Figure 11 the failure probability of monitoringpositions was calculated (Figure 17)

For the mid-span cross sections such as section D andsection E there is no value if the temperature gradientload stress presents as tensile on the bottom plate Cor-respondingly the failure probabilities of the bottom plates

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 11

DS4-3GEV PDF

0

02

04

06

08

10

12

14

Prob

abili

tyminus1 minus08 minus06 minus04minus12 minus02 0 02 0604 108 12 14

Temperature gradient stress 휎 (MPa)

Figure 15 Probability density function fitting of the temperature gradient stress of DS4-DS3

04 05 06 07 08 09 1 1103Vehicles load stress 휎 (MPa)

0

1

2

3

4

Prob

abili

ty

DS3GEV PDFLognormal PDF

Weibull PDFNormal PDF

(a) Probability density function fitting of the vehicle load stress ofDS3

0

2

4

6

8

Prob

abili

ty

03 04 05 06 07 0802Vehicles load stress 휎 (MPa)

DS4GEV PDFLognormal PDF

Weibull PDFNormal PDF

(b) Probability density function fitting of the vehicle load stress ofDS4

Figure 16 Histogram of vehicle induced stress and probability density functions

(DS1 and DS4) present much bigger on June 14 June 17and June 18 (Figure 17(a)) However the trend of failureprobabilities shows obviously individual difference day byday which is mainly caused by the temperature gradientstress alternative variation between the top plate and thebottom plate From Figure 17(b) it is obvious to find outthat the failure probability of ES2 located on the top plate ismuch bigger than that in other measured positions For crosssection E it seems that the temperature gradient inducedtensile stress plays a leading role on the top plate whichillustrates that the monitored place ES2 is greatly prone tocracking with long-term repeatedly temperature load effectOn support cross sections due to vehicle load responsesbeing very small the failure probability calculation resultsonly take account of temperature gradient load (Figure 17(c))and the failure probabilities of section C and section F arelower than 5eminus4 during the whole week which indicates thatthese cross sections are in the safe states In conclusion fromthe results of failure probability during a week the bridge isin good condition while more attention should be paid totemperature gradient induced tensile stress

4 Conclusion

Strain measurements of a prestressed concrete continuousbox-girder bridge were presented based on the long-termfield monitoring systemThese measurements were recordedjust after the bridge was open for traffic A reliability assess-ment method for PSC continuous box-girder bridges basedon SHM strain measurements was proposed The probabilitydensity function fitting of the load effect dissatisfying thenormal distribution was transformed according to equivalentnormalization method The daily failure probabilities ofmonitored positions were calculated for assessment of thisbridge

The study has led to the following conclusions(1) The measured daily strain represents the positive

correlation with the ambient temperature of outsidebox girderThe slopes of the top plate aremuch biggerthan the bottom plate which means the top plateis more sensitive than the bottom plate to the hightemperature whereas the low temperaturemore easilyproduced strain on the bottom plate

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Sensors

times10minus3

620616 617 618 619615614Time (D)

DS1DS2

DS3DS4

0

2

4

6

8Fa

ilure

pro

babi

lity

(a) Failure probability of DS1simDS4

0

0005

0010

0015

0020

0025

0030

Failu

re p

roba

bilit

y

615 616 617 618 619 620614Time (D)

ES1ES2

ES3ES4

(b) Failure probability of ES1simES4

times10minus4

0

1

2

3

4

5

Failu

re p

roba

bilit

y

614 616 617 618615 620619Time (D)

CS1-CS2CS4-CS3

FS1-FS2FS4-FS3

(c) Failure probability of sections C and F

Figure 17 Failure probability

(2) The seasonal strain variation presents a negativecorrelation with the uniform temperature

(3) The solar energy needs a few hours for transferringalong the vertical cross sections from the top plateto the bottom plate The relative tensile strain isalternating between the top plate and the bottomplateduring the daily time series It is a factor causingcracks and damage with this temperature gradient onthe cross section

(4) Generalized extreme value distribution is recom-mended for temperature gradient stress and vehicleinduced stress fitting for this box-girder bridge

(5) The failure probability calculation results of crosssections can be used to assess the local security stateFor this case the failure probabilities of each sectionare all very small One should obtain the verificationof a bridge in unsafe condition while the failureprobability continues to increase

(6) The reliability method has great potential in pre-dicting the bridge safety condition with determiningpartial factors of the limit equation

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Surre T Sun and K T Grattan ldquoFiber optic strain moni-toring for long-term evaluation of a concrete footbridge underextended test conditionssrdquo IEEE Sensors Journal vol 13 no 3pp 1036ndash1043 2013

[2] S Chakraborty and J T DeWolf ldquoDevelopment and implemen-tation of a continuous strain monitoring system on a multi-girder composite steel bridgerdquo Journal of Bridge Engineeringvol 11 no 6 pp 753ndash762 2006

[3] B J A Costa and J A Figueiras ldquoFiber optic based monitoringsystem applied to a centenary metallic arch bridge design andinstallationrdquo Engineering Structures vol 44 pp 271ndash280 2012

[4] F Matta F Bastianini N Galati P Casadei and A NannildquoDistributed strain measurement in steel bridge with fiber opticsensors validation through diagnostic load testrdquo Journal ofPerformance of Constructed Facilities vol 22 no 4 pp 264ndash2732008

[5] B H M P Wijesinghe S A Zacharie K D Mish and J DBaldwin ldquoDesign and development of in situ fatigue sensors

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 13

for structural health monitoring of highway bridgesrdquo Journal ofBridge Engineering vol 18 no 4 pp 297ndash307 2013

[6] M R Delgrego M P Culmo and J T Dewolf ldquoPerformanceevaluation through field testing of century-old railroad trussbridgerdquo Journal of Bridge Engineering vol 13 no 2 pp 132ndash1382008

[7] D M Frangopol A Strauss and S Kim ldquoBridge reliabilityassessment based onmonitoringrdquo Journal of Bridge Engineeringvol 13 no 3 pp 258ndash270 2008

[8] Y Q Ni HW Xia K YWong and J M Ko ldquoIn-service condi-tion assessment of bridge deck using long-termmonitoring dataof strain responserdquo Journal of Bridge Engineering vol 17 no 6pp 876ndash885 2012

[9] D S Li Z Zhou and J P Ou ldquoDynamic behavior monitoringand damage evaluation for arch bridge suspender using GFRPoptical fiber bragg grating sensorsrdquoOptics and Laser Technologyvol 44 no 4 pp 1031ndash1038 2012

[10] B J A Costa and J A Figueiras ldquoEvaluation of a strainmonitoring system for existing steel railway bridgesrdquo Journal ofConstructional Steel Research vol 72 pp 179ndash191 2012

[11] S R Debbarma and S Saha ldquoBehavior of pre-stressed concretebridge girders due to time dependent and temperature effectsrdquoin Proceedings of the First Middle East conference on monitoringAssessment and Rehabilitation of Civil Structures Dubai UAE2011

[12] L E Rodriguez P J Barr and M W Halling ldquoTemperatureeffects on a box-girder integral-abutment bridgerdquo Journal ofPerformance of Constructed Facilities vol 28 no 3 pp 583ndash5912014

[13] Y Q Ni X G Hua and J M Ko ldquoReliability-based assessmentof bridges using long-term monitoring datardquo Advanced Nonde-structive Evaluation I vol 321-323 pp 217ndash222 2006

[14] M Liu D M Frangopol and S Kim ldquoBridge safety evaluationbased onmonitored live load effectsrdquo Journal of Bridge Engineer-ing vol 14 no 4 pp 257ndash269 2009

[15] M Liu D M Frangopol and S Kim ldquoBridge system perfor-mance assessment from structural health monitoring a casestudyrdquo Journal of Structural Engineering vol 135 no 6 pp 733ndash742 2009

[16] S Li S Zhu Y-L Xu Z-W Chen and H Li ldquoLong-termcondition assessment of suspenders under traffic loads basedon structural monitoring system application to the Tsing Mabridgerdquo Structural Control and Health Monitoring vol 19 no 1pp 82ndash101 2012

[17] H W Xia Y Q Ni K Y Wong and J M Ko ldquoReliability-based condition assessment of in-service bridges using mixturedistribution modelsrdquo Computers amp Structures vol 106-107 no5 pp 204ndash213 2012

[18] Y LiuNW Lu andQ YWang ldquoReliability assessment of long-span cable-stayed bridges based onhybrid algorithmrdquo Journal ofHighway amp Transportation Research amp Development vol 31 no7 pp 72ndash79 2014

[19] X Wang Y-Q Ni and K-C Lin ldquoComparison of statisticalcounting methods in SHM-based reliability assessment ofbridgesrdquo Journal of Civil Structural HealthMonitoring vol 5 no3 pp 275ndash286 2015

[20] C Chen R K Mosbeh Z Wang Q Gao and J ZhongldquoDesign of a long-termmonitoring system for a PSC continuousBoxgirder bridgerdquo Key Engineering Materials vol 619 pp 1ndash92014

[21] C Chen M R Kaloop Q Gao and Z Wang ldquoEnvironmentaleffects and output-only model identification of continuousbridge responserdquo KSCE Journal of Civil Engineering vol 19 no7 pp 2198ndash2207 2014

[22] P J Barr J F Stanton and M O Eberhard ldquoEffects oftemperature variations on precast prestressed concrete bridgegirdersrdquo Journal of Bridge Engineering vol 10 no 2 pp 186ndash1942005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of