Construction Monitoring of Cable-stayed Bridges Based on Gray Prediction Model

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1 Sen Oes fo Repints to 736 The Open Civil Engineeing Jounal, 25, 9, Open Access Constuction Monitoing of Cable-staye Biges Base on Gay Peiction Moel Wu Fangwen *, Ji Zhengi an Yang Caofang School of Highway, Chang an Univesity, Xi an, Shaanxi,764, China Abstact: The constuction pocess of cable-staye biges is complex an has many influencing paametes. Constuction monitoing plays an impotant ole in the constuction pocess to ensue the stuctual safety an meet the esign equiements. Gay system theoy is applie to analyze an peict stuctual efomation an cable tension fo constuction monitoing, which egas the cable-staye bige une constuction as an intefeential gay system with a physical pototype an analyzes the anom pocess as a gay pocess. The gay peiction moel has been establishe by using an evaluating gie an cable tension as two contol inputs of the system in the constuction pocess of cablestaye biges. The gie an cable tension of subsequent constuction stages wee peicte, ajuste, an evaluate by using feeback infomation obtaine fom measuing an ectifying the gay peiction moel to effectively contol an ajust the bige configuation an cable tension. Results show that gay peiction moel has goo peiction pecision, which can contol the stuctual configuation in the ieal state an meet the esign equiements. Keywos: Cable-staye bige, stuctue analysis, gay peiction moel, constuction contol. INTRODUCTION A cable-staye bige is compose of incline cables, towe, an gie an has the chaacteistics of lage cossove ability, lightweight stuctue, lage cleaance height, an goo eathquake esistance. Theefoe, the cablestaye bige has been extensively aopte as a beautiful style of moen bige stuctues. The gie configuation an intenal stuctual foce in the complete stage have a close elationship with the constuction metho because the cable-staye bige is a supe high-oe static stuctue. The constuction pocess is not only complex (e.g., tensioning the cables, moving the hanging basket, an pouing the concete) but has many influencing paametes, such as the mateial elastic moulus, weight of the stuctue, an constuction loas. Geneally, these paametes ae assume ieal base on the esign coe at the esign stage. In the constuction pocess, eos between the actual an theoetical values ae ifficult to avoi because of vaious factos. If the eos ae not ajuste an contolle in time, they accumulate an change the theoetical configuation of the gie an enange the stuctual safety. The closue eo was appoximately 7 cm when the Pasco Kennewick cablestaye bige in Washington was complete because the constuction eos wee neglecte. When the bige was complete, it i not meet the ieal state an esign equiements []. Thus, the paamete eos shoul be ajuste an contolle to ensue that the bige can meet the esign equiements an ieal state. Moe attention shoul be given to the constuction monitoing of long-span cablestaye biges. *Aess coesponence to this autho at the School of Highway, Bige Engineeing Chang an Univesity, Xi an, Shanxi, 764, P.R. China; Tel: ; ibige24@63.com Some methos, such as Kalman s theoy, gay peiction theoy moel, an least squaes metho, have been use to ientify an peict paamete eos in the constuction monitoing of bige stuctues. Li Yan-pei an Zhao Yinu successfully applie Kalman s theoy base on anom pocess contol to the constuction monitoing of cablestaye biges [2-3]. The gay peiction moel consies the chaacteistics of constuction that can contol the bige configuation an cable tension of cable-staye biges [, 4, 5]. Cable tension is a key facto in etemining the gie configuation an intenal foce istibution. When the gie configuation eviates fom the ieal state, it can be ajuste by inceasing o eceasing the cable foce. Shang Xin aopte gay theoy to ajust the evaluation of a cablestaye bige base on cable safety [6]. Chen Changsong integate the minimum squae metho, gay peiction theoy moel, an influence matix ajustment metho to contol the concete cable-staye bige to achieve the optimum mechanical state [7]. When moe complicate paametes ae consiee in the constuction of biges, the backpopagation neual netwok metho is capable of computing an extensive ange of paametes. Zhou Jiagang an Li Qiao attempte to use the backpopagation neual netwok metho on cable-staye bige constuction contol an obtaine a goo ageement with the esign equiements [8, 9]. In the constuction pocess, the mechanical behavios ae change by the paamete eos. These eos show stong uncetainty, that is, gay chaacteistics. In this stuy, the gay peiction moel is applie to analyze the paamete eos an peict eck elevation an initial cable tension in the cable-staye bige constuction pocess /5 25 Bentham Open

2 Constuction Monitoing of Cable-staye Biges Base on Gay Peiction Moel The Open Civil Engineeing Jounal, 25, Volume PRINCIPLES OF THE GRAY PREDICTION MODEL Gay system theoy, an analytical system base on gay elation, pocesses an manages the oiginal seies of ata though gay pocessing an gay geneation by using the existing infomation an the oiginal ata []. Gay iffeential equations ae establishe as the main boy of the gay peiction moel GM(,), which can peict futue changes in the system. This peictive contol metho allows the application of gay theoy in bige constuction contol technology. The metho egas the gay ynamic moel GM(,) as a peiction moel. Subsequently, the metho is optimize an ectifie accoingly. All of the factos that affect the status of bige constuction ae eliminate by gay theoy an eflecte in the taget vecto concentation, theeby allowing the completion of the peiction pocess by using the taget vecto. The peictive contol metho peicts the stuctue state befoe an afte each constuction stage, with full consieation of the vaious factos that affect the constuction pocess an the constuction goal fo each stage to ensue that the constuction pocees as intene. An eo inevitably occus between the peicte an actual states. Thus, specific eos that affect the constuction goal ae consiee in the subsequent stage. The afoementione ules ae followe until the constuction is finishe an the stuctue state fulfills the esign. The constuction of long-span biges is a multivaiable, high-level, time-vaying, an complex pocess. Although builing an accuate moel though this pocess is ifficult, peictive contol is an effective pogam to solve the ifficulties in builing the moel an contolling the system s complexity. In this stuy, gay system theoy is aopte to peict an analyze the constuction pocess of a cable-staye bige. The cable-staye bige an its vaious loas ae egae as a system. Although consieable infomation is available about the system, futhe infomation emains unknown. Theefoe, this system is a gay technology system that is affecte by noise an has a physical pototype. In gay system theoy, a ynamic moel with a goup of iffeential equations is evelope, which is calle gay iffeential moel GM(,). The gay iffeential moel GM(,) is a peiction function moel with a iffeential equation expesse as follows: ( ) x + a( x) = b, () t ( ) Whee x is a cumulative value of the aw ata seies ( ) x an calculate as follows: n ( ) ( ). x = x k (2) k = Thus, the peiction moel is geneate by using the ata ( ) seies x. The accuacy of the moel can be teste by esiual size, posteioi, an olling inspection. If the accuacy of the moel cannot meet the equiements, then the moel is ectifie by the esiuals. Following this, feeback coection of the moel is implemente though moel metabolism. Only a few ata (as few as fou) ae neee to istinguish an buil a GM moel. The equation x k az k b, k,2,, n + = = L (3) is a gay iffeential moel, calle GM(,), as it inclues ( ) only one vaiable x, whee z k x k x k k n =.5 +.5, =,2, L,. (4) a an b ae the coefficients. In the gay system theoy, a enotes a eveloping coefficient an b enotes the gay input. ( x ) ( k ) is a gay eivative that maximizes the infomation ensity of a given seies to be moele. Base on the least squaes metho, the paamete â is efine as follows: [ ] T T T aˆ = a b = B B B y N, Whee () () () z (2).5 x ().5 x (2) B = L L = L L, () () () z ( n).5 x ( n ).5 x ( n) y n () x (2) = L, () x ( n) an B is a ata matix. Base on the peviously pesente equation, the esponse equations fo GM(,) ae expesse as follows: b a b a () () ak xˆ ( k+ ) = x () e +, ˆ ( + ) = ˆ ( + ) ˆ, (6) () () () x k x k x k whee () xˆ k an () xˆ (5) k enote the calculate values of () () x an x, espectively, at point k. The moel GM(,) plays an impotant ole in gay foecasting, gay pogamming an gay contol. CONSTRUCTION PROCESS OF THE CABLE- STAYED BRIDGE Upon completion of the pies, pylons, an othe associate woks in the constuction pocess, steel gie eection an cable installation become typical epetitive cycles, as shown in Fig. (). The lifting cane, which is mounte on the last eecte segment, hooks up the segment fom the tanspotation bage. This segment is lifte to the esign level an is secue to the tempoay suppot fame as a tempoay fixing. This segment is wele to the peceing segment. Following this, the incline cable is installe on the segment. The cable is fist anchoe to the towe an the eck. Afte the anchoage wok is complete, the cable is stesse by a heavy jack until the esigne length is achieve. One back-span cable an one mi-span cable shoul be stesse simultaneously to balance the bening

3 738 The Open Civil Engineeing Jounal, 25, Volume 9 Fangwen et al. Next Segment Lift the Segment an Connect Install an the Fist Tension the Cable Cane Fowa The Secon Tension about the Cable T T2 Fig. (). Constuction pocess of a stana gie. foce acting on the towe. The typical eection cycle is epeate until the last closue segment, which is opeate with a istinct metho. CONSTRUCTION MONITORING OF CABLE- STAYED BRIDGES Fo cable-staye biges, when vaious factos ae effectively contolle uing the constuction pocess, the alignment an intenal foce of the gie can be ajuste only by initializing the heights of gies an the tension foces of cables. Theefoe, the initial heights of gies an the tension foces of cables ae two contol inputs of the system. Given that a change in initial gie height oes not affect the intenal stuctual foce, the alignment can be ajuste using the initial height without changing the intenal stuctual foce. As a esult, the complete stage alignment nee not be change fo the esign alignment taget. Intenal stuctual foces ae geneate by the iffeence between vaious paametes of constuction an the esign values. Only the tension foces of cables ae ajuste to allow the intenal foce istibution to meet the esign expectations. Theefoe, the ultimate goal of the contol metho is to ajust the gie alignment in the complete stage an ensue that the istibution of intenal stuctual foces meets the esign equiements. () Ajustment of Cable Tension The incement of vetical isplacement of the cantileve en gie an seveal ajacent segments uing constuction shoul be consistent with the esign value by confiming the initial tension foces of cables in the succeeing phase, in which T ( k+ ) segment is tensione an ( k + ) segment is wele. The cable to be tensione at the cantileve en is enote as the fist i numbe, an the coesponing cantileve en noe is the i noe. The gie segment constucte befoe the i numbe cable is tensione an enote as the i numbe segment. The initial tension foce of the cable is T ( k+ ) when the ( k + ) segment is wele, an it is expesse as follows: T ( k+ ) = β( k+ ) T ( k+ ), (7) Whee β ( k + ) is the tension ajustment facto of the ( k + ) numbe cable. (2) Confimation of Gie Elevation Peiction of the vetical isplacement incement at the cantileve en befoe an afte the cable is tensione The ajustment value of the ( k + ) numbe cable tension foce is etemine base on the efinition seies x. The esign value is T ( k+ ), an the vetical isplacement incement esign value is Δ ( k ) +. Thus, the coesponing moel output value Δ ( k ) m + is expesse as follows: Δ ( k + ) Δ ( k+ ) = T ( k+ ) x ( k+ ). T ( k+ ) 2 Peiction of the Vetical Displacement Incement at the Cantileve en Befoe an Afte the Gie Segment is Lifte Base on the efinition seies y, the vetical isplacement incement of the esign value fo the cantileve (8) Nan Tong Su Zhou # 2# 3# 4# 5# 6# 7# 8# ` Fig. (2). Layout of the Sutong cable-staye bige.

4 Constuction Monitoing of Cable-staye Biges Base on Gay Peiction Moel The Open Civil Engineeing Jounal, 25, Volume Table. Measue an peicte values of x () i. No. Cable No. Measue Displacement (mm)/measue Cable Tension (kn) Theoetical Displacement (mm)/design Cable Tension (kn) x () Sie Span Main Span Sie Span Main Span 6 4/4,58 47/4,53 56/4, /4,82 82/4,85 96/4, /5,2 37/5,32 48/5, /5,53 92/5,542 23/5, /5,84 (.835) (.884) en is Δ ( k ) + when the ( k + ) numbe gie segment is poue. Thus, the coesponing moel output value Δ ( k ) m + is expesse as follows: Δ ( k+ ) = y ( k+ ) Δ ( k+ ). (9) Peiction of the Hanging Basket Defomation when Lifting the Gie Segment If gie elevation is etemine uing constuction, then efomation of the cane must be peicte accoingly. z () i is efine as the atio between the actual efomation value of the hanging basket an the theoetical value when the i numbe gie segment is lifte. The peiction moel GM(,) is set up fo z () i, an the cane efomation value is Δ ( k ) +. As a esult, the moel output value is expesse as follows: Δ ( k+ ) = z ( k+ ) Δ ( k+ ). () Confimation of Segment Elevation at ( k + ) Stage Hl ( k+ ) Gie elevation at the ( k + ) numbe stage is calculate as follows: H ( k+ ) = H ( k+ ) +Δ ( k+ ) +Δ ( k+ ) Δ ( k+ ), () Whee H ( k+ ) is the esign elevation value of the cantileve en afte the ( k + ) numbe cable is tensione. Consequently, once the cable tension is etemine at the ( k + ) stage, the peicte values of Δ ( k + ), Δ ( k + ), m m an Δ ( k ) m + can be obtaine fom the past an pesent ata. Subsequently, the unique elevation value can be ientifie. APPLICATION OF GM(,) MODEL TO THE CONSTRUCTION MONITORING OF CABLE- STAYED BRIDGES () Poject Oveview of Sutong Cable-Staye Bige The Sutong Bige cosses the Yangtze Rive appoximately km upsteam fom Shanghai, China an connects the cities of Suzhou an Nantong locate at the southen an nothen banks, espectively. The bige is a seven-span ouble-pylon an ouble-cable plane steel box gie cable-staye bige, with a span aangement of , = 2,88 m, as shown in Fig. (2). The Sutong Bige is the secon longest cablestaye bige in the wol, with a eco-beaking constuction in the histoy of bige builing. Table 2. Measue an peicte values of y () i. No. Gie Segment No. Measue Displacement (mm) y () i Theoetical Displacement (mm) Sie Span Main Span Sie Span Main Span (.783) (.82)

5 74 The Open Civil Engineeing Jounal, 25, Volume 9 Fangwen et al. (2) Engineeing Application Gay theoy is applie to the constuction contol of the cable-staye bige. The constuction state is as follows. No. 5 cable is tensione, an the initial height of the No. 6 segment is peicte. At the same time, the initial tension foce of the No. 6 cable is etemine. ) Confimation of x () i, the Vetical Displacement Incement Peiction fo the Cantileve En When the No. Cable is Tensione The measue seies x () i ientifies fou cables (Nos. 6, 7, 8, an 9) that have been tensione, an the No. cable, which will be tensione, as a goup. The moel GM(,) is establishe base on the actual an theoetical ata. The peiction esults ae shown in Table. 2) Confimation of y () i, the Vetical Displacement Incement Peiction fo the Cantileve en when the No. Gie Segment is Eecte The measue seies y () i ientifies the ajacent fou gie segments, which have been constucte. The moel GM(,) is establishe base on the actual an theoetical ata. The peiction esults ae shown in Table 2. 3) Confimation of z () i, Peiction of Cane Defomation The theoetical cane efomation is 8 mm. Fom the measue ata, the peiction esults of cane efomation ae as follows:.36 fo sie span z (5) an.7 fo the main span z (5). 4) Peiction of the Initial Cable Tension fo the No. Cable Base on the etemine value of x (5) an the peicte value of y (5), the ajustment facto β () of the tension foce of the No. cable an the coesponing cable foce ae obtaine as follows: No. cable of the sie span: β () =.26 ; T () =.26 T () = 5,992 kn, No. cable of the main span: β () =.4 ; Upsteam Downsteam Theoetical 6 5 Cable Foce (kn) A34 A33 A32 A3 A3 A29 A28 A27 A26 A25 A24 A23 A22 A2 A2 A9 A8 A7 A6 A5 A4 A3 A2 A A A9 A8 A7 A6 A5 A4 A3 A2 A C able Numbe (a) Sie span cable foces Upsteam Downsteam Theoetical Cable Foce (kn) J J2 J3 J4 J5 J6 J7 J8 J9 J J J2 J3 J4 J5 J6 J7 J8 J9 J2 J2 J22 J23 J24 J25 J26 J27 J28 J29 J3 J3 J32 J33 J34 Cable Numbe (b) Main span cable foces. Fig. (3). Cable tension at the complete stage (kn).

6 Constuction Monitoing of Cable-staye Biges Base on Gay Peiction Moel The Open Civil Engineeing Jounal, 25, Volume 9 74 T () =.4 T () = 5,922 kn. (3) Peicte Value of the Initial Evaluation of the No. Gie Segment Pio to builing the No. gie segment, the initial evaluation of the sie span an main span is fist analyze. Subsequently, the peicte initial height is compae with the theoetical height. Fist, the esult T () = 5,992 kn obtaine fom the peviously pesente equation is substitute into fomula (8). Thus, the peicte value of the vetical isplacement incement of the cantileve en Δ () is obtaine as m follows: Δ () Δ () = T () x () T () = = 242 mm. Secon, when the No. segment is set up, the peicte value of the vetical isplacement Δ () m can be obtaine by using fomula (9), as follows: Δ () = y (5) Δ () = = 35 mm. Finally, when the No. segment is set up, the peicte value of the hanging basket efomation may be obtaine by using fomula (), as follows: Δ () = z (5) Δ () =.36 8 = 9 mm. The esign evaluation value of the gie bottom is H () = m afte the No. cable is tensione. The esults ae substitute into fomula (). Theefoe, the peicte value of initial height H () is calculate as follows: H() = H () +Δ () +Δ () Δ () = m. The theoetical value of the No. gie segment was obseve to be m, wheeas the actual value shoul be lowe by 2.6 cm. As the No. segment of the main span was eecte, the peicte value of the initial evaluation H () was m, which was calculate using the afoementione metho. The theoetical value of the initial evaluation of this segment was m. Consequently, the actual initial height shoul be highe by 2.9 cm. When the gay system theoy was use in the constuction contol of the cable-staye bige, positive esults wee obtaine uing constuction. Geneally, the eviation eo of the cable foce uing the complete stage was not geate than % an the closue eo was only 5 mm. The gay peiction moel GM(,) was applie to constuction monitoing of the Sutong cable-staye bige. This moel can contol the paametes an peict the eos in the subsequent stage effectively. When the stuctue was complete, the cable foce istibution was obseve to be smooth an i not involve non-mutation. Futhemoe, the tensions in the cables wee in an ieal state. The actual configuation of the gie was in goo ageement with the theoetical alignment, as shown in Fig. (4). The upsteam an ownsteam cable foces wee measue in the fiel afte the Sutong cable-staye bige was complete []. A compaison of the calculate an measue esults shows that a slight iffeence existe between them, as shown in Fig. (3). The eviation eo of the cable foce uing the completion stage was not geate than %. Futhemoe, cable tension stess was in the ange of Chinese esign stanas. The efomation of the gie an the towe is sensitive to the cable foce. Duing constuction, the cable foces ae usually ajuste to change the intenal foce as well as the isplacement of the gie an the towe Evaluation/m # Theoetical Actual 5# Longituinal Distance/m Fig. (4). Theoetical an actual evaluation at the complete stage.

7 742 The Open Civil Engineeing Jounal, 25, Volume 9 Fangwen et al. Futhemoe, the cable foce is a key facto in etemining the actual geometic pofile of the complete stage. CONCLUSION The intenal elation between constuction monitoing ata an the gay peiction moel GM(,) was investigate in this stuy. The moel GM(,) was set up base on the bige chaacteistics, which wee applie to peict the efomation of the gie an the cable tension in the constuction monitoing of the Sutong cable-staye bige in China. The paametes of the constuction pocess wee successfully peicte, an goo esults wee achieve. Base on the peviously pesente analysis, the following conclusions can be awn: () The constuction pocess of the cable-staye bige was egae as a gay pocess an was investigate by gay system theoy. Although anomness weakene the ata, gay system theoy highlighte the egulaity of the ata geneate. Seveal anom vaiables uing the constuction of the cable-staye bige wee successfully peicte using the moel GM(,). (2) Initial cable tension an initial evaluation of the cablestaye bige constucte via the cantileve metho wee egae as two contol inputs, which enable peiction of the subsequent stage. At the same time, the gay peiction moel GM(,) was ectifie accoingly base on specific cicumstances in the constuction site. Finally, constuction contol of the cable-staye bige achieve goo peiction pecision. CONFLICT OF INTEREST The autho confims that this aticle content has no conflict of inteest. ACKNOWLEDGMENTS This stuy was suppote by the National Natual Science Funs (No. 5484) an the Funamental Reseach Funs fo Cental Univesities (No. 23G22). REFERENCES [] F. Zhi, L. Guangong, an W. Guangjiong, A gey peictive contol system fo the constuction of cable-staye biges, Jounal of Hunan Univesity, vol. 24, pp. 74-8,997. [2] L. Yuanpei, The application of kalman filte at cable-staye bige constuction, Jounal of Civil Engineeing, vol. 6, pp. 7-4, 983. [3] Z. Yin-u, Application of Kalman Filteing Theoy an Pactice to Constuction Contol of Concete Cable-Staye Bige, MS thesis, Southwest Jiaotong Univesity, 26. [4] H. Dajian, G. Wanyi, an Y. Quansheng, Peiction an contol of constuction of cable-staye biges, Jounal of South China Univesity of Technology, vol. 29, pp. 4-7, 23. [5] Z. Yongshui, Application of the Gey System metho to constuction contol fo pc continuous igi fame bige, Jounal of Chongqing Jiao Tong Univesity, vol. 2, pp. 6-8, 22. [6] S. Xin, an X. Yue, Safety-base cables conition evaluation of cable-staye bige with gey theoy, Jounal of Chang'an Univesity, vol. 24, pp , 24. [7] C. Changsong, Self-aapte constuction contol analysis of longspan Pe-stesses concete cable-staye bige, In: Intenational Confeence on Intelligent Computation Technology an Automation, Washington, DC, USA, 28, pp [8] Z. Jiagang, The application of BP netwok at constuction contol of long span cable-staye biges, MS thesis, Changan Univesity, 23. [9] R. Zhihong, an L. Qiao, The application of BP neual netwoks metho in cable-staye constuction contol, Jounal of Cental South Highway Engineeing, vol. 3, pp. 8-, 26. [] D. Juling, Intouction to gey theoy, Jounal of Gey System, vol., pp. -24,988. [] Y. B. Li, an Q. W. Zhong, Global mechanical behavio of Sutong bige une static loas, In: Poc. SPIE7649. Nonestuctive Chaacteization fo Composite Mateials, Aeospace Engineeing, Civil Infastuctue, an Homelan Secuity, 2. Receive: Mach 24, 25 Revise: June 6, 25 Accepte: July 24, 25 Fangwen et al.; Licensee Bentham Open. This is an open access aticle license une the tems of the Ceative Commons Attibution Non-Commecial License ( by-nc/4./) which pemits unesticte, non-commecial use, istibution an epouction in any meium, povie the wok is popely cite.