research article long-term structural health monitoring...

Research ArticleLong-Term Structural Health Monitoring System fora High-Speed Railway Bridge Structure

You-Liang Ding1 Gao-Xin Wang1 Peng Sun2 Lai-Yi Wu3 and Qing Yue3

1Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education Southeast UniversityNanjing 210096 China2Department of Civil and Environmental Engineering Rice University Houston TX 77005 USA3China Railway Major Bridge (Nanjing) Bridge and Tunnel Inspect amp Retrofit Co Ltd Nanjing 210032 China

Correspondence should be addressed to You-Liang Ding civilchinahotmailcom

Received 27 February 2015 Revised 30 July 2015 Accepted 24 August 2015

Academic Editor Ahmed El-Shafie

Copyright copy 2015 You-Liang Ding et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Nanjing Dashengguan Bridge which serves as the shared corridor crossing Yangtze River for both Beijing-Shanghai high-speedrailway and Shanghai-Wuhan-Chengdu railway is the first 6-track high-speed railway bridge with the longest span throughoutthe world In order to ensure safety and detect the performance deterioration during the long-time service of the bridge aStructural Health Monitoring (SHM) system has been implemented on this bridge by the application of modern techniques insensing testing computing and network communication The SHM system includes various sensors as well as correspondingdata acquisition and transmission equipment for automatic data collection Furthermore an evaluation system of structural safetyhas been developed for the real-time condition assessment of this bridge The mathematical correlation models describing theoverall structural behavior of the bridge can be obtained with the support of the health monitoring system which includes cross-correlation models for accelerations correlation models between temperature and static strains of steel truss arch and correlationmodels between temperature and longitudinal displacements of piers Some evaluation results using the mean value control chartbased onmathematical correlationmodels are presented in this paper to show the effectiveness of this SHM system in detecting thebridgersquos abnormal behaviors under the varying environmental conditions such as high-speed trains and environmental temperature

1 Introduction

The environmental actions (wind temperature rain earth-quake etc) and the bridge usage (traffic loading) can con-tinually modify the behavior and cause deterioration of long-span bridges in their long-term lifespan Over the past severaldecades a significant research effort has focused on the devel-opment of long-term Structural Health Monitoring (SHM)systems [1 2] Generally the objective of the SHM systemis to gather various reliable information that can be used todetect and follow the evolution of the bridgersquos condition statelocate and quantify damage and perform reliability-basedassessment so as to give the engineer or administrant a greatvariety of options with respect to maintenance interventionIn China governments as well as scientists and engineerspay much attention to the long-term health monitoring oflong-span highway bridges Typical SHM implementations

in highway bridges include Tsing Ma Bridge [3] Kap ShuiMun Bridge [3] Ting Kau Bridge [3] Stonecutters Bridge[3] Sutong Bridge [4] and Runyang Bridge [5] The modularconcept used in the design of the SHM systems for Tsing MaBridge Kap Shui Mun Bridge and Ting Kau Bridge has asignificant influence on the design of new SHM systems inHong Kong and China The six integrated modules are thesensory system the data acquisition and transmission systemthe data processing and control system the structural healthevaluation system the structural health data managementsystem and the inspection and maintenance system A SHMsystem for long-span bridges should be able to monitor theloading and structural parameters set by the bridge designerso that the bridge performance under current and futureloading conditions can be evaluated

With the recent development of design theories and con-struction techniques for high-speed railway in China many

Hindawi Publishing Corporatione Scientific World JournalVolume 2015 Article ID 250562 17 pageshttpdxdoiorg1011552015250562

2 The Scientific World Journal

(a) View of the Nanjing Dashengguan Bridge

192336

1stcross-section

1st cross-section 2nd cross-section

336

2ndcross-section

Beijing

1272

Shanghai

108 192 108

(b) Elevation drawing of the bridge (unit m)

Middle truss arch

Side truss arch

Orthotropic steel deck

Downstream15000

Side truss arch

Upstream15000

(c) Design drawing of the deck cross-section (unit mm)

Figure 1 Nanjing Dashengguan Bridge

high-speed railway bridges have been built during the lastfew years Maintaining the safety of these high-speed railwaybridges is crucial to the safety of passengers and trainsTherefore research efforts should be focused on the SHMsystems of high-speed railway bridges This paper reportsthe development and implementation of a SHM system ofNanjing Dashengguan Bridge Nanjing Dashengguan Bridgewhich serves as the shared corridor crossing Yangtze Riverfor both Beijing-Shanghai high-speed railway and Shanghai-Wuhan-Chengdu railway is the first 6-track high-speedrailway bridge with the longest span throughout the worldIt is the largest bridge with the heaviest design loading of allthe high-speed railway bridges by far because its main spanis 336m and its railway contains 6 tracks Also the designspeed of 300 kmh of the bridge is on the advanced level in theworld Due to these remarkable characteristics including longspan of themain girder heavy design loading and high speedof trains it is necessary to monitor the real-time health statusof the bridge during its service period With the state-of-the-art techniques of current monitoring systems of highwaybridges the health monitoring system for this bridge wasdesigned to be concise practical reliable and cost efficientThe main purpose of this system is to monitor the bridgersquosbehaviors under the varying environmental conditions and

detect the bridgersquos abnormal behaviors which may threatenthe structural safety This paper introduces the deploymentand functions of this system including a sensor system adata acquisition and transmission system a datamanagementsystem and a structural evaluation system Some evaluationresults of the bridge subjected to varying environmentalconditions such as high-speed trains and environmentaltemperature are also presented

2 Structural Health Monitoring System

Nanjing Dashengguan Bridge shown in Figure 1(a) is a steeltruss arched bridge with the span arrangement (108 + 192 +2 times 336 + 192 + 108)m which supports a six-line railwayincluding two regular rails two high-speed railways andtwo subway lines The elevation drawing of the bridge andthe deck cross-section are shown in Figures 1(b) and 1(c)respectively The three truss planes in the longitudinal direc-tion were used with a spacing of 15m which was selected toprovide the large stiffness for such heavy live loadsThe use ofa steel box as the deck system is another feature in the designof this steel truss arc which is adopted as the bottom chord ofthe entire truss segment to reduce uneven deflection on thedeck The bearing system of the bridge is that the 7 pier is

The Scientific World Journal 3

Table 1 Sensitivity analysis of bridge parameters for SHM design

Structure Key position Critical member Parameter ImportanceVariation undertemperature

actionSensitivity Decision

Pier Side spans 4 and 10 piers Longitudinaldisplacement Critical 229mm Sensitive Monitor

Main girder In the middle ofthe main span Steel deck Vertical

displacementLess-

important 35mm Less-sensitive No

Truss arch In the middle ofthe main span

Top chordmember diagonalweb member archrib chord memberand bottom chord

member

Static strain Critical 280 120583120576 Sensitive Monitor


Top chord memberand bottom chord

memberTemperature Critical 60∘C Sensitive Monitor

Main girder In the middle ofthe main span Steel deck Temperature Less-

important 60∘C Less-sensitive No

Whole bridge Frequency Important Nonsensitive Monitor one

Truss arch In the middle ofthe main span Top chord member Wind Less-

important Less-sensitive No

linked to the bridge deck so that the bridge deck is restrictedfrom moving in the longitudinal direction at the 7 pierAnd there have no longitudinal restraints between the bridgedeck and other piers Due to the remarkable characteristics ofNanjingDashengguanBridge including long span of themaingirder heavy design loading and high speed of trains a long-term SHM system was designed and installed on the NanjingDashengguan Bridge shortly after it was opened to railwaytraffic This online SHM system was designed to be a concisemonitoring system with a minimum of 28 sensors to monitorthe key parametersThe entire system consists of a sensor sys-tem a data acquisition system a data transmission system adatamanagement system and a structural evaluation systemThe primary purpose of the system is to monitor in-serviceperformance of the bridge structure under the varying envi-ronmental conditions such as high-speed trains and environ-mental temperature and to provide early warning of abnor-mal changes in in-service performance of the bridge thatmight be unsafe to bridge structureThe procedure of design-ing and implementing the SHM system includes three majorstages as follows (1) the stage of planning and design includesthe consideration of the physical quantities to be measuredthe selection of sensors appropriate for measuring such phys-ical parameters and the optimal placement of the sensors (2)The stage of installation and calibration includes a series ofstatic and dynamic experiments performed to check the oper-ation of the monitoring system after the completion of thebridge (3)The stage of main operation includes the test oper-ation of the monitoring system training of the maintenancecrew and the replacement ofmalfunctioning sensing devices

The design objective of the SHM system is to monitor thestructural health under daily service condition With regardto the bridge site of Nanjing Dashengguan Bridge there arevery lowprobability events of Typhoon and earthquakeThus

the train loading and temperature action are the most impor-tant factors that affect the daily performance of the bridgeDue to the design requirements the structural responses ofthe bridge under train loading are small and conservativeHowever the axial movements and thermal stresses of thebridge under temperature action are considerable due to thelong span of the bridge For instance the maximum thermalstrain and train-induced strain in the steel truss arch areabout 250 120583120576 and 50 120583120576 respectively For bridge conditionassessment it is of paramount importance to characterize nor-mal variability of structural parameters due to temperatureeffectsTherefore in order to control the overall budget of theSHM system without losing major information on structuraldaily behavior the structural parameters to be monitoredin the Nanjing Dashengguan Bridge were determined usingthe structural sensitivity analysis with the finite elementmodel under the designed temperature action as shown inTable 1 Other important parameters including accelerationsof steel deck and fatigue of steel deck were also monitoredConsidering that the displacement amplitudes of steel deckunder the train loading can be derived from the accelerationof steel deck the vertical displacements of steel deck were notchosen to monitor

21 Temperature and Static Strain Monitoring of Truss ArchAs shown in Figure 1(b) temperature and static strain mon-itoring of truss arch is performed at the 1st cross-section inthe middle of the first main span of the bridge Eight FBGtemperature and strain gauges are both installed on the 1stcross-section to simultaneously measure temperature fielddata and static strain field data in the steel truss arch as shownin Figure 2 It can be seen from Figures 2(c)sim2(f) that thesensors were installed at the top chordmember diagonal webmember arch rib chord member and bottom chord member


Downstream Upstream

Horizontal bracing of top chord member

Vertical bracing

Vertical web memberof side truss

Vertical web memberof middle truss

Top plate

Transverse stiffening girder

Horizontal bracing ofarch rib chord member


W1

W2

W3

W4

W5

W6

W7 W8

Y1

Y2

Y3Y4

Y5

Y6

Y7 Y8

15000 15000

68007

12000

2

2

(a) 1st cross-section of steel truss arch

Shanghai

Top chord member

Arch rib chord member

Vertical web member

Beijing

Diagonal web member

Bottom chord member

W1

W2

W3

W4

W5

W6

W7

W8

Y1Y2

Y3Y4

Y5

Y6

Y7

Y8

3

3

4

4

5

5

6

6

(b) 2-2 section of steel truss arch

Downstream Upstream

W1 W2Y1 Y2

1000

1000

850 850

150

150

1400

(c) 3-3 section of top chord member

Downstream Upstream

W3W4Y3Y4

150

150

610

610

1398

(d) 4-4 section of diagonal web member

Downstream Upstream

W5

W6Y5

Y6

150

150

1400

650 650

800

(e) 5-5 section of arch rib chord member

Downstream Upstream

W7 W8Y7 Y8

150

150

1266

1266

1400

1416

(f) 6-6 section of bottom chord member

Figure 2 Layout of temperature and static strain gauges on the steel truss arch (unit mm)


DYB-1 DYB-2

2500mm2500mm

Figure 3 Layout of dynamic strain gauges on the steel deck

Vertical accelerometer Z2Z4Transverse accelerometer Z1Z3

Figure 4 Layout of accelerometers on the steel deck

of the truss arch (where 119882119894denotes 119894th temperature sensor

119894 = 1 2 8 119884119894denotes 119894th strain sensor 119894 = 1 2 8)

The specification of FBG temperature sensors and straingauges is FBG4700 and FBG4100 supplied by China GeokonInstrumentsCo Ltd Sampling frequency of temperature andstatic strain data collection is set to 1Hz

22 Dynamic StrainMonitoring of Steel Deck Dynamic straingauges are installed at the 1st cross-section in the middleof the first main span of the bridge so as to monitor thefatigue performance of orthotropic steel deck as shown inFigure 3 It can be seen that the dynamic strain gauges DYB-1and DYB-2 monitor the long-term fatigue effects of deck-ribwelded detail induced by the traveling high-speed trainsThespecification of dynamic strain gauges is FBG4100 suppliedby China Geokon Instruments Co Ltd Sampling frequencyof dynamic strain data collections is set to 50Hz

23 Acceleration Monitoring of Steel Deck In order to moni-tor the transverse and vertical acceleration responses on thetwo main spans induced by the traveling high-speed trainsone transverse accelerometer and one vertical accelerometerwere installed at the 1st cross-section and 2nd cross-sectionin the middle of two main spans respectively as shown inFigure 4 (where 119885

119894denotes 119894th accelerometer 119894 = 1 2 4)

The specification of accelerometers is DH610 supplied byDonghua Testing Technology Co Ltd Sampling frequencyof acceleration data collections is set to 200Hz

24 Longitudinal Displacement Monitoring of Piers In thedesign of Nanjing Dashengguan Bridge the 7 pier is linkedto the bridge deck so that the bridge deck is restricted frommoving in the longitudinal direction at the 7 pier And therehave no longitudinal restraints between the bridge deck andother piersTherefore 6 displacement transducers are locatedon the piers and used for the measurement of longitudinaldisplacements at the 4 pier 5 pier 6 pier 8 pier 9pier and 10 pier as shown in Figure 5 (where 119871

119894denotes 119894th

displacement transducer 119894 = 1 2 6) The specificationof displacement transducers is CLMD2 supplied by ASMrsquosin Germany Finally it should be noted that the DAQs of theSHM system are located in the 6 and 8 piers

3 Evaluation of Structural Condition UsingLong-Term Monitoring Data

Using long-term monitoring data collected from the SHMsystem of Nanjing Dashengguan Bridge structural conditionassessment involves four aspects evaluation of vibration per-formance of themain girder evaluation of static performanceof steel truss arch evaluation of movement performance ofpier and evaluation of fatigue performance of steel deck

31 Evaluation of Vibration Performance of the Main GirderThe main function for the SHM system is to detect theperformance degradation of structures as early as possibleand to provide essential references for maintenance of actualbridges For Nanjing Dashengguan Bridge the vibration andstrain of the main girder together with the longitudinaldisplacement of piers are three important items to moni-tor Three kinds of performance evaluation are conductedaccordingly Those are evaluation of vibration performanceof the main girder evaluation of static performance of steeltruss arch and evaluation of movement performance of pierFirstly degradation or damage of local members may occurwith the increase of service period which will reduce thestructural stiffness of bridge Thus the dynamic propertyof bridge structure is affected significantly by the structuralstiffness reduction and will cause unusual variations ofthe structural vibration Such unusual behavior will affectrunning safety of the train directly Secondly damage of localmembers may induce redistribution of the internal forces inthe whole bridge under the temperature action The reasonis that Nanjing Dashengguan Bridge belongs to staticallyindeterminate structure Therefore static strain monitoringis necessary for typical members under temperature actions


Beijing Shanghai

4 pier 5 pier 6 pier 7 pier 8 pier 9 pier 10 pier

L1 L2 L3 L4 L5 L6

Figure 5 Layout of displacement transducers on the pier

Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40

(a) Accelerometer 1198851

Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40

(b) Accelerometer 1198853

Figure 6 Transverse acceleration time histories of the main girder induced by a high-speed train

Thirdly the longitudinal displacement behavior of the bridgepier is crucial for running safety of the train under thetemperature action Once the abnormal variation of the itemis detected inspection may be evolved timely for detection ofthe bridge piers In this section the evaluation of vibrationperformance of main girder is firstly discussed

For high-speed railway bridges vibration performanceof the main girder subjected to the high-speed trains isimportant for passenger comfort and traffic safety [6 7]For instance Zeng et al [8] point out that the essentialreason of train derailment is that the transverse vibrationof the train-railway-bridge system becomes unstable Henceit is necessary to present a strategy for early warning ofdeterioration of vibration performance of the main girderusing long-term health monitoring data

Figures 6 and 7 illustrate the typical transverse and ver-tical acceleration time histories of the main girder measuredfrom accelerometers Z

1simZ4 respectively It can be observed

that when high-speed train passed the bridge the transverseaccelerations in the middle of the first span are much smallerthan that of the second span and the vertical accelerationsin the middle of the first span are much larger than that ofthe second span These indicate that although the structurallayouts of two main spans of the main girder are the samethere exists significant difference between the transverseand vertical vibration characteristics of two main spans due

to the rail irregularity in transverse and vertical directionsThus there is a need to monitor the transverse and verticalaccelerations of two main spans in the long term so as torealize anomaly alarms for vibration performance of themaingirder

Hence in the present study the RMS values of theaccelerations are utilized as the monitoring parameters torepresent the transverse and vertical vibration characteristicof the main girder The cross-correlation between the RMSvalues of the accelerations in the middle of two main spans isfurther investigated when the high-speed trains pass throughthe bridge Figure 8 shows the scatter plots between the RMSvalues of the accelerations and shows the fitted results byusing quadratic polynomial as well

By using the fitting formula constructed in Figure 8scatter plot between theRMSvalues of the accelerations in themiddle of the second span and the corresponding fitted valuesis drawn in Figure 9 where the fitted values were obtainedby taking the RMS values of the accelerations in the middleof the first span into the fitting formula of the quadraticpolynomialThe correlation coefficient of the measured RMSvalues and fitted values on February 1st 2013 is 09391 and0918 for transverse and vertical accelerations respectively asshown in Figure 9 Computed using the same method all thedaily correlation coefficients in 2013 are more than 090 fortransverse and vertical accelerations as shown in Figure 10

The Scientific World Journal 7Ac

cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60


Figure 7 Vertical acceleration time histories of the main girder caused by a high-speed train

y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45

RMS values of the 1st span (mms2)

0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)

(a) Transverse accelerations

y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)

(b) Vertical accelerations

Figure 8 Cross-correlations between RMS values of accelerations measured in the middle of two main spans

Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545

Measured RMS values (mms2)


R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610



Figure 9 Fitting effect of cross-correlation between RMS values of accelerations by using quadratic polynomial


0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t


Figure 10 Daily computed correlation coefficients in 2013

UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample

Figure 11 Mean value control chart for accelerations in the middle of the second span

The analysis results indicate that good cross-correlationexists between the RMS values of the transverse and verticalaccelerations on the two main spans Multivariable controlchart is used here to monitor the measured changes in thetransverse and vertical accelerations caused by deteriorationof the vibration performance Firstly the condition index 119890

for early warning of abnormal vibration behavior is definedas the difference between the measured and predicted RMSvalues of the accelerations in the middle of the second span

119890 = RMS119898minus RMS

119901 (1)

where RMS119898is themeasured RMS values of the accelerations

in the middle of the second span RMS119901is the predicted

RMS values of the accelerations in the middle of the secondspan which is obtained by taking the RMS values of theaccelerations in the middle of the first span into the fittingformula of the quadratic polynomial in the healthy conditionThen a mean value control chart is employed to monitorthe time series of 119890 with regard to both transverse andvertical accelerations The time series of 119890 taken when thestructural vibration is in good condition will have somedistribution with mean 120583 and variance 120590

2 If the mean andstandard deviation are known a control chart is constructedby drawing a horizontal line CL at 120583 and twomore horizontallines representing the upper and lower control limits Theupper limit UCL is drawn at 120583 + 119896120590 and the lower limit LCL

at 120583 minus 119896120590 For online monitoring the controlling parameter119896 is chosen so that when the structural vibration is in goodcondition all observation samples fall between the controllimits When the new measurement is made the structuralabnormal vibration condition can be detected if an unusualnumber of samples fall beyond the control limits Figure 11shows the mean value control chart using the measuredand predicted RMS values of the accelerations shown inFigure 9 The upper and lower limits are determined usingthe controlling parameter 119896 = 2612 Hence a long-termmonitoring on the cross-correlation model of RMS values ofthe transverse and vertical accelerations can realize the earlywarning of deterioration of the vibration performance

32 Evaluation of Static Performance of Steel Truss Arch

321 Data of Temperature Field and Static Strains Tem-perature data from temperature sensor 119882

119894is denoted by

119879119894 temperature difference data acquired by 119879

119894minus 119879

119895is

denoted by119879119894119895(119879119894119895= 119879119894minus119879119895) and static strain data from strain

sensor119884119894is denoted by 119878

119894(119894 119895 = 1 2 8) As for illustration

the time-history curves of annual change and daily change intemperature 119879

1and temperature difference 119879

12are shown in

Figures 12 and 13 respectively And the time-history curvesof annual change and daily change in static strain data 119878

1

are shown in Figure 14 (negative values denote compressive


4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)

(a) Annual curve fromMarch 2013 to October 2013

4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)

(b) Daily curve (March 4th 2013)

Figure 12 Time-history curves of temperature data 1198791

4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)


Figure 13 Time-history curves of temperature difference data 11987912

4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)


Figure 14 Time-history curves of static strain data 1198781


4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100

(a) Daily extraction result 119878III of 1198781

4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150

(b) Annual extraction result 119878III of 1198781 fromMarch 2013 to October 2013

Figure 15 Extraction results 119878III of static strain data 1198781

static strain and positive values denote tension static strain)From Figure 14 it can be seen that time-history curve of 119878

1

contains many sharp peaks caused by high-speed trains witheach peak corresponding to the time when one train passesthrough the bridge And the static strains caused by high-speed trains are obviously lower than that of temperature fieldincluding temperature data and temperature difference data

As shown in Figure 14 static strain data in steel truss archmainly contains three parts static strain 119878I caused by tem-perature static strain 119878II caused by temperature differenceand static strain 119878III caused by train In order to construct thecorrelation between temperature field and static strain in steeltruss arch static strain 119878I and static strain 119878II (denoted by 119878III)must be extracted from the static strain data In the presentstudy wavelet packet decomposition method is used toextract 119878III considering the high-frequency characteristics ofstatic strain data caused by trains By using the wavelet packetdecomposition static strain data can be decomposed scale byscale into different frequency bands and each decompositioncoefficient corresponds to its frequency band [9 10] Eachdecomposition coefficient can be reconstructed into time-domain signals with constraints of its own frequency bandTaking the daily time-history curve of static strain data1198781shown in Figure 14(b) as an example it is decomposed

within 8 scales and the decomposition coefficient 11986208

119895

isspecially selected and then reconstructed as 119878III shown inFigure 15(a) It can be seen that sharp peaks caused by trainsare removed effectively and the static strains which are causedby temperature field are retained as well Furthermore theannual extraction result 119878III of 1198781 fromMarch 2013 toOctober2013 is shown in Figure 15(b)

322 Correlation Model between Temperature Field andStatic Strains In constructing the correlationmodel betweentemperature field and static strains data from March 2013to October 2013 are chosen as training data and data inNovember 2013 are chosen as test data for verification of

the correlation model The static strain 119878III is expressed asfollows

119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)

where 119879119894is 119894th temperature data from set 119879

1 1198792 1198793 1198794

1198795 1198796 1198797 1198798 119863119895is 119895th temperature difference data from set

11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946

11987948 11987968 120572119894is 119894th linear expansion coefficient of 119879

119894 120573119895is 119895th

linear expansion coefficient of 119879119894119895 and 119888 is the constant term

Considering that total 24 linear expansion coefficientsand one constant term in (2) are very complicated forcalculation principal component analysis is further usedto simplify (2) which aims at finding small amounts ofcomprehensive factors to represent main information of tem-perature and temperature difference data By using principalcomponent analysis the comprehensive factors can be foundby transforming temperature and temperature difference datainto factor component space [11 12] For temperature data theexplained variance of the first potential comprehensive factor1198751reaches 967 apparently larger than the other potential

comprehensive factors Thus 1198751is selected as the compre-

hensive factor Meanwhile for temperature difference datausing principal component analysis the explained varianceof the first three potential comprehensive factors 119877

1 1198772 and

1198773reaches 988 which are selected as the comprehensive

factorsTherefore the correlation models between 119878III and tem-

perature field can be expressed as follows

119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1

denotes one vector containing eight temperaturedata 997888119863

16times1denotes one vector containing sixteen temper-

ature difference data 119863119895(119895 = 1 2 16) [119864]

1times8and


b = minus3632

k = 0946

minus100 minus55 minus10 8035Monitoring SIII (120583120576)

Scattered pointsFitting curve

minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898

minus45minus75 minus15 45 7515Monitoring SIII (120583120576)


minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)

minus30minus60 30 60 900Monitoring SIII (120583120576)


(c) 1198783

b = 2057k = 1126

minus15minus30 15 300Monitoring SIII (120583120576)


minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)

minus105 4515 75minus45minus75 minus15

Monitoring SIII (120583120576)


(e) 1198785

b = minus4094k = 0918

minus145minus205 minus25minus85 9535Monitoring SIII (120583120576)

minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)

minus45 minus23 minus1 43 6521Monitoring SIII (120583120576)


(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788

Figure 16 Correlation between simulative 119878III and monitoring 119878III

Table 2 Performance parameters 1205821

1205741

1205742

1205743

and 119862 in correlationmodels

Static straindata 120582

1

1205741

1205742

1205743

119862

119878III of 1198781 0454 minus4711 minus2597 minus4944 minus46806119878III of 1198782 1585 0013 4104 minus1247 minus70238119878III of 1198783 0301 3416 minus2098 2968 minus6884119878III of 1198784 0350 minus0734 0351 0948 minus23597119878III of 1198785 0179 minus4219 1827 3165 minus22049119878III of 1198786 0062 minus3245 8242 minus5398 minus22862119878III of 1198787 minus0367 2411 minus0598 5531 17075119878III of 1198788 0611 2188 minus1130 2018 minus32799

[119865]3times16

denote transformation matrix which can be cal-culated using principal component analysis [11 12] 120582

1is

performance parameter of first potential comprehensivefactor 119875

1 9978881205741times3

= [1205741 1205742 1205743] is one vector containing

three performance parameters corresponding to first threepotential comprehensive factors 119877

1 1198772 and 119877

3 The values of

performance parameters 1205821 9978881205741times3

and 119888 are estimated usingtraining data by multivariate linear regression method [13]and are shown in Table 2

In order to verify the effectiveness of the correlationmodels shown in (2) test data in November 2013 are usedto obtain the simulative 119878III The scattered points betweensimulative 119878III and monitoring 119878III are plotted as shown inFigure 16 which are further fitted by linear function

119878119904= 119896119878119898+ 119887 (4)

where 119878119904denotes simulative 119878III 119878119898 denotes monitoring

119878III and 119896 119887 are fitting parameters with the fitting resultsshown in Figure 16 as well The fitting results verify theeffectiveness of the correlationmodels Amultivariable mean

value control chart is also employed tomonitor the measuredabnormal changes in the static strains of the steel truss archThe condition index 119890 for early warning of deterioration ofthe static performance of steel truss arch is defined as thedifference between the measured and predicted static strains

119890 = 119878119898minus 119878119901 (5)

where 119878119898is the measured static strain 119878III 119878119901 is the predicted

static strain 119878III which is obtained by using the correlationmodels shown in (2) in the healthy condition Figure 17 showsthemean value control chart for static strains of the steel trussarch using measurement data in November 2013 The upperand lower limits are determined using the controlling param-eter 119896 = 2235 Hence a long-term monitoring on the corre-lation models between temperature field and static strains issuitable for early warning of deterioration of the static per-formance of steel truss arch

33 Evaluation of Movement Performance of Pier Longi-tudinal displacements of piers and temperature field datain steel truss arch collected from March 2013 to October2013 are used for evaluation of movement performanceof piers Longitudinal displacement data from sensors 119871

119894

(119894 = 1 2 6) are denoted by 119889119894(119905) (where 119905 means time)

respectively Meanwhile temperature field data from sensors119882119894(119894 = 1 2 8) are denoted by 119879

119894(119905) respectively and

their averaged value 119879(119905) is used to represent the averagetemperature of the steel truss arch For simplicity taking10 minutes as basic time interval the 10 min average dis-placements and temperatures are calculated and used as therepresentative values of this time interval By this way thedisplacements and temperatures in one day are reduced to144 representative samples Furthermore the temperature-displacement scatter diagrams are plotted in Figure 18 Anoverall increase in longitudinal displacements of piers isobserved with an increase in the average temperature of the


UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample

Figure 17 Mean value control chart for static strains of the steel truss arch

Table 3 Summary of linear regression models

Pier Regression function4 pier 119889

1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879

bridge And the correlation coefficients of the longitudinaldisplacements of piers and average temperature of the steeltruss arch are all larger than 092 as shown in Figure 18

A linear regression analysis between the 10 min averagedisplacement 119889

119894(119905) and the temperature 119879(119905) is further per-

formed to model the temperature-displacement correlationsusing the following equation [14]

119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)

where the regression coefficients 1205731and 120573

0were obtained by

the least-squares method as

1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879

is the covariance between the displacement andthe temperature sequences 119878

119879119879is the variance of the mea-

sured temperature sequences and 119879 and 119889119894are the means

of the measured temperature and displacement sequencesrespectively Table 3 summarizes the expressions of linearregression models of the displacement versus temperature

The analysis results indicate that good correlation existsbetween the longitudinal displacements of piers and averagetemperature of steel truss arch A multivariable mean valuecontrol chart is also employed to monitor the measuredabnormal changes in the longitudinal displacements of piersThe condition index 119890 for early warning of abnormal behaviorof piers is defined as the difference between themeasured andpredicted longitudinal displacements

119890 = 119889119898minus 119889119901 (8)

where 119889119898is the measured displacement of the piers 119889

119901is

the predicted displacement of the piers which is obtainedby using the linear regression models shown in Table 3in the healthy condition Figure 19 shows the mean valuecontrol chart for longitudinal displacements of piers usingmeasurement data in March 2013 The upper and lowerlimits are determined using the controlling parameter 119896 =

2804 Hence a long-term monitoring on the temperature-displacement correlation model is suitable for real-timecondition assessment for movement performance of piers

34 Evaluation of Fatigue Performance of Steel Deck Fatiguecracking is universal for orthotropic steel deck of highwaybridges Once the fatigue crack appears extensive fatiguecracking may occur and repair is very difficult Henceinfinite-fatigue-life design method is applied for NanjingDashengguan Bridge instead of finite-fatigue-life designmethod which is applied extensively in highway bridges Theinfinite-fatigue-life design method is to control the fatiguestress amplitude in the range less than the value of fatiguecut-off limit refrained from fatigue cracking Consequentlythe purpose of equipping stain gauges in the SHM system ofDashengguan Bridge is to monitor the stress amplitude andthe validity of fatigue design can be achieved by comparingthe stress amplitude with fatigue stress limit

The structural dynamic response is asymmetrical becauseof the irregularity of railway and braking force from thetrain even though the structure of Nanjing DashengguanBridge is spatially symmetrical Hence the stresses are notsymmetrical measured by strain gauges from the upstreamand downstream directions However the fatigue amplitudesof two strain gauges induced by trains are both extremelysmall Thus the strain history data of the strain gauge DYB-2are merely selected in this paper to illustrate that the fatiguestress amplitude is much lower than the value of fatigue stresslimit The typical strain time-history curves of DYB-2 whensingle train with 8 carriages or 16 carriages passed throughthe bridge are shown in Figure 20 respectively It can be seenthat during the passing of high-speed trains both 8 carriagesand 16 carriages have led to strain variations reaching to 2ndash8 120583120576 And the number of strain peaks is 16 and 32 for trainswith 8 carriages and 16 carriages respectively because theaxle number of each carriage is 2

To perform fatigue evaluation simplified rainflow cyclecounting algorithm was firstly used to process strain history


R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a) Correlation between 1198891of the 4 pier and average temperature 119879 of

steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746

(b) Correlation between 1198892of the 5 pier and average temperature 119879 of

steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471

(c) Correlation between 1198893of the 6 pier and average temperature 119879 of

steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)

(d) Correlation between 1198894of the 8 pier and average temperature 119879 of

steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)

(e) Correlation between 1198895of the 9 pier and average temperature 119879 of

steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)

(f) Correlation between 1198896of the 10 pier and average temperature 119879 of

steel truss arch

Figure 18 Correlation between longitudinal displacement and average temperature


UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15

Figure 19 Mean value control chart for longitudinal displacements of piers

Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point

(a) Single train with 8 carriages passed through the bridge

Stra

in (120583

120576)

minus180minus178minus176minus174minus172minus170minus168minus166

1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point

(b) Single train with 16 carriages passed through the bridge

Figure 20 Typical strain time-history curves of DYB-2 when single train passed through the bridge

data and the spectrum of stress amplitude was obtained[15] The spectra of stress amplitude calculated using thestrain history data with regard to 8 carriages or 16 carriagesare shown in Figure 21 respectively It can be seen that themaximum stress amplitude is smaller than 10MPa obtainedfrom strain history curves under single trainThen accordingtoMinerrsquos law and standard of Eurocode 3 fatigue parametersof 119878eq (equivalent stress amplitude) and 119873

119904(stress cycle

number) under single train were calculated as follows [16]

119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)

where 119878119894is 119894th stress amplitude 119899

119894is the number of

stress cycles corresponding to 119878119894 and 15 is slope value of

log 119878- log119873 curve in the scope of lower stress amplitudeaccording to the standard of Eurocode 3 [17]

Using (9) the equivalent stress amplitudes 119878eq with regardto 8 carriages or 16 carriages are 075MPa and 071MParespectively And the stress cycle numbers 119873

119904are 22 and 45

respectively Thus the value of 119878eq with regard to 8 carriagesis similar to that of 16 carriages However the value of 119873

119904

with regard to 8 carriages is about twice as much as that of 16carriages Furthermore as recommended by Eurocode 3 forrib-to-deck welded joint the fatigue limit Δ120590

119871is 29MPa [17]

and the value of 119878eq when the high-speed train passes throughbridge is far less than Δ120590

119871 which indicates that fatigue life of

rib-to-deck welded joint in Nanjing Dashengguan Bridge canbe considered infinite Thus the fatigue performance of steel

deck satisfies the requirement of infinite-fatigue-life designmethod

4 Conclusions

In the last few decades Structural Health Monitoring (SHM)system has been widely installed in many highway bridgesto continuously monitor the structural condition over anextended period of time However application of SHMsystem in high-speed railway bridges is far insufficient Thispaper presents an analysis of the SHM system installedin Nanjing Dashengguan Bridge in China The monitoringsystem is composed of a sensor system a data acquisitionand transmission system a data management system and astructural evaluation system The monitoring system is cur-rently in full operation accumulating the bridgersquos behaviorsunder the varying environmental conditions such as high-speed trains and environmental temperature

Based on long-termhealthmonitoring data general prin-ciples and analytical processes for structural evaluation areprovided and some evaluation results are reported It can beshown from the analysis in this paper that the mathematicalcorrelation models describing the overall structural behaviorof the bridge can be obtained with the support of the healthmonitoring system which includes cross-correlation modelsfor accelerations correlation models between temperatureand static strains of steel truss arch and correlation mod-els between temperature and longitudinal displacements ofpiers The mean value control chart is further employed tomonitor the time series of differences between the measuredstructural parameters and the predicted parameters usingthese correlation models The upper and lower control limits


02 03 04 05 06 07 08 09 1001

Stress amplitude (MPa)

Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages

Figure 21 Spectra of stress amplitude calculated using the strain history data

of the control chart are then determined and abnormalbehaviors can be detected if the time series of differencesfall beyond the control limits during the monitoring periodwhich can result in useful suggestions to bridge managementauthorities by reasonably evaluating the monitored data

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge the NationalBasic Research Program of China (973 Program) (no2015CB060000) the National Science and TechnologySupport ProgramofChina (no 2014BAG07B01) theKey Pro-gram of National Natural Science Foundation (no 51438002)and the Program of ldquoSix Major Talent Summitrdquo Foundation(no 1105000268)

References

[1] E Watanabe H Furuta T Yamaguchi and M Kano ldquoOnlongevity and monitoring technologies of bridges a surveystudy by the Japanese Society of Steel Constructionrdquo Structureand Infrastructure Engineering vol 10 no 4 pp 471ndash491 2014

[2] S L LiH Li Y Liu C LanWZhou and JOu ldquoSMCstructuralhealth monitoring benchmark problem using monitored datafrom an actual cable-stayed bridgerdquo Structural Control andHealth Monitoring vol 21 no 2 pp 156ndash172 2014

[3] K-Y Wong ldquoInstrumentation and health monitoring of cable-supported bridgesrdquo Structural Control and Health Monitoringvol 11 no 2 pp 91ndash124 2004

[4] A Q Li Y L Ding H Wang and T Guo ldquoAnalysis and assess-ment of bridge health monitoring mass datamdashprogress inresearchdevelopment of lsquoStructural Health Monitoringrsquordquo Sci-ence China Technological Sciences vol 55 no 8 pp 2212ndash22242012

[5] D Yang D Youliang and L Aiqun ldquoStructural conditionassessment of long-span suspension bridges using long-termmonitoring datardquo Earthquake Engineering and EngineeringVibration vol 9 no 1 pp 123ndash131 2010

[6] C Y Xia H Xia and G De Roeck ldquoDynamic response of atrain-bridge system under collision loads and running safetyevaluation of high-speed trainsrdquo Computers and Structures vol140 pp 23ndash38 2014

[7] S H Ju ldquoImprovement of bridge structures to increase thesafety of moving trains during earthquakesrdquo Engineering Struc-tures vol 56 pp 501ndash508 2013

[8] Q Y Zeng J Xiang P Lou and Z Zhou ldquoMechanical mech-anism of derailment and theory of derailment preventionrdquo Jour-nal of Railway Science and Engineering vol 1 no 1 pp 19ndash312004

[9] T Figlus S Liscak A Wilk and B Łazarz ldquoCondition moni-toring of engine timing system by using wavelet packet decom-position of a acoustic signalrdquo Journal of Mechanical Science andTechnology vol 28 no 5 pp 1663ndash1671 2014

[10] R Wald T M Khoshgoftaar and J C Sloan ldquoFeature selectionfor optimization of wavelet packet decomposition in reliabilityanalysis of systemsrdquo International Journal on Artificial Intelli-gence Tools vol 22 no 5 Article ID 1360011 2013

[11] H F Zhou Y Q Ni and J M Ko ldquoConstructing input toneural networks for modeling temperature-caused modal vari-ability mean temperatures effective temperatures and princi-pal components of temperaturesrdquo Engineering Structures vol32 no 6 pp 1747ndash1759 2010

[12] A Singh S Datta and S S Mahapatra ldquoPrincipal componentanalysis and fuzzy embedded Taguchi approach for multi-res-ponse optimization in machining of GFRP polyester compos-ites a case studyrdquo International Journal of Industrial and SystemsEngineering vol 14 no 2 pp 175ndash206 2013

[13] A Amiri A Saghaei M Mohseni and Y Zerehsaz ldquoDiagnosisaids in multivariate multiple linear regression profiles monitor-ingrdquo Communications in StatisticsmdashTheory and Methods vol43 no 14 pp 3057ndash3079 2014


[14] Y Q Ni X G Hua K Y Wong and J M Ko ldquoAssessment ofbridge expansion joints using long-term displacement and tem-perature measurementrdquo Journal of Performance of ConstructedFacilities vol 21 no 2 pp 143ndash151 2007

[15] S Ya K Yamada and T Ishikawa ldquoFatigue evaluation of rib-to-deck welded joints of orthotropic steel bridge deckrdquo Journal ofBridge Engineering vol 16 no 4 pp 492ndash499 2011

[16] Y S Song and Y L Ding ldquoFatigue monitoring and analysis oforthotropic steel deck considering traffic volume and ambienttemperaturerdquo Science China Technological Sciences vol 56 no7 pp 1758ndash1766 2013

[17] European Committee for Standardization ldquoEurocode 3 designof steel structures part 1ndash9 fatiguerdquo BS EN 1993-1-92005European Committee for Standardization 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



(a) View of the Nanjing Dashengguan Bridge

192336

1stcross-section

1st cross-section 2nd cross-section

336

2ndcross-section

Beijing

1272

Shanghai

108 192 108

(b) Elevation drawing of the bridge (unit m)

Middle truss arch

Side truss arch

Orthotropic steel deck

Downstream15000

Side truss arch

Upstream15000

(c) Design drawing of the deck cross-section (unit mm)

Figure 1 Nanjing Dashengguan Bridge

high-speed railway bridges have been built during the lastfew years Maintaining the safety of these high-speed railwaybridges is crucial to the safety of passengers and trainsTherefore research efforts should be focused on the SHMsystems of high-speed railway bridges This paper reportsthe development and implementation of a SHM system ofNanjing Dashengguan Bridge Nanjing Dashengguan Bridgewhich serves as the shared corridor crossing Yangtze Riverfor both Beijing-Shanghai high-speed railway and Shanghai-Wuhan-Chengdu railway is the first 6-track high-speedrailway bridge with the longest span throughout the worldIt is the largest bridge with the heaviest design loading of allthe high-speed railway bridges by far because its main spanis 336m and its railway contains 6 tracks Also the designspeed of 300 kmh of the bridge is on the advanced level in theworld Due to these remarkable characteristics including longspan of themain girder heavy design loading and high speedof trains it is necessary to monitor the real-time health statusof the bridge during its service period With the state-of-the-art techniques of current monitoring systems of highwaybridges the health monitoring system for this bridge wasdesigned to be concise practical reliable and cost efficientThe main purpose of this system is to monitor the bridgersquosbehaviors under the varying environmental conditions and

detect the bridgersquos abnormal behaviors which may threatenthe structural safety This paper introduces the deploymentand functions of this system including a sensor system adata acquisition and transmission system a datamanagementsystem and a structural evaluation system Some evaluationresults of the bridge subjected to varying environmentalconditions such as high-speed trains and environmentaltemperature are also presented

2 Structural Health Monitoring System

Nanjing Dashengguan Bridge shown in Figure 1(a) is a steeltruss arched bridge with the span arrangement (108 + 192 +2 times 336 + 192 + 108)m which supports a six-line railwayincluding two regular rails two high-speed railways andtwo subway lines The elevation drawing of the bridge andthe deck cross-section are shown in Figures 1(b) and 1(c)respectively The three truss planes in the longitudinal direc-tion were used with a spacing of 15m which was selected toprovide the large stiffness for such heavy live loadsThe use ofa steel box as the deck system is another feature in the designof this steel truss arc which is adopted as the bottom chord ofthe entire truss segment to reduce uneven deflection on thedeck The bearing system of the bridge is that the 7 pier is







displacementLess-




member















Downstream Upstream


Vertical bracing



Top plate




W1

W2

W3

W4

W5

W6

W7 W8

Y1

Y2

Y3Y4

Y5

Y6

Y7 Y8

15000 15000

68007

12000

2

2


Shanghai

Top chord member


Vertical web member

Beijing

Diagonal web member

Bottom chord member

W1

W2

W3

W4

W5

W6

W7

W8

Y1Y2

Y3Y4

Y5

Y6

Y7

Y8

3

3

4

4

5

5

6

6


Downstream Upstream

W1 W2Y1 Y2

1000

1000

850 850

150

150

1400


Downstream Upstream

W3W4Y3Y4

150

150

610

610

1398


Downstream Upstream

W5

W6Y5

Y6

150

150

1400

650 650

800


Downstream Upstream

W7 W8Y7 Y8

150

150

1266

1266

1400

1416




DYB-1 DYB-2

2500mm2500mm


















Beijing Shanghai


L1 L2 L3 L4 L5 L6


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40












cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















displacementLess-




member















Downstream Upstream


Vertical bracing



Top plate




W1

W2

W3

W4

W5

W6

W7 W8

Y1

Y2

Y3Y4

Y5

Y6

Y7 Y8

15000 15000

68007

12000

2

2


Shanghai

Top chord member


Vertical web member

Beijing

Diagonal web member

Bottom chord member

W1

W2

W3

W4

W5

W6

W7

W8

Y1Y2

Y3Y4

Y5

Y6

Y7

Y8

3

3

4

4

5

5

6

6


Downstream Upstream

W1 W2Y1 Y2

1000

1000

850 850

150

150

1400


Downstream Upstream

W3W4Y3Y4

150

150

610

610

1398


Downstream Upstream

W5

W6Y5

Y6

150

150

1400

650 650

800


Downstream Upstream

W7 W8Y7 Y8

150

150

1266

1266

1400

1416




DYB-1 DYB-2

2500mm2500mm


















Beijing Shanghai


L1 L2 L3 L4 L5 L6


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40












cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Downstream Upstream


Vertical bracing



Top plate




W1

W2

W3

W4

W5

W6

W7 W8

Y1

Y2

Y3Y4

Y5

Y6

Y7 Y8

15000 15000

68007

12000

2

2


Shanghai

Top chord member


Vertical web member

Beijing

Diagonal web member

Bottom chord member

W1

W2

W3

W4

W5

W6

W7

W8

Y1Y2

Y3Y4

Y5

Y6

Y7

Y8

3

3

4

4

5

5

6

6


Downstream Upstream

W1 W2Y1 Y2

1000

1000

850 850

150

150

1400


Downstream Upstream

W3W4Y3Y4

150

150

610

610

1398


Downstream Upstream

W5

W6Y5

Y6

150

150

1400

650 650

800


Downstream Upstream

W7 W8Y7 Y8

150

150

1266

1266

1400

1416




DYB-1 DYB-2

2500mm2500mm


















Beijing Shanghai


L1 L2 L3 L4 L5 L6


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40












cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










DYB-1 DYB-2

2500mm2500mm


















Beijing Shanghai


L1 L2 L3 L4 L5 L6


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40












cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Beijing Shanghai


L1 L2 L3 L4 L5 L6


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40


Acce

lera

tion

(mm

s2)

1 80012001 4001 6001 10001

Data point

minus40

minus30

minus20

minus10

0

10

20

30

40












cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










cele

ratio

n (m

ms2)

minus150

minus100

minus50

0

50

100

150

200

1 4001 6001 8001 100012001

Data point


Acce

lera

tion

(mm

s2)

1 4001 6001 8001 100012001

Data point

minus80

minus60

minus40

minus20

0

20

40

60



y = minus02642x2 + 37075x minus 56125

53 4 62 25 5535 45


0

2

4

6

8

10

RMS

valu

es o

f the

2nd

span

(mm

s2)


y = minus00131x2 + 07296x + 35995

50 15 20 2510


0

2

4

6

8

10

12

14

16RM

S va

lues

of t

he2

nd sp

an (m

ms2)



Fitte

d RM

S va

lues

(mm

s2)

R = 09391

0

2

4

6

8

10

63 54 72 25 35 6555 7545



R = 09518

4

6

8

10

12

14

16

Fitte

d RM

S va

lues

(mm

s2)

86 12 14 1610





0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 62 9331 186 217124 310279248155

Day

09

091

092

093

094

095

096

097C

orre

latio

n co

effici

ent


0 60 9030 180 210120 300270240150

Day

09

092

094

096

098

Cor

relat

ion

coeffi

cien

t



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

s2)

minus2

minus1

0

1

2

20 40 60 80 100 120 140 1600Sample





119901 (1)








119894is denoted by


119894minus 119879

119895is






12are shown in


1



4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4 5 6 7 8 9 10 113Time (month)

minus5

5

15

25

35

45Te

mpe

ratu

re (∘

C)


4 8 12 16 20 240Time (h)

5

10

15

20

Tem

pera

ture

(∘C)



4 5 6 7 8 9 10 113Time (month)

minus25

minus15

minus5

5

15

Tem

pera

ture

diff

eren

ce (∘

C)


4 8 12 16 20 240Time (h)

minus10

minus5

0

5Te

mpe

ratu

re (∘

C)



4 5 6 7 8 9 10 113Time (month)

minus300

minus200

minus100

0

100

200

Stat

ic st

rain

(120583120576)


Sharp peak

4 8 12 16 20 240Time (h)

minus120

minus65

minus10

45

100

Stat

ic st

rain

(120583120576)




4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4 8 12 16 20 240Time (h)

Stat

ic st

rain

S III

(120583120576)

minus120

minus65

minus10

45

100


4 5 6 7 8 9 10 113Time (month)

Stat

ic st

rain

S III

(120583120576)

minus200

minus130

minus60

10

80

150




1




119895




119878III =8

sum

119894=1

120572119894119879119894+

16

sum

119895=1

120573119895119863119895+ 119888 (2)


1 1198792 1198793 1198794


11987912 11987934 11987956 11987978 11987913 11987915 11987917 11987935 11987937 11987957 11987924 11987926 11987928 11987946


119894 120573119895is 119895th





1 1198772 and




119878III = 1205821([119864]1times8

997888

1198798times1

) +9978881205741times3

([119865]3times16

997888

11986316times1

) + 119888 (3)

where997888

1198798times1




1times8and


b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










b = minus3632

k = 0946



minus100

minus55

minus10

35

80

Sim

ulat

iveS

III

(120583120576)

(a) 1198781

b = minus2013k = 0898



minus75

minus45

minus15

15

45

75

Sim

ulat

iveS

III

(120583120576)

(b) 1198782

b = minus1844k = 0904

minus60

minus30

0

30

60

90

Sim

ulat

iveS

III

(120583120576)



(c) 1198783

b = 2057k = 1126



minus40

minus25

minus10

5

20

35Si

mul

ativ

eSII

I(120583120576)

(d) 1198784

b = minus4139k = 0935

minus100

minus65

minus30

5

40

75

Sim

ulat

iveS

III

(120583120576)




(e) 1198785

b = minus4094k = 0918


minus185

minus130

minus75

minus20

35

90

Sim

ulat

iveS

III

(120583120576)


(f) 1198786

Figure 16 Continued


b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










b = 2148k = 0881

minus50

minus28

minus6

16

38

60Si

mul

ativ

eSII

I(120583120576)



(g) 1198787

b = 0615k = 1118

minus30

minus15

0

15

30

Sim

ulat

iveS

III

(120583120576)



(h) 1198788



1205741

1205742

1205743



1

1205741

1205742

1205743

119862


[119865]3times16


1is


1 9978881205741times3



1 1198772 and 119877

3 The values of




119878119904= 119896119878119898+ 119887 (4)




119890 = 119878119898minus 119878119901 (5)




119894






UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










UCL

LCL

CL

Con

ditio

n in

dexe

(120583120576)

minus15

minus10

minus5

0

5

10

15

10 20 30 40 50 600Sample




1

= minus11524 + 696119879

5 pier 1198892

= minus9253 + 562119879

6 pier 1198893

= minus6628 + 382119879

8 pier 1198894

= minus4658 + 336119879

9 pier 1198895

= minus7605 + 530119879

10 pier 1198896

= minus9850 + 664119879





119889119894(119905) = 120573

0+ 1205731119879 (119905) (6)


0were obtained by


1205731=

119878119889119894119879

119878119879119879

1205730= 119889119894minus 1205731119879

(7)

where 119878119889119894119879






119890 = 119889119898minus 119889119901 (8)


119901is







R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










R = 09748

10 20 30 40 500

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)


steel truss arch

10 20 30 40 500

Temperature (∘C)

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

R = 09746


steel truss arch

10 200 40 5030

Temperature (∘C)

minus150

minus100

minus50

0

50

100

150

Disp

lace

men

t (m

m)

R = 09471


steel truss arch

R = 09276

10 20 30 40 500

Temperature (∘C)

minus60

minus30

0

30

60

90

120D

ispla

cem

ent (

mm

)


steel truss arch

R = 09536

minus100

minus50

0

50

100

150

200

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch

R = 09537

minus100

minus50

0

50

100

150

200

250

Disp

lace

men

t (m

m)

10 20 30 40 500

Temperature (∘C)


steel truss arch



UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










UCL

LCL

CL

Con

ditio

n in

dexe

(mm

)

500 1000 1500 2000 2500 3000 3500 4000 45000Sample

minus15

minus10

minus5

0

5

10

15


Stra

in (120583

120576)

minus174

minus172

minus170

minus168

minus166

minus164

minus162

1 2714 53

66

79

92

40

118

209

183

222

105

157

196

144

131

235

248

170

Data point


Stra

in (120583

120576)


1

61

91

31

181

211

121

421

301

481

511

361

391

271

451

241

331

541

571

151

Data point




119904(stress cycle


119878eq = (

1198991198941198785

119894

sum119899119894

)

15

119873s = sum119899119894

(9)






119904are 22 and 45


119904


119871is 29MPa [17]





4 Conclusions




02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










02 03 04 05 06 07 08 09 1001


Num

ber o

f stre

ss cy

cles

100

80

70

60

50

40

30

20

10

90

0

(a) 8 carriages

0

5

10

15

20

25

30

35

40

Num

ber o

f stre

ss cy

cles

020 080010 050 060 070030 090040


(b) 16 carriages





Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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